SECTION XXXVII.

Diffusion of Matter through Space—Gravitation—Its Velocity—Simplicity of its Laws—Gravitation independent of the Magnitude and Distances of the Bodies—Not impeded by the intervention of any Substance—Its Intensity invariable—General Laws—Recapitulation and Conclusion.

THE known quantity of matter bears a very small proportion to the immensity of space. Large as the bodies are, the distances which separate them are immeasurably greater; but, as design is manifest in every part of creation, it is probable that, if the various systems in the universe had been nearer to one another, their mutual disturbances would have been inconsistent with the harmony and stability of the whole. It is clear that space is not pervaded by atmospheric air of such density as that we breathe, since its resistance would long ere this have arrested the motion of the planets: it certainly is not a void, but replete with a medium possibly in itself electric or magnetic, but at all events capable of transmitting light, heat, magnetism, gravity, and probably influences of which we can form no idea.

Whatever the laws may be that obtain in the more distant regions of creation, we are assured that one alone regulates the motions, not only of our own system, but also of the binary systems of the fixed stars; and, as general laws form the ultimate object of philosophical research, we cannot conclude these remarks without considering the nature of gravitation—that extraordinary power whose effects we have been endeavouring to trace through some of their mazes. It was at one time imagined that the acceleration in the moon’s mean motion was occasioned by the successive transmission of the gravitating force. It has been proved that, in order to produce this effect, its velocity must be about fifty millions of times greater than that of light, which flies at the rate of 192,000 miles in a second. Its action, even at the distance of the sun, may therefore be regarded as instantaneous; yet, remote as the fixed stars are, the solar gravitation must have some influence on the nearest of them, as, for example, α Centauri, which is only 20,602 times the radius of the earth’s orbit from the sun, while La Place has computed that the solar gravitation extends a hundred millions of times farther than the semidiameter of the terrestrial orbit. Possibly the star dust in the Milky Way may be beyond, or on the verge of, that enormous limit; yet it is very unlikely that either the sun, or any of the stars which form the great cluster to which we belong, should be unconnected bodies.

The curves in which the celestial bodies move by the force of gravitation are only lines of the second order. The attraction of spheroids, according to any other law of force than that of gravitation, would be much more complicated; and, as it is easy to prove that matter might have been moved according to an infinite variety of laws, it may be concluded that gravitation must have been selected by Divine Wisdom out of an infinity of others, as being the most simple, and that which gives the greatest stability to the celestial motions.

It is a singular result of the simplicity of the laws of nature, which admit only of the observation and comparison of ratios, that the gravitation and theory of the motions of the celestial bodies are independent of their absolute magnitudes and distances. Consequently, if all the bodies of the solar system, their mutual distances, and their velocities, were to diminish proportionally, they would describe curves in all respects similar to those in which they now move; and the system might be successively reduced to the smallest sensible dimensions, and still exhibit the same appearances.

The action of the gravitating force is not impeded by the intervention even of the densest substances. If the attraction of the sun for the centre of the earth, and of the hemisphere diametrically opposite to him, were diminished by a difficulty in penetrating the interposed matter, the tides would be more obviously affected. Its attraction is the same also, whatever the substances of the celestial bodies may be; for, if the action of the sun upon the earth differed by a millionth part from his action upon the moon, the difference would occasion a periodical variation in the moon’s parallax, whose maximum would be the 1/15 of a second, and also a variation in her longitude amounting to several seconds—a supposition proved to be impossible by the agreement of theory with observation. Thus all matter is pervious to gravitation, and is equally attracted by it.

Gravitation is a feeble force, vastly inferior to electric action, chemical affinity, and cohesion; yet, as far as human knowledge extends, the intensity of gravitation has never varied within the limits of the solar system; nor does even analogy lead us to expect that it should: on the contrary, there is every reason to be assured that the great laws of the universe are immutable, like their Author. Nor can we suppose the structure of the globe alone to be exempt from the universal fiat of general laws, though ages may pass before the changes it has undergone, or that are now in progress, can be referred to existing causes with the same certainty with which the motions of the planets, and all their periodic and secular variations, are referable to the law of gravitation. The traces of extreme antiquity perpetually occurring to the geologist give that information, as to the origin of things, in vain looked for in the other parts of the universe. They date the beginning of time with regard to our system, since there is ground to believe that the formation of the earth was contemporaneous with that of the rest of the planets; but they show that creation is the work of Him with whom “a thousand years are as one day, and one day as a thousand years.”

In the work now brought to a conclusion, it has been necessary to select from the whole circle of the sciences a few of the most obvious of those proximate links which connect them together, and to pass over innumerable cases both of evident and occult alliance. Any one branch traced through its ramifications would alone have occupied a volume; it is hoped, nevertheless, that the view here given will suffice to show the extent to which a consideration of the reciprocal influence of even a few of these subjects may ultimately lead. It thus appears that the theory of dynamics, founded upon terrestrial phenomena, is indispensable for acquiring a knowledge of the revolutions of the celestial bodies and their reciprocal influences. The motions of the satellites are affected by the forms of their primaries, and the figures of the planets themselves depend upon their rotations. The symmetry of their internal structure proves the stability of these rotatory motions, and the immutability of the length of the day, which furnishes an invariable standard of time; and the actual size of the terrestrial spheroid affords the means of ascertaining the dimensions of the solar system, and provides an invariable foundation for a system of weights and measures. The mutual attraction of the celestial bodies disturbs the fluids at their surfaces, whence the theory of the tides and of the oscillations of the atmosphere. The density and elasticity of the air, varying with every alternation of temperature, lead to the consideration of barometrical changes, the measurement of heights, and capillary attraction; and the doctrine of sound, including the theory of music, is to be referred to the small undulations of the aërial medium. A knowledge of the action of matter upon light is requisite for tracing the curved path of its rays through the atmosphere, by which the true places of distant objects are determined, whether in the heavens or on the earth. By this we learn the nature and properties of the sunbeam, the mode of its propagation through the ethereal medium, or in the interior of material bodies, and the origin of colour. By the eclipses of Jupiter’s satellites the velocity of light is ascertained; and that velocity, in the aberration of the fixed stars, furnishes a direct proof of the real motion of the earth (N. 237). The effects of the invisible rays of the spectrum are immediately connected with chemical action; and heat, forming a part of the solar ray, so essential to animated and inanimated existence, is too important an agent in the economy of creation not to hold a principal place in the connexion of physical sciences; whence follows its distribution in the interior and over the surface of the globe, its power on the geological convulsions of our planet, its influence on the atmosphere and on climate, and its effects on vegetable and animal life, evinced in the localities of organized beings on the earth, in the waters, and in the air. The correlation between molecular and chemical action, light, heat, electricity, and magnetism, is continually becoming more perfect, and there is every reason to believe that these different modes of force, as well as gravity itself, will ultimately be found to merge in one great and universal power. Many more instances might be given in illustration of the immediate connexion of the physical sciences, most of which are united still more closely by the common bond of analysis, which is daily extending its empire, and will ultimately embrace almost every subject in nature in its formulæ.

These formulæ, emblematic of Omniscience, condense into a few symbols the immutable laws of the universe. This mighty instrument of human power itself originates in the primitive constitution of the human mind, and rests upon a few fundamental axioms, which have eternally existed in Him who implanted them in the breast of man when He created him after His own image.

NOTES.

NOTE 1, page 2. Diameter. A straight line passing through the centre, and terminated both ways by the sides or surface of a figure, such as of a circle or sphere. In fig. 1, q Q, N S, are diameters.

NOTE 2, p. 2. Mathematical and mechanical sciences. Mathematics teach the laws of number and quantity; mechanics treat of the equilibrium and motion of bodies.

NOTE 3, p. 2. Analysis is a series of reasoning conducted by signs or symbols of the quantities whose relations form the subject of inquiry.

NOTE 4, p. 3. Oscillations are movements to and fro, like the swinging of the pendulum of a clock, or waves in water. The tides are oscillations of the sea.

NOTE 5, p. 3. Gravitation. Gravity is the reciprocal attraction of matter on matter; gravitation is the difference between gravity and the centrifugal force induced by the velocity of rotation or revolution. Sensible gravity, or weight, is a particular instance of gravitation. It is the force which causes substances to fall to the surface of the earth, and which retains the celestial bodies in their orbits. Its intensity increases as the squares of the distance decrease.

NOTE 6, p. 4. Particles of matter are the indefinitely small or ultimate atoms into which matter is believed to be divisible. Their form is unknown; but, though too small to be visible, they must have magnitude.

NOTE 7, p. 4. A hollow sphere. A hollow ball, like a bomb-shell. A sphere is a ball or solid body, such, that all lines drawn from its centre to its surface are equal. They are called radii, and every line passing through the centre and terminated both ways by the surface is a diameter, which is consequently equal to twice the radius. In fig. 3, Q q or N S is a diameter, and C Q, C N are radii. A great circle of the sphere has the same centre with the sphere as the circles Q E q d and Q N q S. The circle A B is a lesser circle of the sphere.

NOTE 8, p. 4. Concentric hollow spheres. Shells, or hollow spheres, having the same centre, like the coats of an onion.

NOTE 9, p. 4. Spheroid. A solid body, which sometimes has the shape of an orange, as in fig. 1; it is then called an oblate spheroid, because it is flattened at the poles N and S. Such is the form of the earth and planets. When, on the contrary, it is drawn out at the poles like an egg, as in fig. 2, it is called a prolate spheroid. It is evident that in both these solids the radii C q, C a, C N, &c., are generally unequal; whereas in the sphere they are all equal.

NOTE 10, p. 4. Centre of gravity. A point in every body, which if supported, the body will remain at rest in whatever position it may be placed. About that point all the parts exactly balance one another. The celestial bodies attract each other as if each were condensed into a single particle situate in the centre of gravity, or the particle situate in the centre of gravity of each may be regarded as possessing the resultant power of the innumerable oblique forces which constitute the whole attraction of the body.

NOTE 11, pp. 4, 6. Poles and equator. Let fig. 1 or 3 represent the earth, C its centre, N C S the axis of rotation, or the imaginary line about which it performs its daily revolution. Then N and S are the north and south poles, and the great circle q E Q, which divides the earth into two equal parts, is the equator. The earth is flattened at the poles, fig. 1, the equatorial diameter, q Q, exceeding the polar diameter, N S, by about 26-1/2 miles. Lesser circles, A B G, which are parallel to the equator, are circles or parallels of latitude, which is estimated in degrees, minutes, and seconds, north and south of the equator, every place in the same parallel having the same latitude. Greenwich is in the parallel of 51° 28ʹ 40ʺ. Thus terrestrial latitude is the angular distance between the direction of a plumb-line at any place and the plane of the equator. Lines such as N Q S, N G E S, fig. 3, are called meridians; all the places in any one of these lines have noon at the same instant. The meridian of Greenwich has been chosen by the British as the origin of terrestrial longitude, which is estimated in degrees, minutes, and seconds, east and west of that line. If N G E S be the meridian of Greenwich, the position of any place, B, is determined, when its latitude, Q C B, and its longitude, E C Q, are known.

NOTE 12, p. 4. Mean quantities are such as are intermediate between others that are greater and less. The mean of any number of unequal quantities is equal to their sum divided by their number. For instance, the mean between two unequal quantities is equal to half their sum.

NOTE 13, p. 4. A certain mean latitude. The attraction of a sphere on an external body is the same as if its mass were collected into one heavy particle in its centre of gravity, and the intensity of its attraction diminishes as the square of its distance from the external body increases. But the attraction of a spheroid, fig. 1, on an external body at m in the plane of its equator, E Q, is greater, and its attraction on the same body when at mʹ in the axis N S less, than if it were a sphere. Therefore, in both cases, the force deviates from the exact law of gravity. This deviation arises from the protuberant matter at the equator; and, as it diminishes towards the poles, so does the attractive force of the spheroid. But there is one mean latitude, where the attraction of a spheroid is the same as if it were a sphere. It is a part of the spheroid intermediate between the equator and the pole. In that latitude the square of the sine is equal to 1/3 of the equatorial radius.

NOTE 14, p. 4. Mean distance. The mean distance of a planet from the centre of the sun, or of a satellite from the centre of its planet, is equal to half the sum of its greatest and least distances, and, consequently, is equal to half the major axis of its orbit. For example, let P Q A D, fig. 6, be the orbit or path of the moon or of a planet; then P A is the major axis, C the centre, and C S is equal to C F. Now, since the earth or the sun is supposed to be in the point S according as P D A Q is regarded as the orbit of the moon or that of a planet, S A, S P are the greatest and least distances. But half the sum of S A and S P is equal to half of A P, the major axis of the orbit. When the body is at Q or D, it is at its mean distance from S, for S Q, S D, are each equal to C P, half the major axis by the nature of the curve.

NOTE 15, p. 4. Mean radius of the earth. The distance from the centre to the surface of the earth, regarded as a sphere. It is intermediate between the distances of the centre of the earth from the pole and from the equator.

NOTE 16, p. 5. Ratio. The relation which one quantity bears to another.

NOTE 17, p. 5. Square of moon’s distance. In order to avoid large numbers, the mean radius of the earth is taken for unity: then the mean distance of the moon is expressed by 60; and the square of that number is 3600, or 60 times 60.

NOTE 18, p. 5. Centrifugal force. The force with which a revolving body tends to fly from the centre of motion: a sling tends to fly from the hand in consequence of the centrifugal force. A tangent is a straight line touching a curved line in one point without cutting it, as m T, fig. 4. The direction of the centrifugal force is in the tangent to the curved line or path in which the body revolves, and its intensity increases with the angular swing of the body, and with its distance from the centre of motion. As the orbit of the moon does not differ much from a circle, let it be represented by m d g h, fig. 4, the earth being in C. The centrifugal force arising from the velocity of the moon in her orbit balances the attraction of the earth. By their joint action, the moon moves through the arc m n during the time that she would fly off in the tangent m T by the action of the centrifugal force alone, or fall through m p by the earth’s attraction alone. T n, the deflection from the tangent, is parallel and equal to m p, the versed sine of the arc m n, supposed to be moved over by the moon in a second, and therefore so very small that it may be regarded as a straight line. T n, or m p, is the space the moon would fall through in the first second of her descent to the earth, were she not retained in her orbit by her centrifugal force.

NOTE 19, p. 5. Action and reaction. When motion is communicated by collision or pressure, the action of the body which strikes is returned with equal force by the body which receives the blow. The pressure of a hand on a table is resisted with an equal and contrary force. This necessarily follows from the impenetrability of matter, a property by which no two particles of matter can occupy the same identical portion of space at the same time. When motion is communicated without apparent contact, as in gravitation, attraction, and repulsion, the quantity of motion gained by the one body is exactly equal to that lost by the other, but in a contrary direction; a circumstance known by experience only.

NOTE 20, p. 5. Projected. A body is projected when it is thrown: a ball fired from a gun is projected; it is therefore called a projectile. But the word has also another meaning. A line, surface, or solid body, is said to be projected upon a plane, when parallel straight lines are drawn from every point of it to the plane. The figure so traced upon a plane is a projection. The projection of a terrestrial object is therefore its daylight shadow, since the sun’s rays are sensibly parallel.

NOTE 21, p. 5. Space. The boundless region which contains all creation.

NOTE 22, pp. 5, 11. Conic sections. Lines formed by any plane cutting a cone. A cone is a solid figure, like a sugar-loaf, fig. 5, of which A is the apex, A D the axis, and the plane B E C F the base. The axis may or may not be perpendicular to the base, and the base may be a circle, or any other curved line. When the axis is perpendicular to the base, the solid is a right cone. If a right cone with a circular base be cut at right angles to the base by a plane passing through the apex, the section will be a triangle. If the cone be cut through both sides by a plane parallel to the base, the section will be a circle. If the cone be cut slanting quite through both sides, the section will be an ellipse, fig. 6. If the cone be cut parallel to one of the sloping sides as A B, the section will be a parabola, fig. 7. And if the plane cut only one side of the cone, and be not parallel to the other, the section will be a hyperbola, fig. 8. Thus there are five conic sections.

NOTE 23, p. 5. Inverse square of distance. The attraction of one body for another at the distance of two miles is four times less than at the distance of one mile; at three miles, it is nine times less than at one; at four miles, it is sixteen times less, and so on. That is, the gravitating force decreases in intensity as the squares of the distance increase.

NOTE 24, p. 5. Ellipse. One of the conic sections, fig. 6. An ellipse may be drawn by fixing the ends of a string to two points, S and F, in a sheet of paper, and then carrying the point of a pencil round in the loop of the string kept stretched, the length of the string being greater than the distance between the two points. The points S and F are called the foci, C the centre, S C or C F the excentricity, A P the major axis, Q D the minor axis, and P S the focal distance. It is evident that, the less the excentricity C S, the nearer does the ellipse approach to a circle; and from the construction it is clear that the length of the string S m F is equal to the major axis P A. If T t be a tangent to the ellipse at m, then the angle T m S is equal to the angle t m F; and, as this is true for every point in the ellipse, it follows that, in an elliptical reflecting surface, rays of light or sound coming from one focus S will be reflected by the surface to the other focus F, since the angle of incidence is equal to the angle of reflection by the theories of light and sound.

NOTE 25, p. 5. Periodic time. The time in which a planet or comet performs a revolution round the sun, or a satellite about its planet.

NOTE 26, p. 5. Kepler discovered three laws in the planetary motions by which the principle of gravitation is established:—1st law, That the radii vectores of the planets and comets describe areas proportional to the time.—Let fig. 9 be the orbit of a planet; then, supposing the spaces or areas P S p, p S a, a S b, &c., equal to one another, the radius vector S P, which is the line joining the centres of the sun and planet, passes over these equal spaces in equal times; that is, if the line S P passes to S p in one day, it will come to S a in two days, to S b in three days, and so on. 2nd law, That the orbits or paths of the planets and comets are conic sections, having the sun in one of their foci. The orbits of the planets and satellites are curves like fig. 6 or 9, called ellipses, having the sun in the focus S. Several comets are known to move in ellipses; but the greater part seem to move in parabolas, fig. 7, having the sun in S, though it is probable that they really move in very long flat ellipses; others appear to move in hyperbolas, like fig. 8. The third law is, that the squares of the periodic times of the planets are proportional to the cubes of their mean distances from the sun. The square of a number is that number multiplied by itself, and the cube of a number is that number twice multiplied by itself. For example, the squares of the numbers 2, 3, 4, &c., are 4, 9, 16, &c., but their cubes are 8, 27, 64, &c. Then the squares of the numbers representing the periodic times of two planets are to one another as the cubes of the numbers representing their mean distances from the sun. So that, three of these quantities being known, the other may be found by the rule of three. The mean distances are measured in miles or terrestrial radii, and the periodic times are estimated in years, days, and parts of a day. Kepler’s laws extend to the satellites.

NOTE 27, p. 5. Mass. The quantity of matter in a given bulk. It is proportional to the density and volume or bulk conjointly.

NOTE 28, p. 5. Gravitation proportional to mass. But for the resistance of the air, all bodies would fall to the ground in equal times. In fact, a hundred equal particles of matter at equal distances from the surface of the earth would fall to the ground in parallel straight lines with equal rapidity, and no change whatever would take place in the circumstances of their descent, if 99 of them were united in one solid mass; for the solid mass and the single particle would touch the ground at the same instant, were it not for the resistance of the air.

NOTE 29, p. 5. Primary signifies, in astronomy, the planet about which a satellite revolves. The earth is primary to the moon.

NOTE 30, p. 6. Rotation. Motion round an axis, real or imaginary.

NOTE 31, p. 7. Compression of a spheroid. The flattening at the poles. It is equal to the difference between the greatest and least diameters, divided by the greatest, these quantities being expressed in some standard measure, as miles.

NOTE 32, p. 7. SATELLITES. Small bodies revolving about some of the planets. The moon is a satellite to the earth.

NOTE 33, p. 7. Nutation. A nodding motion in the earth’s axis while in rotation, similar to that observed in the spinning of a top. It is produced by the attraction of the sun and moon on the protuberant matter at the terrestrial equator.

NOTE 34, p. 7. Axis of rotation. The line, real or imaginary, about which a body revolves. The axis of the earth’s rotation is that diameter, or imaginary line, passing through the centre and both poles. Fig. 1 being the earth, N S is the axis of rotation.

NOTE 35, p. 7. Nutation of lunar orbit. The action of the bulging matter at the earth’s equator on the moon occasions a variation in the inclination of the lunar orbit to the plane of the ecliptic. Suppose the plane N p n, fig. 13, to be the orbit of the moon, and N m n the plane of the ecliptic, the earth’s action on the moon causes the angle p N m to become less or greater than its mean state. The nutation in the lunar orbit is the reaction of the nutation in the earth’s axis.

NOTE 36, p. 7. Translated. Carried forward in space.

NOTE 37, p. 7. Force proportional to velocity. Since a force is measured by its effect, the motions of the bodies of the solar system among themselves would be the same whether the system be at rest or not. The real motion of a person walking the deck of a ship at sea is compounded of his own motion and that of the ship, yet each takes place independently of the other. We walk about as if the earth were at rest, though it has the double motion of rotation on its axis and revolution round the sun.

NOTE 38, p. 8. Tangent. A straight line which touches a curved line in one point without cutting it. In fig. 4, m T is tangent to the curve in the point m. In a circle the tangent is at right angles to the radius, C m.

NOTE 39, p. 8. Motion in an elliptical orbit. A planet m, fig. 6, moves round the sun at S in an ellipse P D A Q, in consequence of two forces, one urging it in the direction of the tangent m T, and another pulling it towards the sun in the direction m S. Its velocity, which is greatest at P, decreases throughout the arc to P D A to A, where it is least, and increases continually as it moves along the arc A Q P till it comes to P again. The whole force producing the elliptical motion varies inversely as the square of the distance. See note 23.

NOTE 40, p. 8. Radii vectores. Imaginary lines adjoining the centre of the sun and the centre of a planet or comet, or the centres of a planet and its satellite. In the circle, the radii are all equal; but in an ellipse, fig. 6, the radius vector S A is greater, and S P less than all the others. The radii vectores S Q, S D, are equal to C A or C P, half the major axis P A, and consequently equal to the mean distance. A planet is at its mean distance from the sun when in the points Q and D.

NOTE 41, p. 8. Equal areas in equal times. See Kepler’s 1st law, in note 26, p. 5.

NOTE 42, p. 8. Major axis. The line P A, fig. 6 or 10.

NOTE 43, p. 8. If the planet described a circle, &c. The motion of a planet about the sun, in a circle A B P, fig. 10, whose radius C A is equal to the planet’s mean distance from him, would be equable, that is, its velocity, or speed, would always be the same. Whereas, if it moved in the ellipse A Q P, its speed would be continually varying, by note 39; but its motion is such, that the time elapsing between its departure from P and its return to that point again would be the same whether it moved in the circle or in the ellipse; for these curves coincide in the points P and A.

NOTE 44, p. 8. True motion. The motion of a body in its real orbit P D A Q, fig. 10.

NOTE 45, p. 9. Mean motion. Equable motion in a circle P E A B, fig. 10, at the mean distance C P or C m, in the time that the body would accomplish a revolution in its elliptical orbit P D A Q.

NOTE 46, p. 9. The equinox. Fig. 11 represents the celestial sphere, and C its centre, where the earth is supposed to be. q ♈ Q ♎ is the equinoctial or great circle, traced in the starry heavens by an imaginary extension of the plane of the terrestrial equator, and E ♈ e ♎ is the ecliptic, or apparent path of the sun round the earth. ♈ ♎, the intersection of these two planes, is the line of the equinoxes; ♈ is the vernal equinox, and ♎ the autumnal. When the sun is in these points, the days and nights are equal. They are distant from one another by a semicircle, or two right angles. The points E and e are the solstices, where the sun is at his greatest distance from the equinoctial. The equinoctial is everywhere ninety degrees distant from its poles N and S, which are two points diametrically opposite to one another, where the axis of the earth’s rotation, if prolonged, would meet the heavens. The northern celestial pole N is within 1° 24ʹ of the pole star. As the latitude of any place on the surface of the earth is equal to the height of the pole above the horizon, it is easily determined by observation. The ecliptic E ♈ e ♎ is also everywhere ninety degrees distant from its poles P and p. The angle P C N, between the poles P and N of the equinoctial and ecliptic, is equal to the angle e C Q, called the obliquity of the ecliptic.

NOTE 47, p. 9. Longitude. The vernal equinox, ♈, fig. 11, is the zero point in the heavens whence celestial longitudes, or the angular motions of the celestial bodies, are estimated from west to east, the direction in which they all revolve. The vernal equinox is generally called the first point of Aries, though these two points have not coincided since the early ages of astronomy, about 2233 years ago, on account of a motion in the equinoctial points, to be explained hereafter. If S ♈, fig. 10, be the line of the equinoxes, and ♈ the vernal equinox, the true longitude of a planet p is the angle ♈ S p, and its mean longitude is the angle ♈ C m, the sun being in S. Celestial longitude is the angular distance of a heavenly body from the vernal equinox; whereas terrestrial longitude is the angular distance of a place on the surface of the earth from a meridian arbitrarily chosen, as that of Greenwich.

NOTE 48, pp. 9, 58. Equation of the centre. The difference between ♈ C m and ♈ S p, fig. 10; that is, the difference between the true and mean longitudes of a planet or satellite. The true and mean places only coincide in the points P and A; in every other point of the orbit, the true place is either before or behind the mean place. In moving from A through the arc A Q P, the true place p is behind the mean place m; and through the arc P D A the true place is before the mean place. At its maximum, the equation of the centre measures C S, the excentricity of the orbit, since it is the difference between the motion of a body in an ellipse and in a circle whose diameter A P is the major axis of the ellipse.

NOTE 49, p. 9. Apsides. The points P and A, fig. 10, at the extremities of the major axis of an orbit. P is commonly called the perihelion, a Greek term signifying round the sun; and the point A is called the aphelion, a Greek term signifying at a distance from the sun.

NOTE 50, p. 9. Ninety degrees. A circle is divided into 360 equal parts, or degrees; each degree into 60 equal parts, called minutes; and each minute into 60 equal parts, called seconds. It is usual to write these quantities thus, 15° 16ʹ 10ʺ, which means fifteen degrees, sixteen minutes, and ten seconds. It is clear that an arc m n, fig. 4, measures the angle m C n; hence we may say, an arc of so many degrees, or an angle of so many degrees; for, if there be ten degrees in the angle m C n, there will be ten degrees in the arc m n. It is evident that there are 90° in a right angle, m C d, or quadrant, since it is the fourth part of 360°.

NOTE 51, p. 9. Quadratures. A celestial body is said to be in quadrature when it is 90 degrees distant from the sun. For example, in fig. 14, if d be the sun, S the earth, and p the moon, then the moon is said to be in quadrature when she is in either of the points Q or D, because the angles Q S d and D S d, which measure her apparent distance from the sun, are right angles.

NOTE 52, p. 9. Excentricity. Deviation from circular form. In fig. 6, C S is the excentricity of the orbit P Q A D. The less C S, the more nearly does the orbit or ellipse approach the circular form; and, when C S is zero, the ellipse becomes a circle.

NOTE 53, p. 9. Inclination of an orbit. Let S, fig. 12, be the centre of the sun, P N A n the orbit of a planet moving from west to east in the direction N p. Let E N m e n be the shadow or projection of the orbit on the plane of the ecliptic, then N S n is the intersection of these two planes, for the orbit rises above the plane of the ecliptic towards N p, and sinks below it at N P. The angle p N m, which these two planes make with one another, is the inclination of the orbit P N p A to the plane of the ecliptic.

NOTE 54, p. 9. Latitude of a planet. The angle p S m, fig. 12, or the height of the planet p above the ecliptic E N m. In this case the latitude is north. Thus, celestial latitude is the angular distance of a celestial body from the plane of the ecliptic, whereas terrestrial latitude is the angular distance of a place on the surface of the earth from the equator.

NOTE 55, p. 9. Nodes. The two points N and n, fig. 12, in which the orbit N A n P of a planet or comet intersects the plane of the ecliptic e N E n. The part N A n of the orbit lies above the plane of the ecliptic, and the part n P N below it. The ascending node N is the point through which the body passes in rising above the plane of the ecliptic, and the descending node n is the point in which the body sinks below it. The nodes of a satellite’s orbit are the points in which it intersects the plane of the orbit of the planet.

NOTE 56, p. 10. Distance from the sun. S p in fig. 12. If ♈ be the vernal equinox, then ♈ S p is the longitude of the planet p, m S p is its latitude, and S p its distance from the sun. When these three quantities are known, the place of the planet p is determined in space.

NOTE 57, pp. 10, 59. Elements of an orbit. Of these there are seven. Let P N A n, fig. 12, be the elliptical orbit of a planet, C its centre, S the sun in one of the foci, ♈ the point of Aries, and E N e n the plane of the ecliptic. The elements are—the major axis A P; the excentricity C S; the periodic time, that is, the time of a complete revolution of the body in its orbit; and the fourth is the longitude of the body at any given instant—for example, that at which it passes through the perihelion P, the point of its orbit nearest to the sun. That instant is assumed as the origin of time, whence all preceding and succeeding periods are estimated. These four quantities are sufficient to determine the form of the orbit, and the motion of the body in it. Three other elements are requisite for determining the position of the orbit in space. These are, the angle ♈ S P, the longitude of the perihelion; the angle A N e, which is the inclination of the orbit to the plane of the ecliptic; and, lastly, the angle ♈ S N, the longitude of N the ascending node.

NOTE 58, p. 10. Whose planes, &c. The planes of the orbits, as P N A n, fig. 12, in which the planets move, are inclined or make small angles e N A with the plane of the ecliptic E N e n, and cut it in straight lines, N S n passing through S, the centre of the sun.

NOTE 59, p. 11. Momentum. Force measured by the weight of a body and its speed, or simple velocity, conjointly. The primitive momentum of the planets is, therefore, the quantity of motion which was impressed upon them when they were first thrown into space.

NOTE 60, p. 11. Unstable equilibrium. A body is said to be in equilibrium when it is so balanced as to remain at rest. But there are two kinds of equilibrium, stable and unstable. If a body balanced in stable equilibrium be slightly disturbed, it will endeavour to return to rest by a number of movements to and fro, which will continually decrease till they cease altogether, and then the body will be restored to its original state of repose. But, if the equilibrium be unstable, these movements to and fro, or oscillations, will become greater and greater till the equilibrium is destroyed.

NOTE 61, p. 14. Retrograde. Going backwards, as from east to west, contrary to the motion of the planets.

NOTE 62, p. 14. Parallel directions. Such as never meet, though prolonged ever so far.

NOTE 63, pp. 14, 16. The whole force, &c. Let S, fig. 13, be the sun, N m n the plane of the ecliptic, p the disturbed planet moving in its orbit n p N, and d the disturbing planet. Now, d attracts the sun and the planet p with different intensities in the directions d S, d p: the difference only of these forces disturbs the motion of p; it is therefore called the disturbing force. But this whole disturbing force may be regarded as equivalent to three forces, acting in the directions p S, p T, and p m. The force acting in the radius vector p S, joining the centres of the sun and planet, is called the radial force. It sometimes draws the disturbed planet p from the sun, and sometimes brings it nearer to him. The force which acts in the direction of the tangent p T is called the tangential force. It disturbs the motion of p in longitude, that is, it accelerates its motion in some parts of its orbit and retards it in others, so that the radius vector S p does not move over equal areas in equal times. (See note 26.) For example, in the position of the bodies in fig. 14, it is evident that, in consequence of the attraction of d, the planet p will have its motion accelerated from Q to C, retarded from C to D, again accelerated from D to O, and lastly retarded from O to Q. The disturbing body is here supposed to be at rest, and the orbit circular; but, as both bodies are perpetually moving with different velocities in ellipses, the perturbations or changes in the motions of p are very numerous. Lastly, that part of the disturbing force which acts in the direction of a line p m, fig. 13, at right angles to the plane of the orbit N p n, may be called the perpendicular force. It sometimes causes the body to approach nearer, and sometimes to recede farther from, the plane of the ecliptic N m n, than it would otherwise do. The action of the disturbing forces is admirably explained in a work on gravitation, by Mr. Airy, the Astronomer Royal.

NOTE 64, pp. 16, 74. Perihelion. Fig. 10, P, the point of an orbit nearest the sun.

NOTE 65, p. 16. Aphelion. Fig. 10, A, the point of an orbit farthest from the sun.

NOTE 66, pp. 16, 17. In fig. 15 the central force is greater than the exact law of gravity; therefore the curvature P p a is greater than P p A the real ellipse; hence the planet p comes to the point a, called the aphelion, sooner than if it moved in the orbit P p A, which makes the line P S A advance to a. In fig. 16, on the contrary, the curvature P p a is less than in the true ellipse, so that the planet p must move through more than the arc P p A, or 180°, before it comes to the aphelion a, which causes the greater axis P S A to recede to a.

NOTE 67, pp. 16, 17. Motion of apsides. Let P S A, fig. 17, be the position of the elliptical orbit of a planet, at any time; then, by the action of the disturbing forces, it successively takes the position Pʹ S Aʹ, Pʺ S Aʺ, &c., till by this direct motion it has accomplished a revolution, and then it begins again; so that the motion is perpetual.

NOTE 68, p. 17. Sidereal revolution. The consecutive return of an object to the same star.

NOTE 69, p. 17. Tropical revolution. The consecutive return of an object to the same tropic or equinox.

NOTE 70, p. 17. The orbit only bulges, &c. In fig. 18 the effect of the variation in the excentricity is shown where P p A is the elliptical orbit at any given instant; after a time it will take the form P pʹ A, in consequence of the decrease in the excentricity C S; then the forms P pʺ A, P pʹʹʹ A, &c., consecutively from the same cause; and, as the major axis P A always retains the same length, the orbit approaches more and more nearly to the circular form. But, after this has gone on for some thousands of years, the orbit contracts again, and becomes more and more elliptical.

NOTE 71, pp. 18, 19. The ecliptic is the apparent path of the sun in the heavens. See note 46.

NOTE 72, p. 18. This force tends to pull, &c. The force in question, acting in the direction p m, fig. 13, pulls the planet p towards the plane N m n, or pushes it farther above it, giving the planet a tendency to move in an orbit above or below its undisturbed orbit N p n, which alters the angle p N m, and makes the node N and the line of nodes N n change their positions.

NOTE 73, p. 18. Motion of the nodes. Let S, fig. 19, be the sun; S N n the plane of the ecliptic; P the disturbing body; and p a planet moving in its orbit p n, of which p n is so small a part that it is represented as a straight line. The plane S n p of this orbit cuts the plane of the ecliptic in the straight line S n. Suppose the disturbing force begins to act on p, so as to draw the planet into the arc p pʹ; then, instead of moving in the orbit p n, it will tend to move in the orbit p pʹ nʹ, whose plane cuts the ecliptic in the straight line S nʹ. If the disturbing force acts again upon the body when at pʹ, so as to draw it into the arc pʹ pʺ, the planet will now tend to move in the orbit pʹ pʺ nʺ, whose plane cuts the ecliptic in the straight line S nʺ. The action of the disturbing force on the planet when at pʺ will bring the node to nʹʹʹ, and so on. In this manner the node goes backwards through the successive points n, nʹ, nʺ, nʹʹʹ, &c., and the line of nodes S n has a perpetual retrograde motion about S, the centre of the sun. The disturbing force has been represented as acting at intervals for the sake of illustration: in nature it is continuous, so that the motion of the node is continuous also; though it is sometimes rapid and sometimes slow, now retrograde and now direct; but, on the whole, the motion is slowly retrograde.

NOTE 74, p. 18. When the disturbing planet is anywhere in the line S N, fig. 19, or in its prolongation, it is in the same plane with the disturbed planet; and, however much it may affect its motions in that plane, it can have no tendency to draw it out of it. But when the disturbing planet is in P, at right angles to the line S N, and not in the plane of the orbit, it has a powerful effect on the motion of the nodes: between these two positions there is great variety of action.

NOTE 75, p. 19. The changes in the inclination are extremely minute when compared with the motion of the node, as evidently appears from fig. 19, where the angles n p nʹ, nʹ pʹ nʺ, &c., are much smaller than the corresponding angles n S nʹ, S nʺ, &c.

NOTE 76, p. 20. Sines and cosines. Figure 4 is a circle; n p is the sine, and C p is the cosine of an arc m n. Suppose the radius C m to begin to revolve at m, in the direction m n a; then at the point m the sine is zero, and the cosine is equal to the radius C m. As the line C m revolves and takes the successive positions C n, C a, C b, &c., the sines n p, a q, b r, &c., of the arcs m n, m a, m h, &c., increase, while the corresponding cosines C p, C q, C r, &c., decrease; and when the revolving radius takes the position C d, at right angles to the diameter g m, the sine becomes equal to the radius C d, and the cosine is zero. After passing the point d, the contrary happens; for the sines e K, l V, &c., diminish, and the cosines C K, C V, &c., go on increasing, till at g the sine is zero, and the cosine is equal to the radius C g. The same alternation takes place through the remaining parts g h, h m, of the circle, so that a sine or cosine never can exceed the radius. As the rotation of the earth is invariable, each point of its surface passes through a complete circle, or 360 degrees, in twenty-four hours, at a rate of 15 degrees in an hour. Time, therefore, becomes a measure of angular motion, and vice versâ, the arcs of a circle a measure of time, since these two quantities vary simultaneously and equably; and, as the sines and cosines of the arcs are expressed in terms of the time, they vary with it. Therefore, however long the time may be, and how often soever the radius may revolve round the circle, the sines and cosines never can exceed the radius; and, as the radius is assumed to be equal to unity, their values oscillate between unity and zero.

NOTE 77, p. 20. The small excentricities and inclinations of the planetary orbits, and the revolutions of all the bodies in the same direction, were proved by Euler, La Grange, and La Place, to be conditions necessary for the stability of the solar system. Subsequently, however, the periodicity of the terms of the series expressing the perturbations was supposed to be sufficient alone, but M. Poisson has shown that to be a mistake; that these three conditions are requisite for the necessary convergence of the series, and that therefore the stability of the system depends on them conjointly with the periodicity of the sines and cosines of each term. The author is aware that this note can only be intelligible to the analyst, but she is desirous of correcting an error, and the more so as the conditions of stability afford one of the most striking instances of design in the original construction of our system, and of the foresight and supreme wisdom of the Divine Architect.

NOTE 78, p. 22. Resisting medium. A fluid which resists the motions of bodies, such as atmospheric air, or the highly elastic fluid called ether, with which space is filled.

NOTE 79, p. 23. Obliquity of the ecliptic. The angle e ♈ q, fig. 11, between the plane of the terrestrial equator q ♈ Q, and the plane of the ecliptic E ♈ e. The obliquity is variable.

NOTE 80, p. 23. Invariable plane. In the earth the equator is the invariable plane which nearly maintains a parallel position with regard to itself while revolving about the sun, as in fig. 20, where E Q represents it. The two hemispheres balance one another on each side of this plane, and would still do so if all the particles of which they consist were moveable among themselves, provided the earth were not disturbed by the action of the sun and moon, which alters the parallelism of the equator by the small variation called nutation, to be explained hereafter.

NOTE 81, p. 24. If each particle, &c. Let P, Pʹ, Pʺ, &c., fig. 21, be planets moving in their orbits about the centre of gravity of the system. Let P S M, Pʹ S Mʹ, &c., be portions of these orbits moved over by the radii vectores S P, S Pʹ, &c., in a given time, and let p S m, pʹ S mʹ, &c., be their shadows or projections on the invariable plane. Then, if the numbers which represent the masses of the planets P, Pʹ, &c., be respectively multiplied by the numbers representing the areas or spaces p S m, pʹ S mʹ, &c., the sum of the whole will be greater for the invariable plane than it would be for any plane that could pass through S, the centre of gravity of the system.

NOTE 82, p. 24. The centre of gravity of the solar system lies within the body of the sun, because his mass is much greater than the masses of all the planets and satellites added together.

NOTE 83, pp. 25, 36. Conjunction. A planet is said to be in conjunction when it has the same longitude with the sun, and in opposition when its longitude differs from that of the sun by 180 degrees. Thus two bodies are said to be in conjunction when they are seen exactly in the same part of the heavens, and in opposition when diametrically opposite to one another. Mercury and Venus, which are nearer to the sun than the earth, are called inferior planets; while all the others, being farther from the sun than the earth, are said to be superior planets. Suppose the earth to be at E, fig. 24; then a superior planet will be in conjunction with the sun at C, and in opposition to him when at O. Again, suppose the earth to be in O, then an inferior planet will be in conjunction when at E, and in opposition when at F.

NOTE 84, p. 26. The periodic inequalities are computed for a given time; and consequently for a given form and position of the orbits of the disturbed and disturbing bodies. Although the elements of the orbits vary so slowly that no sensible effect is produced on inequalities of a short period, yet, in the course of time, the secular variations of the elements change the forms and relative positions of the orbits so much, that Jupiter and Saturn, which would have come to the same relative positions with regard to the sun and to one another after 850 years, do not arrive at the same relative positions till after 918 years.

NOTE 85, p. 26. Configuration. The relative position of the planets with regard to one another, to the sun, and to the plane of the ecliptic.

NOTE 86, p. 27. In the same manner that the excentricity of an elliptical orbit may be increased or diminished by the action of the disturbing forces, so a circular orbit may acquire less or more ellipticity from the same cause. It is thus that the forms of the orbits of the first and second satellites of Jupiter oscillate between circles and ellipses differing very little from circles.

NOTE 87, p. 28. The plane of Jupiter’s equator is the imaginary plane passing through his centre at right angles to his axis of rotation, and corresponds to the plane q E Q e, in fig. 1. The satellites move very nearly in the plane of Jupiter’s equator; for, if J be Jupiter, fig. 22, P p his axis of rotation, e Q his equatorial diameter, which is 6000 miles longer than P p, and if J O and J E be the planes of his orbit and equator seen edgewise, then the orbits of his four satellites seen edgewise will have the positions J1, J2, J3, J4. These are extremely near to one another, for the angle E J O is only 3° 5ʹ 30ʺ.

NOTE 88, p. 28. In consequence of the satellites moving so nearly in the plane of Jupiter’s equator, when seen from the earth, they appear to be always very nearly in a straight line, however much they may change their positions with regard to one another and to their primary. For example, on the evenings of the 3rd, 4th, 5th, and 6th of January, 1835, the satellites had the configurations given in fig. 23, where O is Jupiter, and 1, 2, 3, 4, are the first, second, third, and fourth satellites. The satellite is supposed to be moving in a direction from the figure towards the point. On the sixth evening the second satellite was seen on the disc of the planet.

NOTE 89, p. 28. Angular motion or velocity is the swiftness with which a body revolves—a sling, for example; or the speed with which the surface of the earth performs its daily rotation about its axis.

NOTE 90, p. 29. Displacement of Jupiter’s orbit. The action of the planets occasions secular variations in the position of Jupiter’s orbit J O, fig. 22, without affecting the plane of his equator J E. Again, the sun and satellites themselves, by attracting the protuberant matter at Jupiter’s equator, change the position of the plane J E without affecting J O. Both of these cause perturbations in the motions of the satellites.

NOTE 91, p. 29. Precession, with regard to Jupiter, is a retrograde motion of the point where the lines J O, J E, intersect fig. 22.

NOTE 92, p. 30. Synodic motion of a satellite. Its motion during the interval between two of its consecutive eclipses.

NOTE 93, p. 30. Opposition. A body is said to be in opposition when its longitude differs from that of the sun by 180°. If S, fig. 24, be the sun, and E the earth, then Jupiter is in opposition when at O, and in conjunction when at C. In these positions the three bodies are in the same straight line.

NOTE 94, p. 30. Eclipses of the satellites. Let S, fig. 25, be the sun, J Jupiter, and a B b his shadow. Let the earth be moving in its orbit, in the direction E A R T H, and the third satellite in the direction a b m n. When the earth is at E, the satellite, in moving through the arc a b, will vanish at a, and reappear at b, on the same side of Jupiter. If the earth be in R, Jupiter will be in opposition; and then the satellite, in moving through the arc a b, will vanish close to the disc of the planet, and will reappear on the other side of it. But, if the satellite be moving through the arc m n, it will appear to pass over the disc, and eclipse the planet.

NOTE 95, pp. 30, 43. Meridian. A terrestrial meridian is a line passing round the earth and through both poles. In every part of it noon happens at the same instant. In figures 1 and 3, the lines N Q S and N G S are meridians, C being the centre of the earth, and N S its axis of rotation. The meridian passing through the Observatory at Greenwich is assumed by the British as a fixed origin from whence terrestrial longitudes are measured. And as each point on the surface of the earth passes through 360°, or a complete circle, in twenty-four hours, at the rate of 15° in an hour, time becomes a representative of angular motion. Hence, if the eclipse of a satellite happens at any place at eight o’clock in the evening, and the Nautical Almanac shows that the same phenomenon will take place at Greenwich at nine, the place of observation will be in the 15° of west longitude.

NOTE 96, p. 31. Conjunction. Let S be the sun, fig. 24, E the earth, and J O Jʹ Cʹ the orbit of Jupiter. Then the eclipses which happen when Jupiter is in O are seen 16^m 26^s sooner than those which take place when the planet is in C. Jupiter is in conjunction when at C, and in opposition when in O.

NOTE 97, p. 31. In the diagonal, &c. Were the line A S, fig. 26, 100,000 times longer than A B, Jupiter’s true place would be in the direction A Sʹ, the diagonal of the figure A B Sʹ S, which is, of course, out of proportion.

NOTE 98, p. 31. Aberration of light. The celestial bodies are so distant that the rays of light coming from them may be reckoned parallel. Therefore, let S A, Sʹ B, fig. 26, be two rays of light coming from the sun, or a planet, to the earth moving in its orbit in the direction A B. If a telescope be held in the direction A S, the ray S A, instead of going down the tube, will impinge on its side, and be lost in consequence of the telescope being carried with the earth in the direction A B. But, if the tube be held in the position A E, so that A B is to A S as the velocity of the earth to the velocity of light, the ray will pass through Sʹ E A. The star appears to be in the direction A Sʹ, when it really is in the direction A S; hence the angle S A Sʹ is the angle of aberration.

NOTE 99, p. 32. Density proportional to elasticity. The more a fluid, such as atmospheric air, is reduced in dimensions by pressure, the more it resists the pressure.

NOTE 100, p. 32. Oscillations of pendulum retarded. If a clock be carried from the pole to the equator, its rate will be gradually diminished, that is, it will go slower and slower: because the centrifugal force, which increases from the pole to the equator, diminishes the force of gravity.

NOTE 101, p. 34. Disturbing action. The disturbing force acts here in the very same manner as in note 63; only that the disturbing body d, fig. 14, is the sun, S the earth, and p the moon.

NOTE 102, pp. 35, 36, 86. Perigee. A Greek word, signifying round the earth. The perigee of the lunar orbit is the point P, fig. 6, where the moon is nearest to the earth. It corresponds to the perihelion of a planet. Sometimes the word is used to denote the point where the sun is nearest to the earth.

NOTE 103, p. 35. Evection. The evection is produced by the action of the radial force in the direction S p, fig. 14, which sometimes increases and sometimes diminishes the earth’s attraction to the moon. It produces a corresponding temporary change in the excentricity, which varies with the position of the major axis of the lunar orbit in respect of the line S d, joining the centres of the earth and sun.

NOTE 104, p. 35. Variation. The lunar perturbation called the variation is the alternate acceleration and retardation of the moon in longitude, from the action of the tangential force. She is accelerated in going from quadratures in Q and D, fig. 14, to the points C and O, called syzygies, and is retarded in going from the syzygies C and O to Q and D again.

NOTE 105, p. 36. Square of time. If the times increase at the rate of 1, 2, 3, 4, &c., years or hundreds of years, the squares of the times will be 1, 4, 9, 16, &c., years or hundreds of years.

NOTE 106, p. 37. In all investigations hitherto made with regard to the acceleration, it was tacitly assumed that the areas described by the radius vector of the moon were not permanently altered; that is to say, that the tangential disturbing force produced no permanent effect. But Mr. Adams has discovered that, in consequence of the constant decrease in the excentricity of the earth’s orbit, there is a gradual change in the central disturbing force which affects the aërial velocity, and consequently it alters the amount of the acceleration by a very small quantity, as well as the variation and other periodical inequalities of the moon. On the latter, however, it has no permanent effect, because it affects them in opposite directions in very moderate intervals of time, whereas a very small error in the amount of the acceleration goes on increasing as long as the excentricity of the earth’s orbit diminishes, so that it would ultimately vitiate calculations of the moon’s place for distant periods of time. This shows how complicated the moon’s motions are, and what rigorous accuracy is required in their determination.

To give an idea of the labour requisite merely to perfect or correct the lunar tables, the moon’s place was determined by observation at the Greenwich Observatory in 6000 different points of her orbit, each of which was compared with the same points calculated from Baron Plana’s formulæ, and to do that sixteen computers were constantly employed for eight years. Since the longitude is determined by the motions of the moon, the lunar tables are of the greatest importance.

NOTE 107, p. 37. Mean anomaly. The mean anomaly of a planet is its angular distance from the perihelion, supposing it to move in a circle. The true anomaly is its angular distance from the perihelion in its elliptical orbit. For example, in fig. 10, the mean anomaly is P C m, and the true anomaly is P S p.

NOTE 108, pp. 38, 68. Many circumferences. There are 360 degrees or 1,296,000 seconds in a circumference; and, as the acceleration of the moon only increases at the rate of eleven seconds in a century, it must be a prodigious number of ages before it accumulates to many circumferences.

NOTE 109, p. 39. Phases of the moon. The periodical changes in the enlightened part of her disc, from a crescent to a circle, depending upon her position with regard to the sun and earth.

NOTE 110, p. 39. Lunar eclipse. Let S, fig. 27, be the sun, E the earth, and m the moon. The space a A b is a section of the shadow, which has the form of a cone or sugar-loaf, and the spaces A a c, A b d, are the penumbra. The axis of the cone passes through A, and through E and S, the centres of the sun and earth, and n m nʹ is the path of the moon through the shadow.

NOTE 111, p. 39. Apparent diameter. The diameter of a celestial body as seen from the earth.

NOTE 112, p. 40. Penumbra. The shadow or imperfect darkness which precedes and follows an eclipse.

NOTE 113, p. 40. Synodic revolution of the moon. The time between two consecutive new or full moons.

NOTE 114, p. 40. Horizontal refraction. The light, in coming from a celestial object, is bent into a curve as soon as it enters our atmosphere; and that bending is greatest when the object is in the horizon.

NOTE 115, p. 40. Solar eclipse. Let S, fig. 28, be the sun, m the moon, and E the earth. Then a E b is the moon’s shadow, which sometimes eclipses a small portion of the earth’s surface at e, and sometimes falls short of it. To a person at e, in the centre of the shadow, the eclipse may be total or annular; to a person not in the centre of the shadow a part of the sun will be eclipsed; and to one at the edge of the shadow there will be no eclipse at all. The spaces P b E, Pʹ a E, are the penumbra.

NOTE 116, p. 43. From the extremities, &c. If the length of the line a b, fig. 29, be measured, in feet or fathoms, the angles S b a, S a b, can be measured, and then the angle a S b is known, whence the length of the line S C may be computed. a S b is the parallax of the object S; and it is clear that, the greater the distance of S, the less the base a b will appear, because the angle a Sʹ b is less than a S b.

NOTE 117, p. 44. Every particle will describe a circle, &c. If N S, fig. 3, be the axis about which the body revolves, then particles at B, Q, &c., will whirl in the circles B G A a, Q E q d, whose centres are in the axis N S, and their planes parallel to one another. They are, in fact, parallels of latitude, Q E q d being the equator.

NOTE 118, p. 44. The force of gravity, &c. Gravity at the equator acts in the direction Q C, fig. 30. Whereas the direction of the centrifugal force is exactly contrary, being in the direction C Q; hence the difference of the two is the force called gravitation, which makes bodies fall to the surface of the earth. At any point, m, not at the equator, the direction of gravity is m b, perpendicular to the surface, but the centrifugal force acts perpendicularly to N S, the axis of rotation. Now the effect of the centrifugal force is the same as if it were two forces, one of which acting in the direction b m, diminishes the force of gravity, and another which, acting in the direction m t, tangent to the surface at m, urges the particles towards Q, and tends to swell out the earth at the equator.

NOTE 119, p. 45. Homogeneous mass. A quantity of matter, everywhere of the same density.

NOTE 120, p. 45. Ellipsoid of revolution. A solid formed by the revolution of an ellipse about its axis. If the ellipse revolve about its minor axis Q D, fig. 6, the ellipsoid will be oblate, or flattened at the poles like an orange. If the revolution be about the greater axis A P, the ellipsoid will be prolate, like an egg.

NOTE 121, p. 45. Concentric elliptical strata. Strata, or layers, having an elliptical form and the same centre.

NOTE 122, p. 46. On the whole, &c. The line N Q S q, fig. 1, represents the ellipse in question, its major axis being Q q, its minor axis N S.

NOTE 123, p. 46. Increase in the length of the radii, &c. The radii gradually increase from the polar radius C N, fig. 30, which is least, to the equatorial radius C Q, which is greatest. There is also an increase in the lengths of the arcs corresponding to the same number of degrees from the equator to the poles; for, the angle N C r being equal to q C d, the elliptical arc N r is less than q d.

NOTE 124, p. 46. Cosine of latitude. The angles m C a, m C b, fig. 4, being the latitudes of the points a, b, &c., the cosines are C q, C r, &c.

NOTE 125, p. 47. An arc of the meridian. Let N Q S q, fig. 30, be the meridian, and m n the arc to be measured. Then, if Zʹ m, Z n, be verticals, or lines perpendicular to the surface of the earth, at the extremities of the arc m n they will meet in p. Q a n, Q b m, are the latitudes of the points m and n, and their difference is the angle m p n. Since the latitudes are equal to the height of the pole of the equinoctial above the horizon of the places m and n, the angle m p n may be found by observation. When the distance m n is measured in feet or fathoms, and divided by the number of degrees and parts of a degree contained in the angle m p n, the length of an arc of one degree is obtained.

NOTE 126, p. 47. A series of triangles. Let M Mʹ, fig. 31, be the meridian of any place. A line A B is measured with rods, on level ground, of any number of fathoms, C being some point seen from both ends of it. As two of the angles of the triangle A B C can be measured, the lengths of the sides A C, B C, can be computed; and if the angle m A B, which the base A B makes with the meridian, be measured, the length of the sides B m, A m, may be obtained by computation, so that A m, a small part of the meridian, is determined. Again, if D be a point visible from the extremities of the known line B C, two of the angles of the triangle B C D may be measured, and the length of the sides C D, B D, computed. Then, if the angle B m mʹ be measured, all the angles and the side B m of the triangle B m mʹ are known, whence the length of the line m mʹ may be computed, so that the portion A mʹ of the meridian is determined, and in the same manner it may be prolonged indefinitely.

NOTE 127, pp. 47, 49. The square of the sine of the latitude. Q b m, fig. 30, being the latitude of m, e m is the sine and b e the cosine. Then the number expressing the length of e m, multiplied by itself, is the square of the sine of the latitude; and the number expressing the length of b e, multiplied by itself, is the square of the cosine of the latitude.

NOTE 128, p. 48. The polar diameter of the earth determined by the survey of Great Britain is 7900 miles; the equatorial is 7926, which gives a compression of 1/299·33.

NOTE 129, p. 50. A pendulum is that part of a clock which swings to and fro.

NOTE 130, p. 52. Parallax. The angle a S b, fig. 29, under which we view an object a b: it therefore diminishes as the distance increases. The parallax of a celestial object is the angle which the radius of the earth would be seen under, if viewed from that object. Let E, fig. 32, be the centre of the earth, E H its radius, and m H O the horizon of an observer at H. Then H m E is the parallax of a body m, the moon for example. As m rises higher and higher in the heavens to the points mʹ, mʺ, &c., the parallax H mʹ E, H mʺ E, &c., decreases. At Z, the zenith, or point immediately above the head of the observer, it is zero; and at m, where the body is in the horizon, the angle H m E is the greatest possible, and is called the horizontal parallax. It is clear that with regard to celestial bodies the whole effect of parallax is in the vertical, or in the direction m mʹ Z; and as a person at H sees mʹ in the direction H mʹ A, when it really is in the direction E mʹ B, it makes celestial objects appear to be lower than they really are. The distance of the moon from the earth has been determined from her horizontal parallax. The angle E m H can be measured. E H m is a right angle, and E H, the radius of the earth, is known in miles; whence the distance of the moon E m is easily found. Annual parallax is the angle under which the diameter of the earth’s orbit would be seen if viewed from a star.

NOTE 131, p. 52. The radii n B, n G, &c., fig. 3, are equal in any one parallel of latitude, A a B G; therefore a change in the parallax observed in that parallel can only arise from a change in the moon’s distance from the earth; and when the moon is at her mean distance, which is a constant quantity equal to half the major axis of her orbit, a change in the parallax observed in different latitudes, G and E, must arise from the difference in the lengths of the radii n G and C E.

NOTE 132, p. 52. When Venus is in her nodes. She must be in the line N S n where her orbit P N A n cuts the plane of the ecliptic E N e n, fig. 12.

NOTE 133, p. 53. The line described, &c. Let E, fig. 33, be the earth, S the centre of the sun, and V the planet Venus. The real transit of the planet, seen from E the centre of the earth, would be in the direction A B. A person at W would see it pass over the sun in the line v a, and a person at O would see it move across him in the direction vʹ aʹ.

NOTE 134, p. 54. Kepler’s law. Suppose it were required to find the distance of Jupiter from the sun. The periodic times of Jupiter and Venus are given by observation, and the mean distance of Venus from the centre of the sun is known in miles or terrestrial radii; therefore, by the rule of three, the square root of the periodic time of Venus is to the square root of the periodic time of Jupiter as the cube root of the mean distance of Venus from the sun to the cube root of the mean distance of Jupiter from the sun, which is thus obtained in miles or terrestrial radii. The root of a number is that number which, once multiplied by itself, gives its square; twice multiplied by itself, gives its cube, &c. For example, twice 2 are 4, and twice 4 are 8; 2 is therefore the square root of 4, and the cube root of 8. In the same manner 3 times 3 are 9, and 3 times 9 are 27; 3 is therefore the square root of 9, and the cube root of 27.

NOTE 135, p. 55. Inversely, &c. The quantities of matter in any two primary planets are greater in proportion as the cubes of the numbers representing the mean distances of their satellites are greater, and also in proportion as the squares of their periodic times are less.

NOTE 136, p. 55. As hardly anything appears more impossible than that man should have been able to weigh the sun as it were in scales and the earth in a balance, the method of doing so may have some interest. The attraction of the sun is to the attraction of the earth as the quantity of matter in the sun to the quantity of matter in the earth; and, as the force of this reciprocal attraction is measured by its effects, the space the earth would fall through in a second by the sun’s attraction is to the space which the sun would fall through by the earth’s attraction as the mass of the sun to the mass of the earth. Hence, as many times as the fall of the earth to the sun in a second exceeds the fall of the sun to the earth in the same time, so many times does the mass of the sun exceed the mass of the earth. Thus the weight of the sun will be known if the length of these two spaces can be found in miles or parts of a mile. Nothing can be easier. A heavy body falls through 16·0697 feet in a second at the surface of the earth by the earth’s attraction; and, as the force of gravity is inversely as the square of the distance, it is clear that 16·0697 feet are to the space a body would fall through at the distance of the sun by the earth’s attraction, as the square of the distance of the sun from the earth to the square of the distance of the centre of the earth from its surface; that is, as the square of 95,000,000 miles to the square of 4000 miles. And thus, by a simple question in the rule of three, the space which the sun would fall through in a second by the attraction of the earth may be found in parts of a mile. The space the earth would fall through in a second, by the attraction of the sun, must now be found in miles also. Suppose m n, fig. 4, to be the arc which the earth describes round the sun in C, in a second of time, by the joint action of the sun and the centrifugal force. By the centrifugal force alone the earth would move from m to T in a second, and by the sun’s attraction alone it would fall through T n in the same time. Hence the length of T n, in miles, is the space the earth would fall through in a second by the sun’s attraction. Now, as the earth’s orbit is very nearly a circle, if 360 degrees be divided by the number of seconds in a sidereal year of 365-1/4 days, it will give m n, the arc which the earth moves through in a second, and then the tables will give the length of the line C T in numbers corresponding to that angle; but, as the radius C n is assumed to be unity in the tables, if 1 be subtracted from the number representing C T, the length of T n will be obtained; and, when multiplied by 95,000,000, to reduce it to miles, the space which the earth falls through, by the sun’s attraction, will be obtained in miles. By this simple process it is found that, if the sun were placed in one scale of a balance, it would require 354,936 earths to form a counterpoise.

NOTE 137, p. 59. The sum of the greatest and least distances S P, S A, fig. 12, is equal to P A, the major axis; and their difference is equal to twice the excentricity C S. The longitude ♈ S P of the planet, when in the point P, at its least distance from the sun, is the longitude of the perihelion. The greatest height of the planet above the plane of the ecliptic E N e n, is equal to the inclination of the orbit P N A n to that plane. The longitude of the planet, when in the plane of the ecliptic, can only be the longitude of one of the points N or n; and, when one of these points is known, the other is given, being 180° distant from it. Lastly, the time included between two consecutive passages of the planet through the same node N or n, is its periodic time, allowance being made for the recess of the node in the interval.

NOTE 138, p. 60. Suppose that it were required to find the position of a point in space, as of a planet, and that one observation places it in n, fig. 34, another observation places it in nʹ, another in nʺ, and so on; all the points n, nʹ, nʺ, nʹʹʹ, &c., being very near to one another. The true place of the planet P will not differ much from any of these positions. It is evident, from this view of the subject, that P n, P nʹ, P nʺ, &c., are the errors of observation. The true position of the planet P is found by this property, that the squares of the numbers representing the lines P n, P nʹ, &c., when added together, is the least possible. Each line P n, P nʹ, &c., being the whole error in the place of the planet, is made up of the errors of all the elements; and, when compared with the errors obtained from theory, it affords the means of finding each. The principle of least squares is of very general application; its demonstration cannot find a place here; but the reader is referred to Biot’s Astronomy, vol. ii. p. 203.

NOTE 139, p. 61. The true longitude of Uranus was in advance of the tables previous to 1795, and continued to advance till 1822, after which it diminished rapidly till 1830-1, when the observed and calculated longitudes agreed, but then the planet fell behind the calculated place so rapidly that it was clear the tables could no longer represent its motion.

NOTE 140, p. 65. An axis that, &c. Fig. 20 represents the earth revolving in its orbit about the sun in S, the axis of rotation P p being everywhere parallel to itself.

NOTE 141, p. 65. Angular velocities that are sensibly uniform. The earth and planets revolve about their axis with an equable motion, which is never either faster or slower. For example, the length of the day is never more nor less than twenty-four hours.

NOTE 142, p. 68. If fig. 1 be the moon, her polar diameter N S is the shortest; and of those in the plane of the equator, Q E q, that which points to the earth is greater than all the others.

NOTE 143, p. 73. Inversely proportional, &c. That is, the total amount of solar radiation becomes less as the minor axis C Cʹ, fig. 20, of the earth’s orbit becomes greater.

NOTE 144, p. 75. Fig. 35 represents the position of the apparent orbit of the sun as it is at present, the earth being in E. The sun is nearer to the earth in moving through ♎ P ♈ than in moving through ♈ A ♎, but its motion through ♎ P ♈ is more rapid than its motion through ♈ A ♎; and, as the swiftness of the motion and the quantity of heat received vary in the same proportion, a compensation takes place.

NOTE 145, p. 76. In an ellipsoid of revolution, fig. 1, the polar diameter N S, and every diameter in the equator q E Q e, are permanent axes of rotation, but the rotation would be unstable about any other. Were the earth to begin to rotate about C a, the angular distance from a to the equator at q would no longer be ninety degrees, which would be immediately detected by the change it would occasion in the latitudes.

NOTE 146, pp. 50, 80. Let q ♈ Q, and E ♎ e, fig. 11, be the planes of the equator and ecliptic. The angle e ♈ Q, which separates them, called the obliquity of the ecliptic, varies in consequence of the action of the sun and moon upon the protuberant matter at the earth’s equator. That action brings the point Q towards e, and tends to make the plane q ♈ Q coincide with the ecliptic E ♈ e, which causes the equinoctial points ♈ and ♎ to move slowly backwards on the plane e ♈ E, at the rate of 50ʺ·41 annually. This part of the motion, which depends upon the form of the earth, is called luni-solar precession. Another part, totally independent of the form of the earth, arises from the mutual action of the earth, planets, and sun, which, altering the position of the plane of the ecliptic e ♈ E, causes the equinoctial points ♈ and ♎ to advance at the rate of Oʺ·31 annually; but, as this motion is much less than the former, the equinoctial points recede on the plane of the ecliptic at the rate of 50ʺ·1 annually. This motion is called the precession of the equinoxes.

NOTE 147, p. 81. Let q ♈ Q, e ♈ E, fig. 36, be the planes of the equinoctial or celestial equator and ecliptic, and p, P, their poles. Then suppose p, the pole of the equator, to revolve with a tremulous or wavy motion in the little ellipse p c d b in about 19 years, both motions being very small, while the point a is carried round in the circle a A B in 25,868 years. The tremulous motion may represent the half-yearly variation, the motion in the ellipse gives an idea of the nutation discovered by Bradley, and the motion in the circle a A B arises from the precession of the equinoxes. The greater axis p d of the small ellipse is 18ʺ·5, its minor axis b c is 13ʺ·74. These motions are so small that they have very little effect on the parallelism of the axis of the earth’s rotation during its revolution round the sun, as represented in fig. 20. As the stars are fixed, this real motion in the pole of the earth must cause an apparent change in their places.

NOTE 148, p. 83. By means of a transit instrument, which is a telescope mounted so as to revolve only in the plane of the meridian, the instant of the transit or passage of a celestial body across the meridian can be determined. The transits of the principal stars are used to ascertain the time, or, which is the same thing, the amount of the error of clocks. A system of equidistant wires, as represented in the figure, is placed in the focus of the eye-piece, so that the middle wire is perpendicular and at right angles to the axis of the telescope. It consequently represents a portion of the celestial meridian; and when a star is seen to cross that wire it then crosses the celestial meridian of the place of observation. A clock beating seconds being close at hand, the duty of an observer is to note the exact second and part of a second at which a star crosses each wire successively in consequence of the rotation of the earth. Then the mean of all these observations will give the time at which the star crosses the celestial meridian of the place of observation to the tenth of a second, provided the observations are accurate. Now it happens that the simultaneous impression on the eye and ear is estimated differently by different observers, so that one person will note the transit of a star, for example, as happening the fraction of a second sooner or later than another person; and as that is the case in every observation he makes, it is called his personal equation, that is to say, it is a correction that must be applied to all the observations of the individual, and a curious instance of individuality it is. For instance, M. Otto Struve notes every observation Oʺ·11 too soon, M. Peters Oʺ·13 too late; M. Struve noted every observation one second later than M. Bessel, and M. Argelander estimated the transit of a star 1ʺ·2 later than M. Bessel. All these gentlemen were or are first-rate observers; and when the personal equation is known it is easy to correct the observations. However, to avoid that inconvenience Mr. Bond has introduced a method in the Observatory at Cambridge in the United States in which touch is combined with sight instead of hearing, which is now used also at Greenwich. The observer at the moment of the observation presses his fingers on a machine which by means of a galvanic battery conveys the impression to where time is measured and marked, so that the observation is at once recorded and the personal equation avoided.

NOTE 149, p. 84. Let N be the pole, fig. 11, e E the ecliptic, and Q q the equator. Then, N n m S being a meridian, and at right angles to the equator, the arc ♈ m is less than the arc ♈ n.

NOTE 150, p. 85. Heliacal rising of Sirius. When the star appears in the morning, in the horizon, a little before the rising of the sun.

NOTE 151, p. 87. Let P ♈ A ♎, fig. 35, be the apparent orbit or path of the sun, the earth being in E. Its major axis, A P, is at present situate as in the figure, where the solar perigee P is between the solstice of winter and the equinox of spring. So that the time of the sun’s passage through the arc ♈ A ♎ is greater than the time he takes to go through the arc ♎ P ♈. The major axis A P coincided with ♎ ♈, the line of the equinoxes, 4000 years before the Christian era; at that time P was in the point ♈. In 6468 of the Christian era the perigee P will coincide with ♎. In 1234 A.D. the major axis was perpendicular to ♈ ♎, and then P was in the winter solstice.

NOTE 152, p. 88. At the solstices, &c. Since the declination of a celestial object is its angular distance from the equinoctial, the declination of the sun at the solstice is equal to the arc Q e, fig. 11, which measures the obliquity of the ecliptic, or angular distance of the plane ♈ e ♎ from the plane ♈ Q ♎.

NOTE 153, p. 88. Zenith distance is the angular distance of a celestial object from the point immediately over the head of an observer.

NOTE 154, p. 89. Reduced to the level of the sea. The force of gravitation decreases as the square of the height above the surface of the earth increases, so that a pendulum vibrates slower on high ground; and, in order to have a standard independent of local circumstances, it is necessary to reduce it to the length that would exactly make 86,400 vibrations in a mean solar day at the level of the sea.

NOTE 155, p. 90. A quadrant of the meridian is a fourth part of a meridian, or an arc of a meridian containing 90°, as N Q, fig. 11.

NOTE 156, p. 93. Moon’s southing. The time when the moon is on the meridian of any place, which happens about forty-eight minutes later every day.

NOTE 157, p. 96. The angular velocity of the earth’s rotation is at the rate of 180° in twelve hours, which is the time included between the passages of the moon at the upper and under meridian.

NOTE 158, p. 96. If S be the earth, fig. 14, d the sun, and C Q O D the orbit of the moon, then C and O are the syzygies. When the moon is new, she is at C, and when full she is at O; and, as both sun and moon are then on the same meridian, it occasions the spring-tides, it being high water at places under C and O, while it is low water at those under Q and D. The neap-tides happen when the moon is in quadrature at Q or D, for then she is distant from the sun by the angle d S Q, or d S D, each of which is 90°.

NOTE 159, p. 97. Declination. If the earth be in C, fig. 11, and if q ♈ Q be the equinoctial, and N m S a meridian, then m C n is the declination of a body at n. Therefore the cosine of that angle is the cosine of the declination.

NOTE 160, pp. 99, 131. Fig 37 shows the propagation of waves from two points C and Cʹ, where stones are supposed to have fallen. Those points in which the waves cross each other are the places where they counteract each other’s effects, so that the water is smooth there, while it is agitated in the intermediate spaces.

NOTE 161, p. 100. The centrifugal force may, &c. The centrifugal force acts in a direction at right angles to N S, the axis of rotation, fig. 30. Its effects are equivalent to two forces, one of which is in the direction b m perpendicular to the surface Q m n of the earth, and diminishes the force of gravity at m. The other acts in the direction of the tangent m T, which makes the fluid particles tend towards the equator.

NOTE 162, p. 106. Analytical formula or expression. A combination of symbols or signs expressing or representing a series of calculation, and including every particular case that can arise from a general law.

NOTE 163, p. 106. Fig. 38 is a perfect octahedron. Sometimes its angles, A, X, a, a, &c., are truncated, or cut off. Sometimes a slice is cut off its edges A a, X a, a a, &c. Occasionally both these modifications take place.

NOTE 164, p. 107. Prismatic crystals of sulphate of nickel are somewhat like fig. 62, only that they are thin, like a hair.

NOTE 165, p. 108. Zinc, a metal either found as an ore or mixed with other metals. It is used in making brass.

NOTE 166, p. 108. A cube is a solid contained by six plane square surfaces, as fig. 39.

NOTE 167, p. 108. A tetrahedron is a solid contained by four triangular surfaces, as fig. 40: of this solid there are many varieties.

NOTE 168, p. 108. There are many varieties of the octahedron. In that mentioned in the text, the base a a a a, fig. 38, is a square, but the base may be a rhomb; this solid may also be elongated in the direction of its axis A X, or it may be depressed.

NOTE 169, pp. 109, 192, 273. A rhombohedron is a solid contained by six plane surfaces, as in fig. 63, the opposite planes being equal and similar rhombs parallel to one another; but all the planes are not necessarily equal or similar, nor are its angles right angles. In carbonate of lime the angle C A B is 105°·55, and the angle B or C is 75°·05.

NOTE 170, p. 109. Sublimation. Bodies raised into vapour which is again condensed into a solid state.

NOTE 171, p. 112. Platinum. The heaviest of metals; its colour is between that of silver and lead.

NOTE 172, p. 113. The surface of a column of water, or spirit of wine, in a capillary tube, is hollow; and that of a column of quicksilver is convex, or rounded, as in fig. 41.

NOTE 173, p. 113. Inverse ratio, &c. The elevation of the liquid is greater in proportion as the internal diameter of the tube is less.

NOTE 174, p. 114. In fig. 41 the line c d shows the direction of the resulting force in the two cases.

NOTE 175, p. 115. When two plates of glass are brought near to one another in water, the liquid rises between them; and, if the plates touch each other at one of their upright edges, the outline of the water will become an hyperbola.

NOTE 176, p. 115. Let A Aʹ, fig. 42, be two plates, both of which are wet, and B Bʹ two that are dry. When partly immersed in a liquid, its surface will be curved close to them, but will be of its usual level for the rest of the distance. At such a distance they will neither attract nor repel one another. But, as soon as they are brought near enough to have the whole of the liquid surface between them curved, as in a aʹ, b bʹ, they will rush together. If one be wet and another dry, as C Cʹ, they will repel one another at a certain distance; but, as soon as they are brought very near, they will rush together, as in the former cases.

NOTE 177, p. 123. In a paper on the atmospheric changes that produce rain and wind, by Thomas Hopkins, Esq., in the Geographical Journal, it is shown that, when vapour is condensed and falls in rain, a partial vacuum is formed, and that heavier air presses in as a current of wind. Thus the vacuum arising from the great precipitation at the tropics causes the polar winds to descend from the upper regions of the atmosphere and blow along the surface to the equator as trade winds to supply the place of the hot currents that are continually raising them into the higher regions. This circumstance removes the only difficulty in Lieutenant Maury’s theory of the winds.

NOTE 178, p. 134. Latent or absorbed heat. There is a certain quantity of heat in all bodies, which cannot be detected by the thermometer, but which may become sensible by compression.

NOTE 179, p. 137. Reflected waves. A series of waves of light, sound, or water, diverge in all directions from their origin I, fig. 43, as from a centre. When they meet with an obstacle S S, they strike against it, and are reflected or turned back by it in the same form as if they had proceeded from the centre C, at an equal distance on the other side of the surface S S.

NOTE 180, p. 138. Elliptical shell. If fig. 6 be a section of an elliptical shell, then all sounds coming from the focus S to different points on the surface, as m, are reflected back to F, because the angle T m S is equal to t m F. In a spherical hollow shell, a sound diverging from the centre is reflected back to the centre again.

NOTE 181, p. 142. Fig. 44 represents musical strings in vibration; the straight lines are the strings when at rest. The first figure of the four would give the fundamental note, as, for example, the low C. The second and third figures would give the first and second harmonics; that is, the octave and the 12th above C, n n n being the points at rest; the fourth figure shows the real motion when compounded of all three.

NOTE 182, p. 143. Fig. 45 represents sections of an open and of a shut pipe, and of a pipe open at one end. When sounded, the air spontaneously divides itself into segments. It remains at rest in the divisions or nodes n nʹ, &c., but vibrates between them in the direction of the arrow-heads. The undulations of the whole column of air give the fundamental note, while the vibrations of the divisions give the harmonics.

NOTE 183, p. 144. Fig. 1, plate 1, shows the vibrating surface when the sand divides it into squares, and fig. 2 represents the same when the nodal lines divide it into triangles. The portions marked a a are in different states of vibration from those marked b b.

NOTE 184, p. 145. Plates 1 and 2 contain a few of Chladni’s figures. The white lines are the forms assumed by the sand, from different modes of vibration, corresponding to musical notes of different degrees of pitch. Plate 3 contains six of Chladni’s circular figures.

NOTE 185, p. 145. Mr. Wheatstone’s principle is, that when vibrations producing the forms of figs. 1 and 2, plate 3, are united in the same surface, they make the sand assume the form of fig. 3. In the same manner, the vibrations which would separately cause the sand to take the forms of figs. 4 and 5, would make it assume the form in fig. 6 when united. The figure 9 results from the modes of vibration of 7 and 8 combined. The parts marked a a are in different states of vibration from those marked b b. Figs. 1, 2, and 3, plate 4, represent forms which the sand takes in consequence of simple modes of vibration; 4 and 5 are those arising from two combined modes of vibration; and the last six figures arise from four superimposed simple modes of vibration. These complicated figures are determined by computation independent of experiment.

NOTE 186, p. 146. The long cross-lines of fig. 46 show the two systems of nodal lines given by M. Savart’s laminæ.

NOTE 187, p. 146. The short lines on fig. 46 show the positions of the nodal lines on the other sides of the same laminæ.

NOTE 188, p. 146. Fig. 47 gives the nodal lines on a cylinder, with the paper rings that mark the quiescent points.

NOTE 189, pp. 138, 153, 156. Reflection and Refraction. Let P C p, fig. 48, be perpendicular to a surface of glass or water A B. When a ray of light, passing through the air, falls on this surface in any direction I C, part of it is reflected in the direction C S, and the other part is bent at C, and passes through the glass or water in the direction C R. I C is called the incident ray, and I C P the angle of incidence; C S is the reflected ray, and P C S the angle of reflection; C R is the refracted ray, and p C R the angle of refraction. The plane passing through S C and I C is the plane of reflection, and the plane passing through I C and C R is the plane of refraction. In ordinary cases, C I, C S, C R, are all in the same plane. We see the surface by means of the reflected light, which would otherwise be invisible. Whatever the reflecting surface may be, and however obliquely the light may fall upon it, the angle of reflection is always equal to the angle of incidence. Thus I C, Iʹ C, being rays incident on the surface at C, they will be reflected into C S, C Sʹ, so that the angle S C P will be equal to the angle I C P, and Sʹ C P equal to Iʹ C P. That is by no means the case with the refracted rays. The incident rays I C, Iʹ C, are bent at C towards the perpendicular, in the direction C R, C Rʹ; and the law of refraction is such, that the sine of the angle of incidence has a constant ratio to the sine of the angle of refraction; that is to say, the number expressing the length of I m, the sine of I C P, divided by the number expressing the length of R n, the sine of R C p, is the same for all the rays of light that can fall upon the surface of any one substance, and is called its index of refraction. Though the index of refraction be the same for any one substance, it is not the same for all substances. For water it is 1·336; for crown-glass it is 1·535; for flint-glass, 1·6; for diamond, 2·487; and for chromate of lead it is 3, which substance has a higher refractive power than any other known. Light falling perpendicularly on a surface passes through it without being refracted. If the light be now supposed to pass from a dense into a rare medium, as from glass or water into air, then R C, Rʹ C, become the incident rays; and in this case the refracted rays, C I, C Iʹ, are bent from the perpendicular instead of towards it. When the incidence is very oblique, as r C, the light never passes into the air at all, but it is totally reflected in the direction C rʹ, so that the angle p C r is equal to p C rʹ; that frequently happens at the second surface of glass. When a ray I C falls from air upon a piece of glass A B, it is in general refracted at each surface. At C it is bent towards the perpendicular, and at R from it, and the ray emerges parallel to I C; but, when the ray is very oblique to the second surface, it is totally reflected. An object seen by total reflection is nearly as vivid as when seen by direct vision, because no part of the light is refracted. When light falls upon a plate of crown-glass, at an angle of 4° 32ʹ counted from the surface, the glass reflects 4 times more light than it transmits. At an angle of 7° 1ʹ the reflected light is double of the transmitted; at an angle of 11° 8ʹ the light reflected is equal to that transmitted; at 17° 17ʹ the reflected is equal to 1/2 the transmitted light; at 26° 38ʹ it is equal to 1/4, the variation, according to Arago, being as the square of the cosine.

NOTE 189, p. 154. Atmospheric refraction. Let a b, a b, &c., fig. 49, be strata, or extremely thin layers, of the atmosphere, which increase in density towards m n, the surface of the earth. A ray coming from a star meeting the surface of the atmosphere at S would be refracted at the surface of each layer, and would consequently move in the curved line S v v v A; and as an object is seen in the direction of the ray that meets the eye, the star, which really is in the direction A S, would seem to a person at A to be in s. So that refraction, which always acts in a vertical direction, raises objects above their true place. For that reason, a body at Sʹ, below the horizon H A O, would be raised, and would be seen in sʹ. The sun is frequently visible by refraction after he is set, or before he is risen. There is no refraction in the zenith at Z. It increases all the way to the horizon, where it is greatest, the variation being proportional to the tangent of the angles Z A S, Z A Sʹ, the distances of the bodies S Sʹ from the zenith. The more obliquely the rays fall, the greater the refraction.

NOTE 190, p. 154. Bradley’s method of ascertaining the amount of refraction. Let Z, fig. 50, be the zenith or point immediately above an observer at A; let H O be his horizon, and P the pole of the equinoctial A Q. Hence P A Q is a right angle. A star as near to the pole as s would appear to revolve about it, in consequence of the rotation of the earth. At noon, for example, it would be at s above the pole, and at midnight it would be in sʹ below it. The sum of the true zenith distances, Z A s, Z A sʹ, is equal to twice the angle Z A P. Again, S and Sʹ being the sun at his greatest distances from the equinoctial A Q when in the solstices, the sum of his true zenith distances, Z A S, Z A Sʹ, is equal to twice the angle Z A Q. Consequently, the four true zenith distances, when added together, are equal to twice the right angle Q A P; that is, they are equal to 180°. But the observed or apparent zenith distances are less than the true on account of refraction; therefore the sum of the four apparent zenith distances is less than 180° by the whole amount of the four refractions.

NOTE 191, p. 155. Terrestrial refraction. Let C, fig. 51, be the centre of the earth, A an observer at its surface, A H his horizon, and B some distant point, as the top of a hill. Let the arc B A be the path of a ray coming from B to A; E B, E A, tangents to its extremities; and A G, B F, perpendicular to C B. However high the hill B may be, it is nothing when compared with C A, the radius of the earth; consequently, A B differs so little from A D that the angles A E B and A C B are supplementary to one another; that is, the two taken together are equal to 180°. A C B is called the horizontal angle. Now B A H is the real height of B, and E A H its apparent height; hence refraction raises the object B, by the angle E A B, above its real place. Again, the real depression of A, when viewed from B, is F B A, whereas its apparent depression is F B E, so E B A is due to refraction. The angle F B A is equal to the sum of the angles B A H and A C B; that is, the true elevation is equal to the true depression and the horizontal angle. But the true elevation is equal to the apparent elevation diminished by the refraction; and the true depression is equal to the apparent depression increased by refraction. Hence twice the refraction is equal to the horizontal angle augmented by the difference between the apparent elevation and the apparent depression.

NOTE 192, p. 155. Fig. 52 represents the phenomenon in question. S P is the real ship, with its inverted and direct images seen in the air. Were there no refraction, the rays would come from the ship S P to the eye E in the direction of the straight lines; but, on account of the variable density of the inferior strata of the atmosphere, the rays are bent in the curved lines P c E, P d E, S m E, S n E. Since an object is seen in the direction of the tangent to that point of the ray which meets the eye, the point P of the real ship is seen at p and pʹ, and the point S seems to be in s and sʹ; and, as all the other points are transferred in the same manner, direct and inverted images of the ship are formed in the air above it.

NOTE 193, p. 156. Fig. 53 represents the section of a poker, with the refraction produced by the hot air surrounding it.

NOTE 194, p. 156. The solar spectrum. A ray from the sun at S, fig. 54, admitted into a dark room, through a small round hole H in a window-shutter, proceeds in a straight line to a screen D, on which it forms a bright circular spot of white light, of nearly the same diameter with the hole H. But when the refracting angle B A C of a glass prism is interposed, so that the sunbeam falls on A C the first surface of the prism, and emerges from the second surface A B at equal angles, it causes the rays to deviate from the straight path S D, and bends them to the screen M N, where they form a coloured image V R of the sun, of the same breadth with the diameter of the hole H, but much longer. The space V R consists of seven colours—violet, indigo, blue, green, yellow, orange, and red. The violet and red, being the most and least refrangible rays, are at the extremities, and the green occupy the middle part at G. The angle D g G is called the mean deviation, and the spreading of the coloured rays over the angle V g R the dispersion. The deviation and dispersion vary with the refracting angle B A C of the prism, and with the substance of which it is made.

NOTE 195, pp. 159, 164. Under the same circumstances, and where the refracting angles of the two prisms are equal, the angles D g G and V g R, fig. 54, are greater for flint-glass than for crown-glass. But, as they vary with the angle of the prism, it is only necessary to augment the refracting angle of the crown-glass prism by a certain quantity, to produce nearly the same deviation and dispersion with the flint-glass prism. Hence, when the two prisms are placed with their refracting angles in opposite directions, as in fig. 54, they nearly neutralize each other’s effects, and refract a beam of light without resolving it into its elementary coloured rays. Sir David Brewster has come to the conclusion that there may be refraction without colour by means of two prisms, or two lenses, when properly adjusted, even though they be made of the same kind of glass.

NOTE 196, p. 165. The object glass of the achromatic telescope consists of a convex lens A B, fig. 55, of crown-glass placed on the outside, towards the object, and of a concave-convex lens C D of flint-glass, placed towards the eye. The focal length of a lens is the distance of its centre from the point in which the rays converge, as F, fig. 60. If, then, the lenses A B and C D be so constructed that their focal lengths are in the same proportion as their dispersive powers, they will refract rays of light without colour.

NOTE 197, p. 165. If the mean refracting angle of the prism D g G, fig. 54, were the same for all substances, then the difference D g V - D g R would be the dispersion. But the angle of the prism being the same, all these angles are different in each substance, so that in order to obtain the dispersion of any substance the angle D g V - D g R must be divided by the angle D g G or its excess above unity, to which the mean refraction is always proportional. According to Mr. Fraunhofer the refraction of the extreme violet and red rays in crown-glass is 1·5466 and 1·5258; so D g V - D g R = 1·5466 - 1·5258 = ·0208, and half the sum of the excess of each above unity is = ·5362; consequently

(D g V - D g R)/D g G = ·0208/·5362 = 0·03879; for diamond

(D g V - D g R)/D g G = (2·467 - 2·411)/1·439 = 0·0389;

so that the dispersive power of diamond is a little less than that of crown-glass; hence the splendid refracted colours which distinguish diamond from every other precious stone are not owing to its high dispersive power, but to its great mean refraction.—SIR DAVID BREWSTER.

NOTE 198, p. 168. When a sunbeam, after having passed through a coloured glass V Vʹ, fig. 56, enters a dark room by two small slits O Oʹ in a card, or piece of tin, they produce alternate bright and black bands on a screen S Sʹ at a little distance. When either one or other of the slits O or Oʹ is stopped, the dark bands vanish, and the screen is illuminated by a uniform light, proving that the dark bands are produced by the interference of the two sets of rays. Again, let H m, fig. 57, be a beam of white light passing through a hole at H, made with a fine needle in a piece of lead or a card, and received on a screen S Sʹ. When a hair, or a small slip of card h hʹ, about the 30th of an inch in breadth, is held in the beam, the rays bend round on each side of it, and, arriving at the screen in different states of vibration, interfere and form a series of coloured fringes on each side of a central white band m. When a piece of card is interposed at C, so as to intercept the light which passes on one side of the hair, the coloured fringes vanish. When homogeneous light is used, the fringes are broadest in red, and become narrower for each colour of the spectrum progressively to the violet, which gives the narrowest and most crowded fringes. These very elegant experiments are due to Dr. Thomas Young.

NOTE 199, pp. 171, 200. Fig. 58 shows Newton’s rings, of which there are seven, formed by screwing two lenses of glass together. Provided the incident light be white, they always succeed each other in the following order:—

1st ring, or 1st order of colours: Black, very faint blue, brilliant white, yellow, orange, red.

2nd ring: Dark purple, or rather violet, blue, a very imperfect yellow green, vivid yellow, crimson red.

3rd ring: Purple, blue, rich grass green, fine yellow, pink, crimson.

4th ring: Dull blueish green, pale yellowish pink, red.

5th ring: Pale blueish green, white, pink.

6th ring: Pale blue green, pale pink.

7th ring: Very pale blueish green, very pale pink.

After the seventh order the colours become too faint to be distinguished. The rings decrease in breadth, and the colours become more crowded together, as they recede from the centre. When the light is homogeneous, the rings are broadest in the red, and decrease in breadth with every successive colour of the spectrum to the violet.

NOTE 200, p. 172. The absolute thickness of the film of air between the glasses is found as follows:—Let A F B C, fig. 59, be the section of a lens lying on a plane surface or plate of glass P Pʹ, seen edgewise, and let E C be the diameter of the sphere of which the lens is a segment. If A B be the diameter of any one of Newton’s rings, and B D parallel to C E, then B D or C F is the thickness of the air producing it. E C is a known quantity; and when A B, the diameter, is measured with compasses, B D or F C can be computed. Newton found that the length of B D, corresponding to the darkest part of the first ring, is the 98,000th part of an inch when the rays fall perpendicularly on the lens, and from this he deduced the thickness corresponding to each colour in the system of rings. By passing each colour of the solar spectrum in succession over the lenses, Newton also determined the thickness of the film of air corresponding to each colour, from the breadth of the rings, which are always of the same colour with the homogeneous light.

NOTE 201, p. 174. The focal length or distance of a lens is the distance from its centre to the point F, fig. 60, in which the refracted rays meet. Let L Lʹ be a lens of very short focal distance fixed in the window-shutter of a dark room. A sunbeam S L Lʹ passing through the lens will be brought to a focus in F, whence it will diverge in lines F C, F D, and will form a circular image of light on the opposite wall. Suppose a sheet of lead, having a small pin-hole pierced through it, to be placed in this beam; when the pin-hole is viewed from behind with a lens at E, it is surrounded with a series of coloured rings, which vary in appearance with the relative positions of the pin-hole and eye with regard to the point F. When the hole is the 30th of an inch in diameter and at the distance of 6-1/2 feet from F, when viewed at the distance of 24 inches, there are seven rings of the following colours:—

1st order: White, pale yellow, yellow, orange, dull red.

2nd order: Violet, blue, whitish, greenish yellow, fine yellow, orange red.

3rd order: Purple, indigo blue, greenish blue, brilliant green, yellow green, red.

4th order: Blueish green, blueish white, red.

5th order: Dull green, faint blueish white, faint red.

6th order: Very faint green, very faint red.

7th order: A trace of green and red.

NOTE 202, p. 175. Let L Lʹ, fig. 61, be the section of a lens placed in a window-shutter, through which a very small beam of light S L Lʹ passes into a dark room, and comes to a focus in F. If the edge of a knife K N be held in the beam, the rays bend away from it in hyperbolic curves K r, K rʹ, &c., instead of coming directly to the screen in the straight line K E, which is the boundary of the shadow. As these bending rays arrive at the screen in different states of undulation, they interfere, and form a series of coloured fringes, r rʹ, &c., along the edge of the shadow K E S N of the knife. The fringes vary in breadth with the relative distances of the knife-edge and screen from F.

NOTE 203, p. 177. Fig. 43 represents the phenomena in question, where S S is the surface, and I the centre of incident waves. The reflected waves are the dark lines returning towards I, which are the same as if they had originated in C on the other side of the surface.

NOTE 204, p. 180. Fig. 62 represents a prismatic crystal of tourmaline, whose axis is A X. The slices that are used for polarising light are cut parallel to A X.

NOTE 205, p. 181. Double refraction. If a pencil of light R r, fig. 63, falls upon a rhombohedron of Iceland spar A B X C, it is separated into two equal pencils of light at r, which are refracted in the directions r O, r E: when these arrive at O and E they are again refracted, and pass into the air in the directions O o, E o, parallel to one another and to the incident ray R r. The ray r O is refracted according to the ordinary law, which is, that the sines of the angles of incidence and refraction bear a constant ratio to one another (see Note 184), and the rays R r, r O, O o, are all in the same plane. The pencil r E, on the contrary, is bent aside out of that plane, and its refraction does not follow the constant ratio of the sines; r E is therefore called the extraordinary ray, and r O the ordinary ray. In consequence of this bisection of the light, a spot of ink at O is seen double at O and E, when viewed from r I; and when the crystal is turned round, the image E revolves about O, which remains stationary.

NOTE 206, p. 182. Both of the parallel rays O o and E o, fig. 63, are polarised on leaving the doubly refracting crystal, and in both the particles of light make their vibrations at right angles to the lines O o, E o. In the one, however, these vibrations lie, for example, in the plane of the horizon, while the vibrations of the other lie in the vertical plane perpendicular to the horizon.

NOTE 207, p. 183. If light be made to fall in various directions on the natural faces of a crystal of Iceland spar, or on faces cut and polished artificially, one direction A X, fig. 63, will be found, along which the light passes without being separated into two pencils. A X is the optic axis. In some substances there are two optic axes forming an angle with each other. The optic axis is not a fixed line, it only has a fixed direction; for if a crystal of Iceland spar be divided into smaller crystals, each will have its optic axis; but if all these pieces be put together again, their optic axes will be parallel to A X. Every line, therefore, within the crystal parallel to A X is an optic axis; but as these lines have all the same direction, the crystal is still said to have but one optic axis.

NOTE 208, p. 184. If I C, fig. 48, be the incident and C S the reflected rays, then the particles of polarised light make their vibrations at right angles to the plane of the paper.

NOTE 209, p. 184. Let A A, fig. 48, be the surface of the reflector, I C the incident and C S the reflected rays; then, when the angle S C B is 57°, and consequently the angle P C S equal to 33°, the black spot will be seen at C by an eye at S.

NOTE 210, p. 185. Let A B, fig. 48, be a reflecting surface, I C the incident and C S the reflected rays; then, if the surface be plate-glass, the angle S C B must be 57°, in order that C S may be polarised. If the surface be crown-glass or water, the angle S C B must be 56° 55ʹ for the first, and 53° 11ʹ for the second, in order to give a polarised ray.

NOTE 211, p. 186. A polarising apparatus is represented in fig. 64, where R r is a ray of light falling on a piece of glass r at an angle of 57°: the reflected ray r s is then polarised, and may be viewed through a piece of tourmaline in s, or it may be received on another plate of glass, B, whose surface is at right angles to the surface of r. The ray r s is again reflected in s, and comes to the eye in the direction s E. The plate of mica, M I, or of any substance that is to be examined, is placed between the points r and s.

NOTE 212, p. 187. In order to see these figures, the polarised ray r s, fig. 64, must pass through the optic axis of the crystal, which must be held as near as possible to s on one side, and the eye placed as near as possible to s on the other. Fig. 65 shows the image formed by a crystal of Iceland spar which has one optic axis. The colours in the rings are exactly the same with those of Newton’s rings given in Note 199, and the cross is black. If the spar be turned round its axis, the rings suffer no change; but if the tourmaline through which it is viewed, or the plate of glass, B, be turned round, this figure will be seen at the angles 0°, 90°, 180°, and 270° of its revolution. But in the intermediate points, that is, at the angles 45°, 135°, 225°, and 315°, another system will appear, such as represented in fig. 66, where all the colours of the rings are complementary to those of fig. 65, and the cross is white. The two systems of rings, if superposed, would produce white light.

NOTE 213, p. 188. Saltpetre, or nitre, crystallises in six-sided prisms having two optic axes inclined to one another at an angle of 5°. A slice of this substance about the 6th or 8th of an inch thick, cut perpendicularly to the axis of the prism, and placed very near to s, fig. 64, so that the polarised ray r s may pass through it, exhibits the system of rings represented in fig. 67, where the points C and C mark the position of the optic axes. When the plate B, fig. 64, is turned round, the image changes successively to those given in figs. 68, 69, and 70. The colours of the rings are the same with those of thin plates, but they vary with the thickness of the nitre. Their breadth enlarges or diminishes also with the colour, when homogeneous light is used.

NOTE 214, p. 189. Fig. 71 represents the appearance produced by placing a slice of rock crystal in the polarised ray r s, fig. 64. The uniform colour in the interior of the image depends upon the thickness of the slice; but whatever that colour may be, it will alternately attain a maximum brightness and vanish with the revolution of the glass B. It may be observed, that the two kinds of quartz, or rock crystal, mentioned in the text, are combined in the amethyst, which consists of alternate layers of right-handed and left-handed quartz, whose planes are parallel to the axis of the crystal.

NOTE 215, p. 193. Suppose the major axis A P of an ellipse, fig. 18, to be invariable, but the excentricity C S continually to diminish, the ellipse would bulge more and more; and when C S vanished, it would become a circle whose diameter is A P. Again, if the excentricity were continually to increase, the ellipse would be more and more flattened till C S was equal to C P, when it would become a straight line A P. The circle and straight line are therefore the limits of the ellipse.

NOTE 216, p. 194. The coloured rings are produced by the interference of two polarised rays in different states of undulation, on the principle explained for common light.

NOTE 217, p. 225. According to Mr. Joule, that heat is produced by motion, and that it is equivalent to it, Mr. Thompson of Glasgow investigates from whence the sun derives his heat, since he shows that neither combustion nor his primitive heat could have supplied the waste during 6000 years. He concludes that the solar heat is maintained by myriads of minute bodies that are revolving at the edge of his dense nebulosity or atmosphere, some of which are often seen by us as falling stars. These, vaporized by his heat, and drawn by his attraction, meet with intense resistance on entering the solar atmosphere as a shower of meteoric rain; through it they descend in spiral lines to the sun’s surface, producing enormous heat by friction during their fall, and serving for fuel on their arrival.

NOTE 218, p. 252. The class Cryptogamia contains the ferns, mosses, funguses, and sea-weeds; in all of which the parts of the flowers are in general too minute to be evident.

NOTE 219, p. 254. Zoophytes are the animals which form madrepores, corals, sponges, &c.

NOTE 220, p. 254. The Saurian tribe are creatures of the crocodile and lizard kind.

NOTE 221, p. 266. If heat from a non-luminous source be polarised by reflection or refraction at r, fig. 64, the polarised ray r s will be stopped or transmitted by a plate of mica M I, under the same circumstances that it would stop or transmit light; and if heat were visible, images analogous to those of figs. 65, 67, &c., would be seen at the point s.

NOTE 222, pp. 275, 329, 357. The foot-pound, or unit of mechanical force established by Mr. Joule, is the force that would raise one pound weight of matter to the height of one foot; or it is the impetus or force generated by a body of one pound weight falling by its gravitation through the height of one foot.

Impetus, vis viva, or living force, is equal to the mass of a body multiplied by the square of the velocity with which it is moving, and is the true measure of work or labour. For if a weight be raised 10 feet, it will require four times the labour to raise an equal weight 40 feet. If both these weights be allowed to descend freely by their gravitation, at the end of their fall their velocities will be as 1 to 2; that is, as the square roots of their heights; but the effect produced will be as their masses multiplied by 1 and 4; but these are the squares of their velocities: hence the impetus or vis viva is as the mass into the square of the velocity.

Thus impetus is the true measure of the labour employed to raise the weights, and of the effect of their descent, and is entirely independent of time. Now heat is proportional to impetus, and impetus is the true measure of labour. In percussion the heat evolved is in proportion to the force of the impetus, and is thus measured by labour.

Travail is a word used in mechanics, to express that work done is equal to the labouring force employed. The work done may be resistance overcome or any other effect produced, while the labouring force may be a horse, a steam-engine, wind, falling water, &c.

NOTE 223, p. 313. When a stream of positive electricity descends from P to n, fig. 72, in a vertical wire at right angles to the plane of the horizontal circle A B, the negative electricity ascends from n to P, and the force exerted by the current makes the north pole of a magnet revolve about the wire in the direction of the arrow-heads in the circumference, and it makes the south pole revolve in the opposite direction. When the current of positive electricity flows upwards from n to P, these effects are reversed.

NOTE 224, p. 314. Fig. 73 represents a helix or coil of copper wire, terminated by two cups containing a little quicksilver. When the positive wire of a Voltaic battery is immersed in the cup p, and the negative wire in the cup n, the circuit is completed. The quicksilver ensures the connection between the battery and the helix, by conveying the electricity from the one to the other. While the electricity flows through the helix, the magnet S N remains suspended within it, but falls down the moment it ceases. The magnet always turns its south pole S towards P, the positive wire of the battery, and its north pole towards the negative wire.

NOTE 225, p. 316. A copper wire coiled in the form represented in fig. 73 was the first and most simple form of the electro-dynamic cylinder. When its extremities P and n are connected with the positive and negative poles of a Voltaic battery, it becomes a perfect magnet during the time that a current of electricity is flowing through it, P and n being its north and south poles.

NOTE 226, p. 344. It is to Halley we are indebted for the first declination chart and the theory of 4 poles of maximum magnetic intensity, since confirmed by observation, as well as the earliest authentic values of the magnetic elements in London and St. Helena, where he went on purpose to make observations on terrestrial magnetism. Since that time M. Gauss has formed charts of the magnetic lines, and published a theory which very nearly represents the magnetic state of the globe. The mass of observations daily making by our cruizers and our Government surveys in every part of the earth is enormous.

NOTE 227, p. 360. In fig. 74 the hyperbola H P Y, the parabola p P R, and the ellipse A E P L, have the focal distance S P, and coincide through a small space on each side of the perihelion P; and, as a comet is only visible when near P, it is difficult to ascertain which of the three curves it moves in.

NOTE 228, p. 363. In fig. 75, E A represents the orbit of Halley’s comet, E T the orbit of the earth, and S the sun. The proportions are very nearly exact.

NOTE 229, p. 382. Fig. 74 represents the curves in question. It is evident that, for the same focal distance S P, there can be but one circle and one parabola p P R, but that there may be an infinity of ellipses between the circle and the parabola, and an infinity of hyperbolas H P Y exterior to the parabola p P R.

NOTE 230, p. 387. Let A B, fig. 26, be the diameter of the earth’s orbit, and suppose a star to be seen in the direction A Sʹ from the earth when at A. Six months afterwards, the earth, having moved through half of its orbit, would arrive at B, and then the star would appear in the direction B Sʹ, if the diameter A B, as seen from Sʹ, had any sensible magnitude. But A B, which is 190,000,000 of miles, does not appear to be greater than the thickness of a spider’s thread, as seen from 61 Cygni, supposed to be the nearest of the fixed stars.

NOTE 231, p. 389. Stars whose parallax and proper motions are known.

Name of Star. Proper Motion. Parallax. Observers and Computers.

α Centauri 3ʺ·764 0ʺ·92 Maclear. „ .. 1ʺ Henderson. 61 Cygni 5ʺ·123 0ʺ·374 Bessel. α Lyræ 0ʺ·364 0ʺ·207 Peters. Sirius 1ʺ·234 0ʺ·230 Henderson. Arcturus 2ʺ·269 0ʺ·127 Peters. Pole Star 0ʺ·035 0ʺ·106 Peters. Capella .. 0ʺ·046 Peters. La Chevre 0ʺ·461 0ʺ·046 Peters. ι Great Bear 0ʺ·746 0ʺ·133 Peters.

The space run through in one second by these stars is therefore—

α Centauri 5 leagues Henderson and Maclear. 61 Cygni 10 leagues Bessel. α Lyræ 2 leagues Struve and Peters. Sirius 6 leagues Henderson and Maclear. Arcturus 22 leagues Peters. Pole Star ½ league Lindenau and Struve. La Chevre 12 leagues Peters. ι Great Bear 7 leagues Peters.

There are three great discrepancies in the parallax of the star Argelander or 1830 Groombridge. M. Otto Struve makes it 0ʺ·034, which gives it a velocity of 251 leagues per second, while M. Faye finds the parallax to be between 0ʺ·03 and 0ʺ·01, which makes its velocity from 30 to 85 leagues per second.

These are all minimum velocities, because we can only determine on the celestial vault a projection perhaps much foreshortened of the real motions of the stars.

NOTE 232, pp. 398, 401. The following are the binary systems whose orbits have been accurately determined:—

Name of Star. Period in Perihelion By whom Computed. Years. Passage.

ζ Herculis 30·216 1831·41 Madler.

η Coronæ 42·500 1807·21 Madler.

ζ Cancri 58·910 1853·37 Madler.

ξ Ursæ Majoris 58·262 1817·25 Savary.

ω Leonis 82·533 1849·76 Villarceaux.

ρ Ophiuchi 73·862 1806·83 Encke.

3062 in Dorpat 94·765 1837·41 Madler. Catalogue

ξ Bootis 117·140 1779·88 Sir J. Herschel.

δ Cygni 178·700 1862·87 Hind.

γ Virginis 182·120 1836·43 Sir J. Herschel.

Castor 252·660 1855·83 Sir J. Herschel.

ς Coronæ 736·880 1826·48 Hind.

γ Virginis 632·270 1699 Hind.

α Centauri 77·000 1851·50 Jacob.

Orbit of γ Virginis.

Perihelion passage 1836·40

Inclination 27° 36ʹ

Position of ascending Node 19 7

Angle between line of Nodes and 295° 13 Apsides

Excentricity 0·8794

Period in years 184·53

Orbit of ζ Herculis.

Perihelion passage 1830·56 Inclination 140° 39ʹ Position of ascending Node 217° 14ʹ Angle between line of Nodes and Apsides 266·53 Eccentricity 0·4381 Period in years 37·21

Computed by J. Fletcher, Esq., 1853.

NOTE 233, p. 403. The mass is found in the manner explained in the text; but the method of computing the distance of the star may be made more clear by what follows. Though the orbit of the satellite star is really and apparently elliptical, let it be represented by C D O, fig. 14, for the sake of illustration, the earth being in d. It is clear that, when the star moves through C D O, its light will take longer in coming to the earth from O than from C, by the whole time it employs in passing through O C, the breadth of its orbit. When that time is known by observation, reduced to seconds, and multiplied by 190,000, which is the number of miles light darts through in a second, the product will be the breadth of the orbit in miles. From this the dimensions of the ellipse will be obtained by the aid of observation; the length and position of any diameter as S p may be found; and as all the angles of the triangle d S p can be determined by observation, the distance of the star from the earth may be computed.

NOTE 234, p. 405. The mean results of MM. Argelander, Otto Struve, and Luhndahl for stars in the northern hemisphere and the epoch 1790, places the point to which the sun is tending in 259° 5ʹ of right ascension and 55° 23ʹ of north polar distance. Mr. Gallaway computed from stars in the southern hemisphere, at the same epoch, the point to have been in 260° 1ʹ right ascension and 55° 37ʹ north polar distance, results nearly identical, though from very different data.

NOTE 235, p. 414. One of the globular clusters mentioned in the text is represented in fig. 1, plate 8. The stars are gradually condensed towards the centre, where they run together in a blaze. The more condensed part is projected on a ground of irregularly scattered stars, which fills the whole field of the telescope. There are few stars near this cluster.

NOTE 236, p. 420. Plate 8 shows five nebulæ as seen in Sir John Herschel’s 20-feet telescope.

1. An enormous ring seen obliquely with a dark centre and a small star at each extremity.

2. The ring in the constellation Lyra.

3. The dumb-bell nebula in Vulpicula.

4. The spiral nebula or brother system in the 20-feet telescope.

5. A spindle-shaped nebula.

Plate 9 represents some of the same objects as seen by Lord Rosse.

1. Nebula in the girdle of Andromeda.

2. The circular nebula of Lyra.

3. The dumb-bell nebula in Vulpicula.

The spiral nebulæ of 51 Messier, as seen by Lord Rosse, 1 in plate 10, represents fig. 4 of plate 8; and fig. 2 in the same plate is part of the great nebula in Orion, for the whole has never been seen, on account of extreme remoteness.

NOTE 237, pp. 32, 427. The motion of the earth is visibly proved by M. Foucault’s experiments. If a pendulum be left to oscillate quite freely, the forces producing the oscillations being in the vertical plane, there is no cause that can produce an absolute change in its position with regard to space; but the motion of the earth changes the position of a spectator with respect to the vertical plane, and he refers his own motion to it, which seems gradually to turn away from its position, precisely as a person in a boat refers his own motion to that of the land, and thus the motion of the earth is truly and visibly proved.

INDEX.

Aberdeen, high water at, 94.

Absorption, influence of, on temperature, 239; difference of sea and land in power of, 242; gradually decreasing, in transmission of radiant heat, 259; of radiant heat, varying with substances, 268; a transfer of force, 275, 276.

Acceleration of the moon’s mean motion, 37, 38.

Adams, Mr., perturbation in Uranus’s motion computed by, 22; discovery of Neptune, 62.

Aërolites, theory of, 420, 423.

Africa, tidal wave passing, 94; mean annual equatorial temperature in, 245; indigenous productions of, 249, 250.

Air, comparative velocity of light in water and, 202. See Atmosphere.

Airy, Professor, periodic inequality in the solar system worked out by, 26; phenomenon observed by, during an eclipse, 41; mass of Jupiter ascertained by, 55; experiments ascertaining its density, 57; astronomical tables improved by, 63; discoveries in polarization of light, 192, 193.

Aldebaran, an optically double star, 401.

Aleutian Islands, the, vegetation of, 252.

Alexandria, arc of the meridian measured between Syene and, 49.

Algæ, districts of distinct species of, 252; banks of, in the Atlantic, 253.

Algol, fluctuations in lustre of, 390, 391.

Alhazen, effects of refraction observed by, 155.

Alkalies, resolved into metallic oxides, 307.

Alpha Antaris, “Coal Sacks” between α Centauri and, 386.

Alpha Aquilæ, an optically double star, 401.

—— Centauri, the parallax of, 54; its rank, 384; the Milky Way near, 386; parallax, as determined by Henderson and Maclear, 387; distance from the sun, 388; orbit and mass of, 399, 400; colour, 401; amount of light emitted by, 404; rate of its proper motion, 404, 405; globular nebulous cluster, 414.

—— Crucis, zone of stars passing through, 385; zone between η Argûs and, 390; nebulous cluster round, 415.

—— Lyræ, the polar star of the northern hemisphere, 82; parallax of, 388; distance from the sun, 389; an optically double star, 400; amount of light emitted by, 404.

—— Orionis, a variable star, 393, 394.

Alum, experiments on the crystallization of, 106, 107; heat transmitted through, 261, 262.

Amazons, the river of, distance from its mouth where tides are perceptible, 98; area occupied by forests on, 243.

America, course of the tidal wave along its coasts, 93, 94; mean annual equatorial temperature in, 245; separation of isothermal lines in high latitudes, ib.; number of known species of plants indigenous in, 249; number of species of trees, 252; shooting stars over the continent of, 421.

——, South, area of country raised by an earthquake in, 234.

Ampère, M., his discovery in electricity, 316; theory of magnetism, 317, 318; experiment testing his theory, 319, 320.

Analysis, boundless dominion of, 427, 428.

Andes, the, proportion of, to the earth’s mass, 6; increasing rarity of the air experienced in ascending, 118.

Andromeda, nebula in, 413; nebulous region of, 417.

Angström, the electric spark defined by, 303.

Animals, specific diversity of, laws regulating their distribution, 254, 255.

Annual equation, the, of the moon, 35, 36.

—— variations in mean values of the magnetic elements, 343.

Annular nebulæ, 409; in the northern hemisphere, 410, 411.

Antarctic Ocean, tidal wave rising in 93; period of its passage to the Thames, 94; depth of the stratum of constant temperature in, 101; depression of the barometer observed in, 120.

Antilles Islands, hurricanes beginning at, 126.

Antinori, Cav., experiments of, in electricity, 333.

Antinous, comet observed in the constellation of, 372; the Milky Way between Orion and, 386.

Antithesis, the general character of magnetism, 339.

Aphelion of a planet’s path defined, 16.

Apogee, solar, its coincidence with the solstices, 86, 87.

April, 1833, disappearance of Saturn’s rings, 67; apparent and mean time coinciding in, 84.

Apsides of an axis defined, 9; direct, variable motion of, 14; cause of their advance, or recession, 16.

Apures, the mission of the, Humboldt’s observations on sound at, 135.

Aqueous vapour, proportion of, in the atmosphere, 117.

Ara, nebula in, 414.

Arabian Gulf, the, monsoons blowing over, 124.

Arabs, the, their observations on planetary irregularities, 26; lunar eclipses observed by, 38; their division of time, 85; the pendulum used as a measure of time by, 90.

Arago, François, experiment by, in proof of the undulatory theory of light, 200; decisive experiment suggested by, 202; observations in photography, 213; observations on the moon’s atmosphere, 226; increase of temperature below the earth’s surface calculated by, 230; slow communication of temperature from the earth, observed, 244; source of magnetism discovered, 330; theory of his magnetic experiments, 332; divergent flames of a comet described by, 364; his treatise on comets, 368; nature of comet’s light determined by, 380, 381; numbers of comets computed, 381, 382; remark of, on fixed stars, 405.

Arc, the Voltaic, 303-305.

Arcet, M. d’, vibration of fibres of the retina according to, 178.

Archer, Scott, stimulus given to photography by, 207.

Arcs of the meridian, mode of measuring, 47.

Arctic Sea, depth of the zone of constant temperature, 101.

—— regions, vegetation found in, 249.

Arcturus, comet bearing comparison with, 379; rank of, 384.

Areas, described by the radii vectores of planets, a test of disturbing forces, 10; unequable description of, 15.

Argelander, M., period of a comet calculated by, 370; his mode of estimating distance of fixed stars, 389; periods of fluctuation in stars computed by, 390, 391; sun’s motion proved, 405.

Argentine preparations in photography, chemical energy varying with, 207, 208; changes effected by washing with alkalies, 210, 211.

Argo, variable star in, 393.

Aries, season of the sun’s entrance into, in Hipparchus’ age, 80.

Arseniate of soda, its crystals, 109.

Artesian wells, mode of sinking, origin of the name, 230.

Asia, indigenous productions of, 249.

Assyrians, the, division of time by, 85.

Astronomers, fruits of their labours, 3; question still to be resolved by, 24; terrestrial orbit differently measured by, 36.

Astronomical distances, method of measuring, 43; tables, method of forming, 58-64.

Astronomy, its rank in the physical sciences, an important office of, 1; studies necessary to the study of, 2; the key to divers problems in physical science, 3; the two greatest discoveries in, 23; the three departments of, 58; standards for measurement afforded by, 83; application of, to chronology, 87-89; furnishing standards of weights and measures, 89, 90; atmospheric effects connecting the laws of molecular attraction with, 102; progress lately made by, 419, 420.

Atalanta, diameter of, 56.

Atlantic Ocean, direction of tidal waves in, 93; conditions modifying tides, 94; depth of, 96; currents, 100; origin of hurricanes, 126; superficial temperature of, 244; distinct vegetation of the polar basin, 252; beds of algæ in, 253; meteors falling in, 421.

—— telegraph, 325, 326; terrestrial magnetism disturbing, 346.

Atmosphere of nebulous stars, 411, 412.

—— of planets, 226, 227.

—— of the sun, its constitution, 42; indications of an absorptive surrounding the luminous, 213; the true, 224.

—— terrestrial, solar rays bent by, in lunar eclipses, 40; influence of, in solar eclipses, 41; its analysis, pressure on the surface of the globe, 117; form of, gradual decrease in density of its strata, 117, 118; influence of temperature on its density, 119; mean pressure of, variable, 120; the medium conveying sound, 129; sympathetic vibrations transmitted by, 147, 148; its action on light, falsifying vision, 153; phenomena produced by accidental changes in its strata, 155-156; effects of increased density in the stratum in the horizon, 157, 158; lunar heat absorbed by, 227; cause of the cooler air in higher regions of, 240, 241; sun’s heat modified by, 244; action of electricity in, 284; transmission of electricity by induction, 286; periodical variations of electricity in, 291; accidental developments of electricity, 291, 292; cause of variations in its magnetism, 344, 345; nebulous bodies made visible by, 421-423.

Atmospheric air, extreme elasticity of, 105.

—— pressure, effect of, on electricity, 288.

Atomic constitution determining crystalline forms, 109.

Atoms, qualities of, determining the nature of substances, 110; differences in weight of, 111.

Attraction, modes of, in spheres, in the celestial bodies, 4; determining the forms of planets, 6; determining the motions of planets, 7; solar, compelling the elliptical revolutions of planets, 8; mutual, of planets, complicating their motions, 10; interference of, disturbing the motions of heavenly bodies, 11; disturbances from the operation of reciprocal, 13; disturbances from inequality of, 14; of satellites to primaries, little disturbed, 26; disturbing force of, in spheroids, 27; its effects on Jupiter’s satellites, 28; sun’s, of the moon, 34; principle modifying the earth’s, 37; local, affecting the plumb-line, 48; comparative force of the sun’s, 57; of an external body affecting a spheroid, 79; producing tides, 91, 92; of particles of matter, 103; capillary, 113; producing annual atmospheric undulations, 121; the lunar atmosphere affected by, 226; expansive force of heat overcoming, 271; of electricities, 283; destruction of, producing electricity, 284; laws of electrical, 286-288; modes of, in static and in voltaic electricity, 317; action of planetary, on comet’s orbits, 361-363; range of solar, 365.

Aurora, the, affecting the compass, 312.

Australia, evidence of deserts in the interior of, 124; species of plants common to Europe and, 251.

Auvergne, temperature of hot springs in, 231.

Axes, change in form of masses revolving round, 6.

——, major, length of, in orbits, invariable, 20; of the orbits of Jupiter’s satellites, cause of the direct motion observed in, 28; position of, in the solar system, 65; a nutation in planetary, 66; of the moon, 68, 69; mechanical law affecting, 76.

——, optic, of crystals, 183.

Axis, greater, of the earth’s orbit, period of its revolution, 38; period of the earth’s revolution, 58; excess of Jupiter’s equatorial over his polar, 66; of rotation, proof of its being invariable, 76, 77.

——, major, of a planet’s orbit, distance from the sun measured by, 8; designation of its extremities, 9; length of, determining the form of the orbit, 10; periods of its revolutions, 17; length of, not permanently changed, 20; Jupiter’s periodically diminished, Saturn’s increased, 26; of the solar ellipse, period of its revolution, 86.

——, magnecrystallic, 349.

Azores, the, icebergs reaching, 100.

Babbage, Charles, his theory of volcanic action, 235-237; quotation from, on the nature of force, 353.

Babinet, M., his theory of dark lines observed in the solar spectrum, 163; comet’s light computed by, 359.

Babylon, eclipse observed at, 36.

Bacon, Francis, anticipation of discovery by, 32.

Baily, Mr., compression of the terrestrial spheroid calculated by, 50; density of the earth determined, 57; fictitious antiquity ascribed to Indian astronomical observations, 88.

Bali, volcanic eruption in, 233.

Balloon, rarity of the air felt in a, 118; observations made from, 119.

Baltic, the, a tideless sea, 98; decreased atmospheric pressure on the shores of, 120.

Barlow, Mr., observations supporting his theory of electric currents, 346.

Barometer, the, principles of cohesion and attraction applied to the construction of, 113; density of the atmosphere measured by, 117; mean heights of, varying with atmospheric densities, 118; mountain heights measured by, 119, 120; atmospheric phenomena affecting, 120; used to trace the course of atmospheric waves, 121; cause of sudden fall in, before hurricanes, 127; refraction varying with, 154.

Barrow, Cape, observations on magnetic storms at, 345, 346.

Battery, voltaic, construction of, 298, 299; Professor Daniell’s improvements, 299, 300; action of, charged with water, 300; constant flow of electricity obtained by means of, 312.

——, magnetic, constructed by Dr. Faraday, 324, 325; Mr. Henley’s magneto-electric, 325; Atlantic telegraph, 326; structure of, for land telegraphs, 328; relation of heat to power of, 329; thermo-electric, 333.

Batsha, port of, tides neutralised in, 99.

Bayle, comparative density of the atmosphere in interplanetary space according to his law, 356.

Bear, Little, the, the polar star in, 82.

Becquerel, M. E., unexplained photographic phenomenon observed by, 213; phosphorescent property in the solar spectrum discovered, 216; cause of phosphorescence, 217; electricity excited by pressure, 283; light attributed to electricity by, 284; cause of phosphorescence investigated, 296; instrument comparing intensities of electricities invented, 300; crystals formed by agency of electricity, 308; thermo-electric battery constructed by, 333; effect of atmospheric on terrestrial magnetism estimated, 345.

Beehive, the, a nebulous star, 415.

Berard, M., experiments of, in polarizing heat, 264.

Berlin, line of coincidence in temperature passing through, 238.

Berne, increasing temperature of a deserted mine in, 230.

Berre, Dr., photographic pictures perfected by, 205.

Bessel, M., his calculations from measurements of arcs of the meridian, 48; calculation of the sun’s mean apparent diameter, 56; his computation of the mass of Saturn’s ring, 68; diminished obliquity of the ecliptic observed by, 81; parallax calculated, 389; his theory of Sirius’s irregular motions, 392; catalogue of double stars, 396; mass of 61 Cygni found by, 404.

Beta Lyræ, a variable star, 391; nebula between γ Lyræ and, 410.

Benzenberg, M., velocities of falling stars computed by, 423.

Biela, M., date of the discovery of his comet, 367; possibility of collision with the earth, 368; present and prospective planetary influence on, 369; becoming two distinct bodies, 369, 370.

Binary systems of stars, 395-406. See Double stars.

Biot, M., his ascent in a balloon, 118; experiments of, on the transmission of sounds through pipes, 137; liquids possessing the power of circular polarization discovered by, 190; his theory of circular polarization, 191; cause of phosphorescence in the solar spectrum investigated by, 217.

Birds, distribution of distinct species of, 255.

Birt, Mr., atmospheric waves measured by, 121, 122.

Bise, in Switzerland, cause of, 242.

Bismuth, its magnetic and electric properties, 347.

Black Sea, the, scarcely affected by tides, 98.

Bode, Baron, law of, assumed in computing Neptune’s position, 61; failing in the case of Neptune, 63.

Bond, Mr., satellite of Saturn discovered by, 32; elliptical nebula resolved, 413.

Bonnycastle, Captain, phosphorescent phenomenon observed by, 295, 296.

Bonpland, M., identical productions of the Old and New World found by, 251.

Boötes, nebulous system in, 417.

Bore, the, of the Hoogly, its origin, 94.

Botanical districts, distinct, of the globe, 251, 252.

Botto, M., thermo-electricity used in decomposition by, 333.

Bouguer, degrees of the meridian measured by, 48.

Boussingault, M., depth of the underground stratum of constant heat calculated by, 228.

Bouvard, M., atmospheric undulations estimated by, 121.

Bradley, Dr., motion of the pole of the equator discovered by, 84; his tables of refraction, 155.

Brahmins, measurement of time by, 85.

Brand, M., observation of, on meteors, 423.

Brewster, Sir David, his analysis of the solar spectrum, 161; experiments on rayless lines, 163; experiments on spectra of flames, 164; law discovered by, determining angles of polarization for light, 183; experiments on fluorescence of light, 197; line of coincidence in temperature of springs and of the atmosphere determined by, 238; temperature of a pole of maximum cold determined, 245; isogeothermal lines determined by, 246; observations on the light of fixed stars, 402.

Brighton, phenomenon caused by reflection observed from, 157.

Brinkley, Bishop, mass of the moon determined by, 56.

British Channel, height of tides in, 98.

—— Isles, atmospheric wave passing over, 121.

Brorsen, M., periods of comets discovered by, 370.

Brown, Dr. Robert, peculiar vegetation found by, in Australia, 251.

Buchan, Dr., phenomenon caused by reflection observed by, 157.

Cæsar, Julius, era computed from his reign, 85.

Cagniard de la Tour, M., instrument designed by, measuring musical notes, 143.

Calms produced by the trade-winds, 122, 123.

Calorific rays. See Rays of heat.

Calotype, the invention of, 204.

Camelopard, nebulous system in, 417.

Canaries, the, vegetation of, 252.

Canary-glass, fluorescence of light in, 196.

Cancer, the calms of, 123; the tropic of, marking the limit of the trade-winds, 126; nebulous cluster in, 415.

Canis Major, position of, 390.

—— Venatica, nebulous system in, 417.

Capillarity, theory of, 113; forces producing, 114; familiar examples of, 115; curious phenomena, 115, 116.

Capricorn, the calms of, 123; the tropic of, hurricanes changing their direction at, 126.

Carbon, its powers contrasted as a crystal and as an opaque amorphous substance, 302, 303.

Carbonate of lime. See Lime.

Carbonic oxide, its constituent parts, 111.

—— acid, proportion of, in the atmosphere, 117.

Cardinal points, the, position of continental masses with regard to, influencing temperature, 244.

Caribbean Islands, hurricanes beginning at, 126.

Castor, discovered by Sir William Herschel, 396.

Cassiopeia, star appearing and vanishing in, 392, 393.

Categat, the, consequence of its narrowness, 98.

Cauchy, M., data furnished by, for investigation of the theory of light, 201.

Cayenne, variation in length of the pendulum between Paris and, 51.

Celestial bodies: law of their mutual attraction, 4; of the solar system: law determining their attraction to the sun, 5; problem to fix the positions of, on occurrence of disturbance in their motions through counteracting attractions, 11; theory of their mutual connection and dependence, 24; mode of finding the absolute distances of, 43; distances of, computed from their parallax, 52, 54; apparent position of, affected by refraction, 153, 154; apparent infinity of, 420.

Centaur, position of, 390; brilliant double star in, 399.

Central Asia, the mountains of, their ascent by Marco Polo, 118.

Centre of gravity. See Gravity.

Centrifugal force, moon’s motions modified by, 5; influence of, on planet-forms, 6; retarding oscillations of the pendulum, 32; action of, in determining the figure of the earth, 44, 45; measurement of its intensity, 49; resolved into two forces, its action on the sea, 100.

Ceres, astronomical tables of, 63; height of her atmosphere, 226; comet of 1770 revolving beyond the orbit of, 361.

Cetus, nebulous patches crossing, 417.

Chaldeans, the, mean longitude found from observations of, 36; result of comparison of their observations with modern, 38.

Challis, Professor, Brewster’s analysis of light questioned by, 161.

Charcoal, light produced by electricity from, 302-303.

Charles V., the Emperor, observations on comets, made in his reign, 370.

Chaudes Aigues, temperature of, 231.

Chemical action of rays of the solar spectrum, 203, 207; varying maximum of energy, 208; action varying with refrangibility, 209-212; action in luminous spectrum not continuous, 213; energy an independent property of rays, 214; properties of the parathermic rays, 219; action of light maintaining vegetation, 249; affinities the source of the power of steam, 278; of electricity on oxygen, 284; eliciting voltaic electricity, 297, 300; voltaic electricity, an agent in, analysis, 307, 308.

—— combinations, theory of, 110; invariable proportions of, 111; cohesive force inducing, 112; producing combustion, 270.

—— force, the power of, 112.

—— rays, causing the deposition of dew, 269.

Chile, elevation of land by an earthquake in, 234.

China, distinct flora of, 251.

—— Sea, the, monsoons blowing over, 124.

—— ink, polarized light reflected from, 193.

Chinese, the, observations of, on the mean motions of Jupiter and Saturn, 25; proof of their early study of astronomy, 88; decimal divisions used by, 90; elements of comets computed from their observation, 365; comet of 1264 recorded by, 370.

—— Tartary, herbarium collected in, 250, 251.

Chladni, discovery of, in musical science, 145.

Christian era, traces of astronomical records before, 365.

Chromatype, the invention of, 206.

Chronology, dependent on astronomy, 87-89.

Chrysotype, the, coloured photographs obtained from, 206.

Circuit, galvanic, modes of obtaining, 332.

Circular arcs, principle with regard to their sines and cosines, a pledge for the stability of the solar system, 20.

—— motion, ratio of forces procuring, 382.

—— orbits of planets distinguished from elliptical, 8; of satellites, 27.

—— polarization of light, 189-192; of heat, 266.

Circumference of the earth, 49.

Civil time, measure of its periods, 83; not precisely adjusted to solar revolutions, 85.

Clairaut, periodic time of Halley’s comet computed by, 362, 363.

Cleavages of crystals, 109; position of, affecting the intensity of magnetic action, 350.

Climates, planetary, 225, 226; cause of the different terrestrial, 237; phenomena affecting, 239, 240; causes of variety of, 243, 244; milder, of the Polar Ocean, 245, 246; like mean annual temperatures not ensuring like, 246; compensations of irregularities, 247.

Clocks, showing apparent sidereal time, 83; regulated to show decimal time, 84; irregular action of, corrected by the laws of unequal expansion, 272.

Clouds, circling the belt of equatorial calms, 123; region of, 124; electricity evolved from, 291-292.

Cloyne, Bishop of, his calculation of the moon’s mass, 56.

Coal-measures, tropical plants in, 72, 73; age of their formation, 75.

Coal, chemical force evolved from, by combustion, 278; source of its combustible qualities, 279, 280.

“Coal Sacks” in the Milky Way, 386.

Cohesion, influence of, on matter, 105; phenomena arising from its force, 106; attraction of, overcome by the expansive power of heat, 271.

Cohesive force, properties of material molecules constituting, 103; effectual only to unite particles of like nature, 110; inducing chemical combination, 112; capillary attraction, an action of, 113.

Coins, impressions taken from, by contact, 220; by electricity, 221.

Cold, contraction caused by, 271, 272; mitigated by slow propagation of heat in air, 273; generated by voltaic electricity, 302; increasing the conducting power of the air, 345.

Colladon, M., experiments of, testing the velocity of sound, 135.

Collision between the earth and comets, possibilities, possible effects of, 367, 369.

Collodion, sensitiveness of, to light, 203; properties of, as an agent in photography, 207.

Colours, seven primary, 159; theory of the decomposition of white light into, 160; degree of refrangibility not invariable, 161; three primary, ib.; new, discovered by Sir John Herschel, 162; rays refracted without, 164; rarely homogeneous, 165; experiments on accidental and complementary, 165, 166; determined by undulations of ether, experiments, 170-175; of material substances, whence derived, 175; produced by analyzing polarized light, 186-188; varying with refrangibility of rays, 198; obtained in photography, 206; images of the solar spectrum imitating the prismatic, 208-209; of seaweeds, 253; not invariably dependent on light, ib.; affected by absorption and reflection, 268; of the electric spark, affected by the atmosphere, 289; of the voltaic spectrum, 303; of the electric spark, 304; produced by oxidation on silver, 305; of the fixed stars, 401, 402; of planetary nebulæ, 412; of nebulous clusters, 415.

Columbus, beds of algæ found by, 253.

Column, capillary, forces producing changes in its form, 114, 115.

Coma Berenices, a nebulous cluster, 415; nebulous zone passing, 416, 417.

Combustion, cause of, 270; defined, 304.

Comets, attraction by the sun of, 5; disturbances in the motion of, a key to the nature of the ethereal medium, 22; retrograde motion in, 33; passing through Jupiter’s satellites, 69; return of, to their perihelia, furnishing historical data, 88; existence of the luminous ether demonstrated by, 168, 169; terrestrial atmosphere unaffected by, 358; amount of their light computed, 358, 359; passages of, through the solar system, 359; velocity, paths of, 359, 360; proof of the return of, 360; disturbing action of planets on their orbits, 361; of 1770, an example, 361, 362; computed return of Halley’s, 362, 363; aspects, records of Halley’s, 363-365; discoveries made by the revolutions of, 365; of the solar system, Encke’s, 365, 366; Biela’s, possibility of collision with, 367, 370; periods of various, 370; cause of their brilliancy, 371; velocity, sun’s influence on, 371, 372; of 1843, 372, 373; their constitution, 373, 374; of 1811, its luminous envelopes, 374, 375; sudden convulsions in, 375; tails, 375-377; causes assigned for contraction of diameter in, 377, 378; Donati’s, 378, 379; nature of their light, 379-381; computations of their numbers, 381, 382; orbits of, 383; nebula resembling, 413.

Compass, mariner’s, phenomena disturbing, 312; intensity of a galvanic current measured by, 315.

Compression of the terrestrial spheroid, calculations of, 48-51; cause of the great, in Jupiter, 66; measures of, from pressure of superincumbent mass, 78; effect of, on magnetic action, 351.

Concord, a, in music, 142.

Conductors of electricity, 284, 285; lightning, 293; molecular structure determining the power of, 303.

Conic sections, conditions compelling bodies in space to move in, 5; principle determining their nature, 11.

Constellations, nearest the sun, 390; where the orbit of the solar system lies, 406; occupied by the nebulous system, 417.

Contraction caused by cold, 271, 272.

Cook, Captain, object of his first voyage, 53.

Cooper, Mr., list of missing stars drawn up by, 395.

Copper, electricity communicated to plates of, 220; lightning-conductors of, 293; action of an electro-magnet on, 351, 352.

Cordier, temperature of mines observed by, 228.

Cordilleras, effect on temperature of their table-lands, 241.

Corn, a, field used to illustrate the propagation of sound, 129, 130.

Cornwall, hot-springs in mines of, 229.

Corona Australis, nebula in, 414.

Corpuscular theory of light, 167; phenomena disproving, 171, 175, 176.

Coseguina, volcanic irruption of, 233.

Coulomb, instrument measuring electrical intensity, invented by, 287.

Creation, vastness and magnificence of, 2.

Crimea, cause of the great storm in the, 122.

Cross, Mr., voltaic battery with constant action invented by, 300.

Cross, the Southern, vacant patches of the Milky Way near, 386.

Crystallization defined, 106; forms of, their variety affected by temperature, 107, 108; permanent and variable forms, 108, 109; cleavages in, 109; common to all substances, ib.; by the agency of electricity, 308, 309.

Crystals, conditions determining their forms, 107-109; optic axes of, 183; used in polarizing light, 186, 188; changes in, effected by compression, 189; transmission of rays of heat by, 258; expansion of, by heat, 272, 273; formed by electricity, 308; action of magnetism in, 349, 350; circumstances determining the set of, 350, 351; effect of temperature on magnetized, 352.

Cumming, Professor, experiments of, in thermo-electricity, 333.

Currents, two great, setting from each pole towards the equator, 100; proving the rotation of winds, 124, 125.

——, electric, flow of, regulated by Volta, 297-299; characteristics of Voltaic, 301; conductors, non-conductors of, 309; continuous flow of Voltaic, 312; action of, on magnets, 313-315; reciprocal and mutual action of magnetic and electric, 316, 317; Ampère’s theory of, unsolved difficulties, 317, 318; effect of, on polarized rays, 319; electric, evolved by magnets, 322, 323; their power of producing induction, 324; direction of, produced by rotation, 330-332; evolved by application of heat, 332, 333; produced by intersecting magnetic curves, 339; induced by crossing terrestrial lines of magnetic force, 342.

Curves, described by bodies projected in space, 5.

——, magnetic, 338; electricity produced by intersecting, 339; nature of, proved by Dr. Faraday, 339, 340; terrestrial, 341, 342; extent of the range of terrestrial, 344; complete connected system of the terrestrial, 345; inductive effect on the Atlantic telegraph, 346; diamagnetic, 348.

Cyanite, changes effected in, by magnetism, 349.

Cyanotypes, coloured photographs obtained by, 206.

Cygni 61, distance from the sun of, 389; orbit and mass of, 398, 399; colours, 401; mass, 404; proper motion, 405.

Cygnus, portion of the Milky Way lying between α Centauri and, 386.

Cylinders, rotating by electricity, 313; electro-dynamic, 316.

Dalcoath copper-mine, its temperature, 228.

Daguerre, M., his inventions in photography, 205; action of light on the iodide of silver explained by, 219.

Daguerreotype, the, invention of, 205.

Dalton, Dr., law of definite proportion established by, 111; law of the wind’s rotation observed by, 125.

Damoiseau, M., perturbations of a comet computed by, 367.

Daniell, Professor, Voltaic battery improved by, 299.

Daubuisson, M., observations of, in mines, 228.

Davy, Sir Humphry, his first attempts to produce photographic pictures, 203-204; experiment of, proving identity of heat and motion, 275; experiments on the electric spectrum, 289; alkalies, earths decomposed by, 307.

Days, law determining the length of, 71; period of the mean sidereal and solar, 83; varying with the seasons, 84; decimal division of, 84; seven, the most permanent division of time, 85.

Deccan, the, wheat ripening in, 250.

December, 1832, disappearance of Saturn’s rings in, 67; coincidence of mean and apparent time in, 84; date of Christ’s nativity, 85; the astronomical year beginning in, 86.

Decimal division of time, 84.

Declinations of the moon, 97.

Decomposition, effected by electricity, 307-308; by magnetism, 323; by thermo-electricity, 333.

Delambre, his computations of the length of the year, 359.

Delta Cephei, a variable star, 391.

Denmark, course of the tidal wave to, 94.

Density, variable, impeding sound, 135, 136: of media, modifying refraction, 153.

Densities of heavenly bodies, formula finding, 56; experiments, 57, 58; comparative of the terrestrial globe, 77, 78.

Deserts, causing monsoons, 124; influence of, on temperature, 243.

Dew, cause of its deposition, 269.

Diamagnetic substances, 335, 336.

Diamagnetism defined, 335; substances it is resident in, 336; discovery, characteristics of, 347; neutral substances obtained by proportionate combination of, with paramagnetism, ib.; polarity of, 348; connected with arrangement of molecules, 350-351; affected by division and compression, 351; possibly identical with paramagnetism, 356, 357.

Diameter of the earth, 21; Jupiter’s polar, 27; excess of his equatorial, 39; apparent, of the sun and moon, nearly equal, 40; of the earth, 49; of bodies composing the solar system, 56; of Neptune, 63; comets lacking a sensible, 373; contraction of, in comets, 377; causes assigned for, 377, 378.

—— of an annular nebula, 410; sensible, of a planetary nebula, 412.

Diamond, the, polarized light reflected from, 193.

Dielectrics in electricity, 286.

Dieppe, seen from Hastings, 157.

Differential telescope, the, experiments to be made by, 227.

Discord, a, in music, 142.

Diurnal tides of the atmosphere, their duration, 121.

—— variations in mean values of the magnetic elements, 343.

Dœbereiner, M., spontaneous combustion discovered by, 112.

Doldrums, region of the, 123.

Dollond, Mr., achromatic telescope perfected by, 165.

Donati, Signore, discovery of his comet, 378; changes in, its irregularities, 379.

Doradus, nebulous patches on, 417.

Dorpat, occultation of a star observed from, 364.

Double nebulæ, 411.

Double stars, catalogues of, 395, 396; formulæ obtaining the relative position and motions, 396, 397; eclipse in γ Virginis, 397; orbit of, determined, 398; eclipse in ζ Herculis, ib.; orbits and periodic times of, 398, 399; anomalies in motions, 400; optically double, 400, 401; colours of, 401; rays composing the light of, 401, 402; passage of light from, furnishing data to ascertaining their actual distance, 402, 403; data for finding their masses, 403, 404; calculations founded on the quantity of light emitted from, 404; real and apparent motions of, 404-406; apparent periodic time, 406, 407; connection of elliptical nebulæ with, 411.

Dove, Professor, law of the wind’s rotation developed by, 125; average temperature of the earth’s surface estimated by, 237.

Draco, nebulous system in, 417.

Draper, Professor, experiments of, on fluorescence of light, 198; experiments in photography, 213; properties of parathermic rays discovered by, 219; spectrum produced from diffracted light, 223; theory of heat propagated by undulations, 267.

Dunlop, Mr., revolution of a double star calculated by, 400.

Dusejour, M., distances of comets computed by, 359.

Dynamic electricity, 297. See Voltaic.

—— theory of heat, fundamental principle of, 357.

Dynamic equator of the earth, 343.

Dynamical theory of heat, 274, 275; illustrated by liquefaction and condensation, 278; by generation of steam, 276, 277; power of nature, 279-281.

Dynamics, principle in, a law, with regard to the earth’s rotation, 72; electro, discovery of action of currents in, 316; the theory of, universal application of, 426, 427.

Earth, the, influence of its form on attraction, 4; square of the moon’s distance from, 5; form of, 6, 7; moon’s influence on its rotations, 7; diameter of, 21; mean distance from the sun, ib. note; permanence of revolution in its times and seasons, 23; perturbation in the mean motion of Venus and, 26; proof of the motion of, in its orbit, of its rotation, 32; variations in its attraction of the moon, 37; compression of its spheroid, 38; internal structure of, 39; its mean distance from the sun, 43; theoretical investigation of its figure, 44-46; dimensions of, determined, 48, 49; figure of, found by calculating its variations in gravitation, 49-51; density compared with the sun, 56; experiments finding its mean density, 57, 58; rate of revolution round its axis, 58; its diurnal rotation immutable, 71, 72; changes in temperature and their causes, 73, 74; nature of the revolutions producing geological changes, 76, 77; conjectures touching its internal structure, 78; effects produced by solar and lunar attraction affecting its equator, 79-81; its form furnishing standards of weight and measure, 89; rotation of, acting on tides, 92; attraction of, affecting the lunar atmosphere, 226; conjectured constitution of its interior, 231, 232; principles regulating the diffusion of solar heat, 237-247; distribution of known species of plants over, 249-252; electric tension of, 291; lines of magnetic force issuing from, 341; magnetic properties of, 342, 343; effect of its collision with a comet, 368; nearest approach of comets to, 369; passage of light from α Centauri to, 388; theories of meteors falling on, 421-423.

Earthquakes in South America, 234.

Earths, decomposed by voltaic electricity, 307.

Eastern coasts, cause of their colder climates, 244.

Ebb, see Tides.

Éboulemens of mountains in Switzerland, cause of, 271.

Echoes, theory of their origin, 137, 138.

Eclipses, lunar, accelerated revolutions proved by observations of, 36; observations of, confirming results of analysis, 38; principle regulating their return, 39; refraction of rays by the terrestrial atmosphere, 40.

——, solar, 40; effects of light in, 41.

——, planetary, 42; the solar atmosphere visible in, 224; of double stars, 397, 398.

Ecliptic, the, forming the equinoxes, 9; latitude reckoned from the plane of, ib.; deviations of planetary orbits from, 10; forces affecting their position towards, 15; their compensated and uncompensated variations to the plane of, 18, 19; secular variation in the plane of, 23; orbits of satellites, nearly perpendicular to, 33; lunar motions towards, 35; inclination of the sun’s plane of rotation to, 65; inclination of the plane of Saturn’s rings, 67; inclination of the plane of the terrestrial equator, 79; tendency of its plane to coincide with the equatorial, ib.; retrograde motion of the equinoctial points on, 80; obliquity of, affecting the duration of time, 84.

Edinburgh, comparatively equal mean annual temperature of, 246.

Egypt, hieroglyphic manuscript from, interpreted by astronomy, 89.

Egyptians, the civil year of, 85.

Elastic impact, the foundation of dynamical theories, 357.

Elasticity, property of, resisting compression, 105.

Electric telegraphs, experiment suggesting the principle of, 323; construction of, 325-328.

Electricity assumed as the medium attracting particles of matter, 103, 104; identical with chemical affinity, 110; in composition and decomposition, subject to laws of definite proportion, 112; influencing winds, 125; its comparative velocity, 138; producing phosphorescence, 217; communicated to metal plates by juxtaposition, 220; impressions traced on glass by, 221; rays exciting, 223; a dual power, 282; modes of exciting by disturbing equilibrium, 282-284; transmission of, 284, 285; transmission by induction, 285, 286; laws of attraction and repulsion determining intensity of, 286-288; heat and light produced by, 288; velocity of, 289; experiment determining its velocity, 290; development of, in the atmosphere, 291, 292; phosphorescence excited by, 294; Voltaic, see Voltaic; conduction of static, contrasted with Voltaic, 309; laws of action in, distinguishing it from Voltaic, 317; relation between 322, 323; telegraphs working by, 323-328; produced by rotation, 330, 331; thermo, 332, 333; exact balance of its dual force, 334; points of analogy between magnetism and, 340, 341; causing convulsions in comets, 375.

Electro-dynamics, see Dynamics.

—— magnetism, see Magnetism.

Elements, the three terrestrial magnetic, 343; variations in, ib.; storms affecting, 344.

Elevation, effect of, on temperature, 240-242; on vegetation, 250.

Ellipses, described by planets, 5; paths of planets describing, 10; preventing compensation of disturbance, 15; cause and measures of variation in, 17; described by comets, 363, 366.

Ellipsoid, an, of revolution, mass assuming the form of, 45; its equatorial and its polar radius, 48; permanent axes of rotation, 76.

Elliptic motion, ratio of forces procuring, 382.

Elliptical polarization of light, 192, 193; of heat, 267.

—— nebulæ, 409; their connection with double stars, 411; frequency, 413; difficult of resolution, 415.

Encke, Professor, sun’s parallax found by, 53; his comet, 169; aspects, period of his comet, 365, 366; cause of acceleration in its revolution, 366, 367; crossing the terrestrial orbit, 368; prospective and present planetary influence on, 369; disappearance of its tail and nucleus, 369; referred to, 377; contraction of diameter, ib.

England, arcs of the meridian measured in, 48; course of the tidal wave towards its west coast, 94; peculiarities of photography in, 213; meteors falling in, 421.

Engravings copied by photography, 204; impressions taken by contact with iodized silver, 221; impressions taken from, by galvanism, 309.

Epipolic light, 197.

Epsilon Orionis, zone of stars passing through, 385.

Equation of the centre, defined, 9; lunar, 35.

Equator, the, forces compelling the wider circle of, 6; inclination of the terrestrial to the plane of the ecliptic, 23; of the solar system, 24; measure of the centrifugal force at, 49; calculation from lunar action on the terrestrial, 55; effects produced by external attraction influencing the direction of its plane, 79, 80; inequality in its polar motion, 81; cause of the calms at, 122; depth of the underground stratum of constant temperature at, 228; maximum of solar heating influence, 238; superficial extent of land, 244; mean annual temperature, 245.

Equator of the sun, maximum of solar heat attained in, 225.

——, dynamic, surrounding the terrestrial globe, 343.

——, magnetic, of the earth, 343.

Equinoctial circle, the, defined, 9.

—— points, effects of solar and lunar attraction on, 79; period of their revolution, 80; measuring time, 83.

Equinoxes, the, defined, 9; venial, a point whence planetary motions are estimated, ib.; of the planets, cause of a precession in, 66; causes preventing their invariable correspondence with points of the ecliptic, 79; precession affecting the seasons, 80; secular motion of, periodic variations, 80, 81; eras depending on the precession of, 86, 87; tides augmented in, 97.

Eras, astronomical, determined by the position of the major axis of the solar ellipse, 86, 87.

Eratosthenes, the earth’s circumference measured by, 49.

Eridanus, nebulous patches crossing, 417.

Erman, M., depression of the barometer observed by, 120.

Eruptions, volcanic, recorded, 234.

Eta Aquilæ, a variable star, 391.

—— Argûs, zone stretching from, 390; nebula round, 418, 419.

—— Coronæ, periodic time of, 398.

Etna, measurements of, 120.

Ethereal medium, undulations of, propagating heat, 267; permeable to lines of magnetic force, 344; its density, 356; transmitting gravity, ib.; magnetic, 356, 357; offices discharged by, 357; pervading the visible creation, 358; influence of, on comet motion, 365; astral revolutions accelerated by, 366; probable increase in density of, 367.

Europe, atmospheric wave passing over, 121; causes of variation of climate in, 244; separation of isothermal lines in high latitudes of, 245; differences of latitude enjoying the same mean temperature, 246; indigenous productions of, 249; number of indigenous productions common to Australia and, 251; number of species of forest trees, 252.

Eudoxus, Plato’s contemporary, astronomical observation of, 88.

Evaporation, conditions affecting, 269, 270.

Everest, Colonel, arc of the meridian measured by, 48.

Excentricity of planetary orbits measured, 17.

Expansion, universal law of, 271; accuracy in measurement ensured by laws of unequal, 272; of crystals, 272, 273; theory of, 275, 277; of steam, 278; by electricity, 285.

Extra-tropical winds, 124.

Fabricius, the comet of 1556 observed by, 370; variable star, 390.

Fahrenheit, mode of ascertaining heights proposed by, 120.

Falling stars, 420; theories of, 422, 423.

Faraday, Dr., gases reduced to liquids by, 105; experiments testing chemical affinity, 111; instance of cohesive force inducing chemical combination, 112; experiments on vibrations producing colour, 173; influence of dialectrics, 286; chemical origin of electricity defended by, 300; electro-chemical decomposition defined by, 308; remarks of, on conduction of voltaic electricity, 309; experiments on magnetic rotation, 313; experiment magnetizing polarized light, 318, 319; importance of his experiment, 320; experiment establishing the identity of magnetism and electricity, 322, 323; his magnetic battery, 324, 325; aid given by, in construction of telegraphs, 326, 328; electricity produced by rotatory motion explained, 330; his classification of substances according to magnetic qualities, 332; quotation from, on conservation of force in electricity, 334; magnetism raised to a new science by, 335; the magnet as represented by, 338; experiment determining the forms of magnetic lines of force, 339, 340; accidental electro-magnetic combinations pointed out by, 342; his discovery of diamagnetism, 347; experiments on magnetic action in crystals, 349; observations on influence of heat in magnetism, 352; definition of gravity questioned by, 354, 355; magnetism of the ethereal medium tested, 356.

Fauna, distinct, of separate regions, 254, 255.

Faye, M., his conception of the sun’s constitution, 41; his theory of phenomena observed in eclipses, 42; comet of 1843 discovered by, 361.

Fiedler, Dr., fulgorites exhibited by, 293.

Fire, chemical combination producing, 270.

—— balls, theory of, 421.

Fires, central, subterranean, 231-237.

Fish, phosphorescent, 294, 295; electric, 310.

Fixed stars. See Stars.

Fizeau, M., decisive experiment in proof of the undulatory theory of light accomplished by, 202.

Flame, chemical combination evolving, 270, 271.

Flames, lambent, caused by electricity, 294.

—— divergent from the nucleus of a comet, 364.

Fletcher, Mr., periodic time of γ Virginis determined by, 398.

Flora of the Himalaya, 250; distinct, in separate regions, 251; condition establishing distinct, in islands, 252.

Florence, comet discovered from, 378.

Fluor-spar, its property of diminishing refrangibility of light, 196.

Fluorescence of light, definition of, 195; vibrations of the substance producing, 196; experiments, 197, 198.

Focus of a meteoric shower, 422.

Fog, yellow, excluding the chemical action of rays, 214.

Forbes, Professor, temperature of the boiling point ascertained by, 120; observations of, on rayless lines, 163; lunar heat tested by, 227; experiments of, in polarization of heat, 264, 267.

Force, relation of, to heat, 275; transforming solids to liquids and to vapour, 275, 277; a power of nature, 279; light and heat modes of, 219, 220; heat a living, 329; lines of magnetic, 338, 340; conservation of, maintained in periodic variation of atmospheric magnetism, 345; increatable, indestructible, 353; examples of conservation of, 354; fundamental principle of conservation, 357; influence and action of the gravitating, 424, 426.

Forces, the unknown cause of motion, 5 et passim; counteraction of solar and tangential, in planetary motion, 8; adjustment of, ensuring the permanence of the solar system, 11, 12; three partial, causing perturbation in planetary motion, 14, 15; excess of equatorial diameter the origin of, 27, 28; three, disturbing lunar motions, 34, 35; determining planet forms, 44, 45; producing tides, 91, 92; combining to form the centrifugal, 100; acting on molecules of matter, 102, 105; producing capillary phenomena, 114; latent, in nature, 279, 280; one universal power, the root of all, 321; exact balance of, in electricity, 334; kindred and convertible, 353; developing comets’ tails, 375; determining the forms of orbits, 382, 383; maintaining the stability of the solar system, 426; mutual relations of, 427.

Forests, change produced in the atmosphere by, 241, 243; number of species of trees found in American and European, 252.

Formentera, quadrant of the meridian passing through, furnishing a unit of linear measure, 89.

Fornix, nebulous patches crossing, 417.

Forster, Lieutenant, conversation carried on by, across Port Bowen Harbour, 136.

Fossil plants, an evidence of change in temperature, 74.

Fourier, mean temperature of space according to, 119; rate of decrease in the earth’s central heat computed by, 232.

Fox, Mr., temperatures in mines tested by, 228, 229; law of paramagnetic force ascertained by, 338; observations in mines, proving agency of electro-magnetism, 346.

France, arcs of the meridian measured in, 48; unit of linear measure in, 89; mode of arithmetical computation, 90; atmospheric pressure in, 120; cliffs of, seen from Hastings, 157.

Fraunhofer, M., discovery of rayless lines in the solar spectrum, 162; comparative refrangibility of rays ascertained by, 163; data furnished by, to determine the dispersive power of rays, 165; his discovery determining the length of waves independently of refraction, 201; spectrum of an electric spark observed by, 289.

Freezing, temperature required for, under pressure, 271; theory of, 276.

Fresnel, M., his testimony in favour of the undulatory theory of light, 171; theory of refraction, 183; discoveries in polarization of light, 191, 193.

Freyberg, green plants found in mines at, 253.

Friction evolving heat, 274, 275; electricity, 282, 283.

Fringes of coloured light bordering shadows, 174, 175; produced by interference of polarized rays, 194.

Fulgorites, found in Silesia, 293.

Fundy, the Gulf of, cross tides pouring into, 94.

Gage, Mr., experiments of, on magnetism, 315.

Gales. See Winds.

Galileo, laws affecting music discovered by, 145; his method of finding distances of fixed stars, 388.

Galle, Dr., Neptune’s place communicated to, by Le Verrier, 62.

Galloway, Mr., sun’s motion proved by, 405.

Galvani, Professor, peculiar effects of electricity suggested to, 297.

Galvanism, phenomenon suggesting the theory of, 297; batteries, 298, 300; heat and light evolved by currents of, 300, 304; decomposition and composition, 307, 308; applied to plating and gilding, 309; effect of heat on, 310; effect of, on the senses, ib.; fish exhibiting analogous phenomena, 310, 311; phenomena exhibited by currents of, on magnets, 312, 314: intensity of a current measured, 315; conditions obtaining a circuit in, 332.

Galvanometer, the principle of its construction, 315; experiment by means of, identifying magnetism and electricity, 322, 323.

Gambart, M., parabolic elements of a comet computed by, 367.

Gamma Andromeda, colours of, 401.

—— Aquarii, planetary nebula near, 412.

—— Hydræ, a variable star, 391.

—— Leonis, focus of a meteoric shower in, 422.

—— Sagittarii, cluster of the Milky Way round, 387.

—— Virginis, eclipse in, 397; orbit of the revolving star determined, 398.

Ganges, the, tidal wave at the mouths of, 94.

Gardner, Mr., extent of diametrically opposite lands estimated by, 244.

Gases, conditions retaining matter in the form of, 104, 105; combinations of, 111; transmission of radiant heat through, 258; expansion of, 271; voltaic spectrum modified by, 303; effect of heat on the conducting powers of, 309.

Gassiot, Mr., experiments of, on the electric discharge, 306; connexion between magnetism and light discovered by, 321; electric apparatus improved, 328.

Geneva, the Lake of, experiment on the velocity of sound in, 135.

Gensanne, M., increasing temperature of mines tested by, 228.

Geographers, lunar motions important to, 42.

Geological changes, probable cause of, 77.

Geology, the lessons of, 326.

Georgia Island, S., excess of cold in, over corresponding latitudes, 241.

Germany, shooting stars seen from, 421.

Gibraltar, the Straits of, turning aside the tidal wave, 98.

Giromagny, temperature of the lead-mines of, 228.

Glass, effect of cohesion on plates of, 106; musical notes elicited from rods and plates of, 144-147; transmission of waves of light in, 177; polarizing light, 184, 185; elliptical polarization produced by, 193, 194; used in photography, 207; impressions on, from bodies in contact with, 220; impressions on, traced by electricity, 221; transmission of radiant heat by, 259; by coloured, 261, 262; its temper altered by magnetism, 352, 353.

Globular clusters of nebulæ, 413-415.

Glow-discharge observed by Captain Bonnycastle, 295, 296.

Gold, action of, on light, 173.

Good Hope, the Cape of, icebergs drifted to, 101.

Goodricke, Mr., variable stars discovered by, 391; opaque bodies represented as revolving round fixed stars by, 394.

Graham, Mrs., account of an earthquake by, 234.

Graham’s compensation pendulum, 272.

Gravitating force of the sun, 365, 424, 425.

Gravitation, offices of, in the material creation, 1, 2; process of reasoning in ascertaining the law of, 3; law determining its intensity in the solar system, 5; complex action of, by attraction in mass and in particles, 6; increase of, towards the poles of the earth, 45; calculations founded on its increase, 49-51; in a mine, its excess over surface, 57; action of, modifying tides, 92, 93; law, universally acting on matter, 105; the air subject to, 117; influence of, in motions of the heavenly bodies, 382, 383; double stars revolving by, 398; stellar systems subject to, 400; influence of, on nebulæ, 416; a general law of the visible creation, 424; mode of its action, 425, 426.

Gravity, centre of, in spheres, effect of impulses passing through, 7; of the solar system, invariable plane passing through, 23; straight line described by, 24; action of, in determining the figure of the earth, 44, 45; definition irreconcilable with the conservation of force, 354, 355; question of its transmission, 355, 356.

Great Bear, the nebulous zone passing, 416.

—— Gobi, the, effect of the expansion of air over, 124.

Greeks, astronomical observations of, confirming results of analysis, 38.

Greenland, ocean on the northern coast of, 94.

Greenwich, lunar distances computed for, 43; quadrant of the meridian passing through, furnishing a unit of linear measure, 89; periodic circuits of winds, 125.

Grimaldi, coloured fringes bordering shadows described by, 175.

Groombridge, velocity of his proper motion, 404.

Grotthus, the transmission of voltaic electricity investigated by, 298.

Grove, Mr., copper and zinc plates electrified by, 220; substances radiating heat of different refrangibilities enumerated by, 257; the transmission of voltaic electricity investigated by, 298; electric heat tested by, 301, 302; remarks of, on carbon, 302, 303; on the voltaic arc, 304, 305; remarks of, on light and heat, 319; electric apparatus improved by, 328; his definition of the ethereal medium, 355.

Grylli, supposed delicate sense of hearing in, 132.

Guanaxato, temperature of the silver-mine of, 228.

Gulfs separating stars, 390.

Gum-guaiacum, chemically affected by rays of the solar spectrum, 203; condition of its sensibility to light, 206; effect of red rays on, 209; used in experiments on parathermic rays, 217, 218.

Gum-lac, electrical intensity measured by means of, 286, 287.

Gymnotus electricus, the, 310.

Haidinger, M., experiments of, proving water an essential part of crystals, 107.

Hail, formation of, 270.

Hales, his calculation of the amount of surface exposed by the leaves of a helianthus, 243.

Hall, Mr., achromatic telescope constructed by, 165.

Halley, elements of a comet’s orbit computed by, 362; return of his comet, 363; changes in its aspect, 363, 364; records of, 365; no solid nucleus in, 374; cause of its luminous sectors, 376; Sir John Herschel’s observations on, 378.

Hare, the, comet observed near, 372, 373.

Harmonics of the fundamental note in music, 140, 141.

Harmony, property of sound regulating, 131; definition of, vibrations producing, 142.

Harris, Sir William Snow, experiments of, in electricity, 287, 288; lightning-conductors invented by, 293.

Harrison, pendulum invented by, 272.

Hastings, coast of France distinctly seen from, 157.

Heat affecting the form of crystals, 107; evolved in chemical combinations, 110; irregular decrease of, in the atmosphere, 119; maxima of, in the solar spectrum, 215; peculiar chemical quality of, in parathermic rays, 218; impressions traced by, 220-222; periodical variations in the sun’s, 225; different proportions of solar, reaching the planets, 225, 226; effect of the terrestrial atmosphere on lunar, 227; mode of its development in opaque bodies, ib.; sources of terrestrial, 228-238; irregular distribution of, 239-247; laws affecting its radiation, 257; its transmission, 258-262; polarization of, 264-267; undulatory theory, 267; absorption and reflection of radiant, 268; phenomena caused by radiation of, 269; accumulation of, producing light, 270; expansive force of, 271, 272; modes of propagation, 273, 274; produced by motion and equivalent to it, 274-277; laws regulating the force of artificial, 279, 280; power evolved by application of, 280; identical in nature with sound, 281; electrical, 288; sheet-lightning caused by, 294; phosphorescence, 294; developed by voltaic electricity, 301, 302; effect of, on electrical conductors, 309; connexion between the production of electricity and, 310; its direct relation to magnetism and electricity, 319, 320; mechanical power and convertible forces, 329; terrestrial magnetism attributed to the action of, 333; measured by electric currents, 334; affecting atmospheric magnetism, 344; fundamental principle of the dynamic theory, 357.

Helena, St., distinct flora of, 252.

Helix, circular and elliptical, described in polarization of light, 192, 193; electrical experiments by means of, 314; induction of, increasing electric power, 322, 323.

Heller, his observations on the comet of 1556, 370, 371.

Helmholtz, Professor, power of chemical force estimated by, 112; his calculation of the chemical force developed by combustion, 278; of the amount of latent force in our system, 280.

Hemisphere, cause of excess of cold in the southern, 241; superficial extent of land in northern and southern, 244.

Henley, Mr., magneto-electric machine constructed by, 325.

Henderson, Professor, parallax of α Centauri calculated by, 387; of Sirius, 389.

Henry, Professor, experiments of, on magnetism, 315.

Herapath, Mr., his view of elastic force preferred to Sir Humphry Davy’s, 276.

Hercules, eclipse of a double star in, 398; globular nebulous cluster, 414.

Herschel, Sir William, observations of Saturn’s and Uranus’s satellites by, 32, 33; theory of, regarding the solar constitution, 41; cause of effects of light in eclipses according to, 42; rotation of Jupiter’s satellites determined by, 70; mutual independence of light and heat, 214, 215; influence of the sun’s spots on heat, 225; point of maximum heat in the solar spectrum, 263; comet of 1811 observed by, 374; its luminous envelopes examined, 375; the Milky Way examined by, 385; his discovery of the orbital motions of double stars, 388; catalogue of double stars by, 395, 396; periodic time of γ Virginis determined by, 398; eclipse of a double star observed, ib.; binary system discovered, 400; remarks on the motions of the stars, 405; nebulæ resolvable into stars, 507.

Herschel, Sir John, approximate periods of satellites ascertained by, 33; thickness of Saturn’s ring computed, 67; observations of, on seasons, 74; difficulty of varying time, in observations at distances, obviated by, 86; tenuity of atmospheric air demonstrated, 110; rapid decrease of density in the atmosphere, 118; mean temperature of space computed by, 119; height of Etna measured, 120; his explanation of anomalies in atmospheric phenomena, ib.; quotation from, on the transmission of sound, 136; observations of, on thunder, 138; remarks on the absorption of light by coloured media, 175, 176; on polarization of light, 179; experimentalising apparatus, 188; discovery of epipolic light, 197; discoveries in photography, 205, 206; analysis of the solar spectrum, discovery of its chemical properties, 207-219; his theory of volcanic action, 235-237; observations showing the maximum of heating influence of the solar rays, 238; theory of the original distribution of plants, 254; divergent flame of a comet observed by, 364; remarks on the possible destruction of the solar system, 372; causes assigned by, for contraction of diameter in comets, 378; comparative lustre of stars measured by, 384, 385; the Milky Way described, 385, 386; number of stars in a group of the Milky Way computed, 387; variable star discovered, 391; remarks of, on the nature of the fixed stars, 392; variable stars discovered by, 393; remarks on variable stars, 394; star missed by, 395; double stars discovered, 396; eclipse of a double star observed, 397; orbits determined, 398, 399; observations on colours of double stars, 401; light of α Centauri compared with the moon’s by, 404; light of the fixed stars calculated, ib.; observations on nebulæ corrected, 407; catalogues of nebulæ, 408; nebulæ discovered by, 409; annular nebula described, 410; magnitude of planetary nebulæ computed, 412; globular nebulous cluster described, 413; law of gravitation ascribed to nebulæ, 416; nebula round η Argus described, 418; his work on Nebulæ, 419.

Herschel, Miss, Encke’s comet seen by, 365; catalogue of nebulæ, 407.

Hevelius, divergent flames of a comet described by, 364; contraction in diameter of comets observed, 377; phases in comets observed, 380.

Hieroglyphics interpreted by astronomy, 89.

Himalaya, the, inappreciable effect of, on the globe’s surface, 6; singular effect of refraction on, 156; cause of greater elevation of the snow-line on the northern side of, 241; flora of, 250.

Hind, Mr., comet’s orbit computed by, 370, 371; observations of, on Donati’s comet, 379; variable stars discovered by, 391; vanishing star discovered, 393; his belief in planetary systems, 394.

Hindostan, the tidal wave striking on its coasts, 94.

Hipparchus, precession discovered by, change of seasons since his age, 80; phenomenon suggesting his catalogue of the stars, 392.

History corroborated and corrected by astronomy, 87, 89.

Hoar-frost, cause of, 269.

Holtzmann, M., opinion of, with regard to the vibrations of polarized light, 223.

Hoogly, the, bore of, 94.

Horizon, effects produced by the denser stratum of air in, 157, 158.

Horologium, nebulous patches in, 417.

Horton coal-mine, experiments with the pendulum in, 57.

Hours, cause of their mal-correspondence over the globe, 86.

Hudson’s Bay, tide in, 98.

Humboldt, his sufferings from rarity of the atmosphere, 118; his explanation of the apparent greater acuteness of hearing observed at night, 135; observations of, in mines, 228; causes of disturbance in the equal diffusion of heat enumerated by, 240; identical productions of the Old and New World found by, 251; his distribution of palms and grasses, 252; green plants found growing in mines by, 253.

Hunt, Mr., coloured image of the solar spectrum obtained by, 209; image obtained in England, 213; his experiments in tracing images by juxtaposition of bodies, 220, 221; experiments on the condensing power of rays, 223.

Hurricanes, origin and cause of, 125, 126; curve described by the axis of, ib.; their extent and velocity, 126,127; phenomena resulting from their revolving motion, 127; laws of, making avoidance possible, 128.

Huygens, theory originated by, 169.

Hydrogen, proportion of, in water and gases, 111; spectrum from, 303; separated from water by electricity, 307.

Hygrometer, dew-point measured by, 269.

Hyperbolic motion, ratio of forces procuring, 382.

Iapetus, seen by Mr. Lassell, 33.

Ibn Junis, progress of science in his time, 90.

Ice, formation of, 271; force acting in its formation, 276; stopping the current of voltaic electricity, 309.

Icebergs, drifting of, 100, 101; farthest range of northern and southern, 241; effect of electricity in collisions, 284.

Iceland spar, its property of double refraction, 181; polarized ray analyzed by, 187; transmission of radiant heat by, 258; electricity elicited from, 284.

Illumination, comparative, of objects, experiments determining, 227.

Images, coloured, of the solar spectrum, 208-211; traced by contact and juxtaposition of bodies, 219, 220; by electricity, 221; by media absorbing hot rays, 222.

India, arcs of the meridian measured in, 48; discovery of Saturn’s ring, 66; ancient monument of astronomical knowledge, 85; observations confirming the antiquity of astronomical science in, 88.

Indian Ocean, the tidal wave in, 94; monsoons blowing over, 124.

Induction, law of, in electricity, 285, 286; magnetic, 314, 315; phenomena of, produced by electric currents, 324; illustrated by the Atlantic telegraph, 325, 326; velocity of electricity modified by power of, 327; possibility of electro, furnishing a motive power, 328; of electricity by rotation of magnets, 330-332; as possessed by magnets, 336; paramagnetism evolved by, 337; means of accelerating, ib.; subject to the laws of mechanics, 338; analogy between electric and magnetic, 341; of heavenly bodies, affecting terrestrial magnetism, 346, 347; diamagnetic substances capable of, 348.

Indus, comet passing through the constellation of, 379.

Inequality, the, of Jupiter and Saturn marking historical epochs, 88.

Insects, law of their dispersion, 255.

Instruments, musical, 143, 149, 150; imitating articulation of letters, 151, 152.

Insulation in electricity, 285.

Interference, laws of, neutralizing undulations, 138, 139; the theory of, referred to a general law, 169.

Iota Cetæ, comet observed near, 372.

—— Orionis, a nebulous star, 411.

Ireland, progress of the tidal wave towards, 94.

Iron, distilled, 305; rotation of its particles, ib.; magnetized by electricity, 314, 315; magnetic properties of, 332; rendered paramagnetic, 336, 337; magnetic and electric properties of, 347; elasticity of, affected by magnetism, 352.

Islands, character of their floras, 252.

Isogeothermal lines of temperature defined, 238, 239; parallel with the isothermal lines, 246.

Isomorphous crystals, 109.

Isothermal lines of temperature defined, 240; latitudes of, deviation from the line of the equator, 245; formula determining, 246; similarity of vegetation in the same, 253.

Italy, local attraction, occasioning inaccuracy in measurement, 48.

Ivory, M., his method of computing heights, 120; his theoretical investigation of planet forms, 44; deduction from measurement of arcs of the meridian, 48.

Jacob, Mr., discovery of Saturn’s ring by, 66; periodic time of α Centauri determined by, 399; periodic time of 70 Ophiuchi, 400.

James, Colonel, measurements of, in the General Survey of Great Britain, 47; density of the earth determined by, 58.

Jamin, M., remarks of, on substances producing elliptical polarization, 193.

January, epoch of its beginning the year, 85.

Jews, denominations of time in their calendars, 85.

Josephstadt, discovery of a comet from, 367.

Joule, Mr., heat considered a mechanical force by, 275; his view of elastic force, 276; amount of latent force in a pound of coal, computed by, 278; furnishing data to Professor Thomson, 279; quantity of heat generated in a unit of time by electricity computed by, 302; powerful magnet obtained by electricity, 315; electric machines constructed by, 328; experiments proving heat and mechanical power convertible, 329.

Jovial system, mass of the whole, 55.

Julian Calendar, year of, the first of our era, 86.

June, 1833, reappearance of Saturn’s rings, 67; coincidence of times in, 84.

Juno, the diameter of, 56; astronomical tables of, 63.

Jupiter, rotation of, distinguished from the other planets, 7; periodical inequality in his motions, 15; discovery of telescopic planets between Mars and, 20, 21; diameter of, 21; his position with respect to the equator of the solar system, 24; inequalities in the motion of, apparently anomalous, 25, 26; his mass proved not homogeneous, 29; eclipses, 30, 31; compression of his spheroid computed, 39; eclipsed by Mars, 42; mass of, compared with the sun, 55; his diameter, 56; increase of density in, 58; astronomical tables of, 60; rapid rotation, 66; period of a year in, ib.; effect of his disturbing energy, 81; photographic images of, 226; light reflected by his atmosphere, 227; action of, on the comet of 1770, 361, 362; on Halley’s comet, 362, 363; comet revolving between the orbits of the earth and, 367; future influence of, on comets, 369; comet nearly approaching his fourth satellite, 370; comets having their perihelia in his orbit, 381.

——, orbit of, revolutions of its major axis, source of variation in excentricity, 17; slow revolution of its nodes, decrease in its inclination to the ecliptic, 19.

—— with his satellites, an epitome of the solar system, 27; effect of his excessive equatorial diameter on their orbits, 28; satellites, libration in, 69; rotation of, 70.

Kane, Dr., Polar Sea discovered by, 94; cold of Northern Greenland marked by, 247.

Kappa Crucis, cluster of coloured stars round, 419.

—— Draconis, seen in the pole of the equator, 88, 89.

Karsten, Mr., impressions made on glass by electricity, 221.

Kasan, summer and winter mean temperature of, compared with Edinburgh, 246, 247.

Kater, Captain, approximate length of the pendulum, determined by, 89.

Kempelen, M., speaking-machine invented by, 151.

Kepler, paths, revolutions of planets discovered by, 5; his law regarding the mean distances of planets from the sun, 19; law of, applied to calculating distances, 53, 54; rapidity of planetary revolutions determined by his law, 66; his law finding areas described by heavenly bodies, referred to, 360.

Kew, balloon ascent from, 119.

Knoblauch, position of the magnecrystallic axis proved by, 349.

Knowledge, limited nature of human, 2.

Kotzebue, stratum in the ocean discovered by, 101.

Kratzenstein, M., instrument invented by, articulating words, 151.

Kupffer, M., observations of, on temperature, 246.

La Basilicata, earthquake in, 234.

Lacaille, his globular nebulous cluster, 414; nebula, 418.

La Grange, his investigations into the stability of the solar system, 20, 21; greatest discovery of, 23.

La Hire, phases in comets observed by, 380.

La Place, stability of the solar system proved by, 20; principle in astronomical calculations established, 23; angle of inclination fixed, 24; his theory accounting for acceleration in the moon’s mean motion, 36, 37; result of observations compared with his theory of Jupiter’s satellites, 55; theory of planetary motion, 65, 66; universal epoch proposed by, 87; scientific observations complementing historical records, 87; date fixed by, for the lunar tables of the Indians, 88; justifies Newton’s theory of tides, 96; density of a liquid column estimated by, 114; action of the earth on a comet, 359; change in a comet’s orbit, 361; cause of error in Clairaut’s calculation pointed out by, 363; opinion of, as to the comet of 1682, 378.

“Lake of the Gazelles” ascribed to an effect of reflection, 157.

Lalande, epochs of conjunctions computed by, 42.

Lambda Herculis, general motion of the stars determined by, 405.

Land, dry, comparative extent of, on the globe, 242, 244; extent of, in diametrical opposition, 244.

Landscapes in chiaroscuro, produced by photography, 207.

Languages, resemblances and analogies between, 255, 256.

Lapland, arcs of the meridian measured in, 48; transit of Venus observed in, 53.

Laroche, M., his experiments on transmission of radiant heat, 259, 261.

Lassell, Mr., satellite of Saturn discovered by, 32; observations of, on Uranus’ satellites, 33; his discovery of Neptune’s satellite, ib.; observations on Saturn’s rings, 66.

Latent heat, energetic action of, on matter, 275-277.

Latitude, the, of a planet defined, mode of obtaining, 9, 10; cause of periodical inequalities in, 15; perturbations from action of the perpendicular force, 18; moon’s motion in, disturbed, 35; effects of disturbance, 38; data of, used in computing a planet’s place in the heavens, 58-60; conditions ensuring the invariability of geographical, 76, 77; change effected by nutation in, 81; climate not invariable in the same, 239; degrees of, where diminution of mean heat is most rapid, 244, 245; the same mean temperature in different, 246, 247; of wine-growing, 250; magnetic storms varying with, 345.

Layang, observations made at, 1100 years before the Christian era, 88.

Le Sueur, specific diversity of marine animals observed by, 254.

Le Verrier, M., principle of La Grange applied by, 21; zone of instability found, ib.; discovery of Neptune, 62; his observations on atmospheric waves, 122; comets identified by, 362; his table of comets’ orbits, ib.

Lenticular nebulæ, 409; haze surrounding the sun, 412.

Leo, nebulous system in, 417.

Léon-Faucault, M., velocity of light in air and water ascertained by, 202.

Lerius, banks of algæ found by, 253.

Leslie, Professor, compression of air calculated by, 78; experiments on radiation of heat, 257.

Lexel, observations of, on the comet of 1770, 361, 362.

Libra, the five great planets in conjunction near, 42.

Librations of the moon, of Jupiter’s satellites, 69; of α Centauri, 399.

Lichen, red, growing on snow, 249.

Light, rate of its velocity, 31; truth deduced from the uniformity of its velocity, 32; from the aberration of, ib.; period required to reach the earth from α Centauri, 54; action of the atmosphere on, 153; conditions regulating the transmission and reflection of, 156; loss of, transmitted by the horizontal stratum, 157; effects of transmission through the atmosphere, 158; Newton’s analysis of, 159; Brewster’s, 161; phenomena disproving Newton’s theory, 167, 168; undulatory theory, 168-170; conditions affecting its intensity and colour, 170; experiments testing the mutual relations of colour and, 171-175; law of its absorption identical with a law of motion, 175-177; repeated vibrations producing the sensation of, 178; polarized, defined, 179; modes of polarization, substances polarizing, 179-185; accidental polarization of, 195; degraded, or fluorescence, 196; objections to the undulatory theory analyzed and disproved, 199-202; comparative velocity of, in air and water, 202; pictures produced by reflected, 203-207; rays of, independent of heat, 214, 215; comparative amounts of solar and lunar, 225; different measures of illumination from, 227; influence of, on vegetation, 249; colour developed without the influence of, 253; separated from heat by Melloni, 265; produced by accumulation of heat, 270; law regulating the force of artificial, 279, 280; electrical, 288, 289; produced by voltaic electricity, 302; stratifications of the electric, 306; influence of magnetism and electricity on, 319, 320; of comets, 379-381; of the fixed stars, 401-404.

Lightning, development of heat exhibited by, 276, 277; experiment showing the velocity of, 289; theory of, 292; the back stroke, ib.; force of the direct stroke, 293; sheet, 294; effect of, on the compass, 312.

Lime, carbonate of, variety of form in its crystals, 107; invariable form ultimately assumed by, 109.

Lines of magnetic force, 338, 339; experiment ascertaining the form of, 339, 340; terrestrial, 341, 342; extensive courses of, 344; a connected system, 345; diamagnetic, 348.

Lion, the, conjunction of planets in, 42.

Liquids, balance of forces constituting, 104, 105; action of capillary attraction on, 113-116.

—— possessing the property of circular polarization of light, 190, 191-193.

Liquids, conditions affecting the transmission of radiant heat by, 263; evaporation from, 269; expansion of, by heat, 271; propagation of heat in, 273; action of heat as a mechanical force on, 275-277.

London, retarding of the tidal wave between Aberdeen and, 94.

——, pendulum vibrating in its latitude, a standard of measurement, 89; fulgorites exhibited in, 293.

Long, Dr., his attempt to measure distances of fixed stars, 388.

Longitude, mode of reckoning mean and true, 9; of the perihelion and of the epoch defined, 10; cause of periodical perturbations in, 14; calculation from the moon’s influence on the sun’s, 55; data of, used in computing a planet’s place in the heavens, 58-60; change effected by precession and nutation in, 81.

Lloyd, experiments of, in polarization of heat, 264.

Lubbock, Sir John, theory of planetary motion completed by, 64; his theory of shooting stars, 423.

Lumière cendré, definition of, 227.

Lunar distance, defined, 43.

—— theory, mean distances obtained from, 43.

—— tides of the terrestrial atmosphere, 121.

Lundahles, M., motions of heavenly bodies investigated by, 405.

Lupus, position of, 390.

Lussac, Gay, M., uniting of gases by volumes discovered by, 111; ascent of, in a balloon, 118; course of a lightning flash ascertained by, 292.

Lutetia, diameter of, 56.

Lyell, Sir Charles, his theory of changes of temperature in the northern hemisphere, 75; annual number of volcanic eruptions computed by, 233; volcanic phenomena related by, 234.

Lyncis 12, a triple star, 395.

Lyra, a variable star in, 391; a double star, 395; nebula, 410.

Machinery, relations of, to force, 353.

Mackintosh, Sir James, quotation from, illustrating the essential advantages of study, 1.

Maclear, Mr., parallax calculated by, 387.

Madeira, vegetation of, 252.

Madras, Saturn’s ring discovered from, 66.

Magellanic clouds, the, 417, 418.

Magnecrystallic action, 349; temperature affecting, 352.

Magnetic bodies, difference in power of, 347.

—— elements, the three terrestrial, 343.

—— equator of the earth, 343.

—— meridian, the, mean action of forces determining, 343.

—— poles of the earth, 343.

—— storms, 344; varying with latitude, 345, 346.

Magnetism, source of, 318; producing electrical phenomena, 322, 323; rotatory motion a source of, 330; classification of substances, with regard to their susceptibility of, 332; residing in substances after two manners, 335; experiment illustrating the forces of, 338; antithesis, its general character, 339; form of its lines of force, 339, 340; analogous properties of electricity and of, 340, 341; terrestrial, 342-347; connexion between solar and terrestrial, 344; action of, in crystals, 349-351; influence of temperature in, 352; affecting elasticity of matter, 352, 353; a property of the ethereal medium (?), 356, 357.

——, electro, discovery, importance of the science, 312; rotation effected by, 313, 314; electric intensity measured, 315; action of currents in, defined, 316; Ampère’s theory of, 317, 318; causing rotation of polarized rays, 319; action of, on light, 320; accidental combinations, 342; influencing metalliferous deposits, 346.

Magneto-electricity, principle suggesting, 322; machine constructed on the principle of, 325; relation of heat to, 329.

Magnets, influence of, on electric light, 307; fish possessing the power of making, 311; effect of an electric stream on, 312-314; obtained by electricity, 315; power of electro, measured, 315; cylinders acting as, 316, 317; producing electrical effects, 322, 323; evolving electricity by rotation, 330; classification of substances in relation to, 332; polarity a property of, 336; effect on themselves of imparting paramagnetism, 337; experiment showing the lines of force of, 338; properties of, indestructible by subdivision, 338, 339; the earth reckoned among, 342; planets reckoned among, 346; action of an electro, on copper, 351.

Maguire, Captain, his observations on magnetic storms, 345, 346.

Malo, St., rising of the tide at, 98.

Malus, M., discovery of polarization of light by, 195; attempts of, to polarize heat, 264.

Malta, observations on Saturn’s rings made at, 66.

Manchester, thunderstorm near, in 1835, 292.

Mankind, distinct tribes of, 255; limited perceptions of, 267.

Marcet, M., rate of increase in temperature below the earth’s surface calculated by, 230.

Marco Polo, atmospheric effects observed by, in ascending mountains, 118.

Marine plants, laws regulating their distribution, 252, 253; animals, specific localities of, 254.

Mariner’s compass. See Compass.

Mars, used in illustrating the possible effects of the radial distributing force, 19; telescopic planets between Jupiter and, 20, 21; diameter of, 21; mean distance from the sun, ib. note; eclipse of Jupiter by, 42; parallax found by observing his oppositions, parallax of, 53; internal structure, 58; astronomical tables of, 63; climate of, 225; approach of the comet of 1770 to, 362; comets having their perihelia in his orbit, 381.

Marseilles, transit of a comet across the sun observed from, 374.

Masses, of the sun, of planets and their satellites, computations finding, 55, 56.

Mathematics, use of, in the study of astronomy, 2.

Matter, theory of its constitution, 102; hypotheses as to forces uniting its particles, 103, 104; counterbalancing action of elasticity and cohesion, 105; crystallization common to all forms of, 109; indestructibility of its particles, 110; composition of unorganised bodies, subject to permanent law, 110, 111; agent composing or decomposing, 112; mode of ascertaining the magnetism of, 335; increatable, indestructible, 353; proportion of, to spare, 424.

Matteucci, M., effect of electricity on polished silver observed by, 221; experiment showing polarization by electricity, 286; doubts of, on the polarity of diamagnetism, 348 note; experiments on magnetic action in crystals, 350; observation on the action of compression, 352.

Maury, Lieutenant, calms named by, 123.

Measurement of astronomical distances, formula assisting, 43.

Mechain, M., Encke’s comet seen by, 365.

Mechanical equivalent of heat, 275.

—— engines, incapable of generating force, 279.

Mediterranean, the, conditions of, shutting out the tidal wave, 98; hurricane in, divided into two storms, 126; vegetation of, 252.

Medium, ethereal, transmitting magnetism, 344; density of, 356; probable relations of, to gravity, ib.; experiment testing its magnetic properties, 356, 357; functions of, 357; pervading the visible creation, 358; unsolved question touching, 365; a cause of accelerated revolutions of comets, 366, 367; direction of its increase in density, 367.

Medium occupying space, 424.

Medusa tribes, the, phosphorescent brilliancy of, 295.

Melloni, M., experiments of, in photography, 214; his application of the principle of thermo-electricity, 333; experiments of, in transmission of heat, 258-263; fixing the maximum of heat in the solar spectrum, 264; in polarization of heat, 264-266; light separated from heat by, 265.

Melville Island, height of the thermometer in, in January, 247.

Mercury, inclination of his orbit to the plane of the ecliptic, 21; eclipse of, 42; cause of his rotation unknown, 65; ellipticity of his orbit compared with the terrestrial, 74; climate of, 226; comet revolving between the orbits of Pallas and, 367; attraction of, determining a comet’s orbit, 369; comets revolving in his orbit, 381; velocity of, 400.

——, propagation of heat in, 273; rotating by electricity, 314.

Meridian, constant, of high water, 92.

——, mode of determining the magnetic, 343.

Meridians, size and form of the earth determined from, 46; measurement of arcs, 47; anomalies from local attraction, 48; result of the computations, 48, 49; permanent, of the moon, 69, 70.

——, magnetic, influencing the direction of metallic veins, 346.

Messier, comet of 1770 observed by, 361; Encke’s comet seen by, 365; nebula described by, 409.

Metallic salts, action of the rays of the solar spectrum on, 203.

—— springs used in construction of musical instruments, 143; rods giving musical notes, 144.

Metallic surfaces, polarized light reflected from, 193; plates, impressions on, from bodies in contact with, 220.

Metals, expansion of, by heat, 271; propagation of heat in, 274; transmission of electricity by, 284; electricity developed by oxidation of, 298; determining the appearance of a spectrum of voltaic flame, 303; distilled in the voltaic arc, 304, 305; electro-plating of, 309; properties of, modifying electric susceptibility, 333; magnetism an agent in the formation of, 346.

Meteor, the bursting of a, 118.

Meteors, 420; theory of, 421-423.

Meteoric stones, proofs of their foreign origin, 420, 421; shower of, 421, 422.

Mètre, adopted by the French as their unit of linear measure, 89.

Mica, polarization by induction effected with, 286.

Milky Way, the, described, 385; Sir John Herschel’s description, 385, 386; “Coal Sacks,” 386; stars composing, 286, 287; zone of stars crossing, 390; position of variable stars with regard to, 395; crowding in, apparent only, 405; orbit in the plane of, 406; relation of, to the stellar universe, 407; nebula resembling, 409; its quarter of the heavens, 414, 415; dividing the nebulous system, 416, 417; great nebula in, 418; remote branches of, 419.

Minerals, possessing the phosphorescent property, 294.

Mines, cause of increased temperature in, 229; green plants growing in, 253.

Mira, periods of its fluctuations in lustre, 390.

Mirage, supposed cause of, 157.

Miraldi, rotation of Jupiter’s satellite determined by, 70.

Mitscherlich, M., his experiments on crystals, 107; discoveries, 108; experiments of, in expansions of crystals, 272.

Mocha, meteors falling at, 421.

Moignot, M., crystals compressed by, 189.

Moisture, an indispensable requisite for vegetation, 248; transmission of electricity effected by, 284, 288.

Molecular polarity, produced by electricity, 282; attraction, electricity developed by destruction of, 284.

—— structure affecting transmission of electricity, 303.

—— vortices, hypothesis of, accounting for the absorption of light, 177.

Molecules, material, attraction and repulsion of, 103; effect of elasticity and cohesion on, 104-106; uniting to form crystals, 107-109; extreme minuteness of ultimate, 110; of ether, modes of their vibration in natural and polarized light, 193; in fluorescent light, 196, 197; images traced by the mutual action of, 219-222; arrangement of, connected with magnetism, 350-352.

Mollusks, distinct species of, 254.

Monocerotis 11, a triple star, 395.

Monsoons, theory of the, 123, 124.

Months, antiquity of, as a measure of time, 85.

Moon, the, force restraining, 4, 5; mean distance of, from the earth, 4; results effected by her nearness to the earth, 7; annual rate of decrease in her orbit’s excentricity, 17; average distance of, from the earth’s centre, period of her circuit of the heavens, 34; her periodic perturbations, 35-38; causes assigned for acceleration of her mean motion, 36, 37; eclipses of, 39, 40; longitudes determined by observations of, 42, 43; her mean horizontal parallax, 52; sources whence her mass may be determined, 55, 56; her diameter, 56; rotation of, 68; librations, 69; mountains, 70; precession resulting from her attraction, 79-81; influence of, producing tides, 91, 92, 96-98; period of her declinations, 97; atmospheric equilibrium disturbed by her attraction, 121; cause of her apparent increased magnitude in the horizon, 158; photographic image of, 214; comparative amount of light emitted by, 225; cause of the rarity of her atmosphere, 226; increased intensity of light at full, ib.; effect of the terrestrial atmosphere on heat radiated from, 227; cause of acceleration in the mean motion of, 366; light reaching the earth from, 404.

Moorcroft, herbarium collected by, 250, 251.

Moser, Professor, mutual influence of bodies in contact tested by, 219, 220.

Mossotti, Professor, his analysis to prove the identity of the cohesive force with gravitation, 103, 104; his definition of gravity, 355.

Motion, a law of the universe, 274; perpetual, impossible, 279.

Mountains, anomalies in measurement caused by, 48; rarity of atmosphere on, 118; cause of perpetual snow, 119; modes of determining heights of, 120; becoming new centres of motion in hurricanes, 126; influence of chains on temperature, 241, 242; cause of éboulemens in, 271; tops of, fused by lightning, 293.

——, lunar, effect of solar rays passing between, in eclipses, 41; influence of, on the moon’s motions, 96; three classes of, 70.

Mu Herculis, direction of solar motion with regard to, 406.

Multiple systems of stars, 395.

Mundy, Captain, mirage described by, 157.

Music, comparison instituted of sympathetic notes in, 2; regulated undulations of sound producing, 142; instruments of, 143; experiments by means of vibrating plates, 144-146; sympathetic vibrations, 147, 148; experiments showing, 148, 149.

Musical instruments constructed by Professor Wheatstone, 143.

Naples, comet discovered from, 370.

Nautical Almanac, computations for calculating longitudes, 43; time calculated by, 84.

Navigation, importance of lunar motions in, 42; laws of storms to be observed in, 127, 128.

Neap-tides, 96, 99.

Nebulæ, number and general aspect of, 407; catalogues, 407, 408; classes, 408; irregular, 408, 409; of definite form, 409; spiral, 409, 410; annular, 410, 411; elliptical, double, 411; distance of a nebulous star discoverable, 411, 412; aspect and colour of planetary, 412; elliptical common, 413; globular clusters, 413-415; resolution of, 415; star clusters, 415, 416; probable law of motion, 416; distribution of, 416, 417; the Magellanic clouds, 417, 418; round η Argûs, 418, 419; remote systems, 419; invisible solar, 421; meteors falling from, 422.

Nebulous appearances of a comet, 364; extent of, matter surrounding a comet, 373; its variable brilliancy, 374; appearances round the sun, 412.

—— stars, 411, 412.

Needle, magnetized, effect of Voltaic electricity on a, 312, 313; suspended by means of electricity, 314; condition of its deviation by an electric current, 317.

Negative electricity defined, 282; mode of exciting, 283.

—— impressions in photography, 204.

Neptune, periodical variations in his orbit, 22; revolution of his satellite from east to west, 33; remoteness of, 54; anticipation of discovery, 61; orbit and motions of, determined, 62; his diameter, mean distance from the sun, 63; temperature of, 225; action of, on Halley’s comet, 363.

Neutral phosphate of soda, its crystals, 109.

New Mexico, monsoons occasioned by its deserts, 124.

Newton, Sir Isaac, steps of his argument for the universal influence of gravitation, 3; his discoveries of modes of attraction, 4; motions of bodies projected in space, ascertained by, 5; form of a fluid mass in rotation ascertained, 45; problem occupying astronomers since, 64; discrepancy between his theory of tides and observations, 96; compound nature of white light proved by, 159; his analysis of the solar spectrum disputed, 161; his theory of light disproved, 167; measurements of coloured rays, 172, 173; scale of colours, 174; decisive experiment disproving the theory of light, 202; remarks on the transmission of gravity, 355.

Niagara, the falls of, not independent of the influence of astronomy, 1.

Nickel, sulphate of, change in its crystals, when exposed to the sun, 107.

Niepcé, M., photographic pictures rendered permanent by, 204; discovery in photography suggested, 207; colours of images of the sun taken, 213; experiments by, on saturation of substances with light, 296.

Nimes, discovery of a telescopic planet at, 21.

Nitrogen, proportion of, in the atmosphere, 117; spectrum from, 303; iron volatilized by the Voltaic arc in, 304; unaffected by magnetism, 344.

Nobili, M., direction of electric currents ascertained by, 333.

Nodes, ascending and descending, of a planet defined, 9; movement of their lines in secular disturbances, 14; advance and recession of, 18; supposed recession of, on the equator of the solar system, 24; of the moon, period of their sidereal revolution, 37; secular inequality affecting, 38; influence of, on eclipses, 39; cause of their rapid motion, 55; points of rest on a vibrating string, 141; in the vibrations of an undulating column of air, 142; in vibrations of solids, 147.

Non-conductors of electricity, 284, 285.

Non-electrics, 285.

North Atlantic, the, winds in, 124.

—— Polar Ocean, tide in the, 94.

Norway, course of the tidal wave to, 94.

Notes in music, 142, 143.

Nubecula, Major and Minor, 417, 418.

Nucleus, of Halley’s comet, changes in its aspect, 364; disappearance of, in Encke’s, 369; division, in Biela’s, 369, 370; diaphanous, 373; solidity of, tested, 374; of a spiral nebula, 409.

Nuremburg, observations on a comet from, 370.

Nutations produced by the moon’s nearness to the earth, 7; in Jupiter’s equator, 29; in the planetary axes, 66; effect of, on the pole of the equator, longitudes and latitudes altered by, 81.

Nysa, nearness of its orbit to the earth, 21.

Oaks, range of, near the equator, 250.

Occultation, central, by Halley’s comet, 364; geographical position ascertained by, 384; prospective, by a sun of α Centauri, 400.

Occultations of stars, 42, 43.

Ocean, the, density and mean depth of, 51; mean density, compared with the earth’s, 77; its form in equilibrio, when revolving round an axis, 92; solar and lunar attraction disturbing its equilibrium, ib.; inequalities in periodic motions, 93; motions of the tidal wave in 95; stability of its equilibrium, 100; circulation of currents in, ib.; stratum of constant temperature in, 101; zones of, ib.; decrease and increase of temperature with depth, 231; absorption and radiation of heat by, 242; electricity evolved from, 291.

Oceans of light and heat, processes producing, 225.

Ochotzk, the sea of, depression of the barometer observed in, 120.

October, 1832, position of Saturn’s rings in, 67.

Olbers, M., computations for a comet by, 367; period of his comet, 370; comet of 1811 observed by, 374.

Opaque bodies, mode in which heat is developed in, 227.

Ophiuchi 70, anomalies in the motions of, 400.

Ophiuchus, clusters of the Milky Way between the Shield and, 387; new star disappearing from, 393.

Optic axis, the, of crystals, 183; phenomena exhibited by transmission of a polarized ray along, 187, 188; affected by compression, 189.

Orbit, the, of the earth, attraction intensified by its diminished excentricity, 37; excentricity of, affecting temperature, 74, 75; crossed by comets, 368.

—— of the moon, force ruling, 4; its excentricity, 34; changes in, 35; its inclination to the plane of the ecliptic, 79.

—— of a nebula, 415.

—— of the solar system, 405, 406.

Orbits of comets, subject to variation, 361; examples, 361-363; prospective changes in, 369, 370; of Donati’s, 379; forces determining their forms, 382, 383.

—— of double stars, 396-400.

—— of planets, force regulating a planet’s velocity in, 8; measurement of their excentricity, 9; seven elements of, determining their position in space, 10; unequal movements in, 15; variation from elliptical to circular, 17; secular variations of, in inclination to the plane of the ecliptic, 18, 19; stable and unstable in form, 21, 22; influence of the ethereal medium on, 22; principle facilitating observations on secular inequalities, 23, 24; revolutions of Saturn compared with Jupiter, 25; periodic inequality increased by secular variations in their elements, 26; comets revolving in, 381, 382; cause of diversity in form of, 382.

Orbits of satellites, forms of Jupiter’s, 27; their inclinations, 28; inclinations of Saturn’s, 32; positions of Uranus’s, 33; forms of data in computing a planet’s place in the heavens, 59.

Orinoco, the cataracts of the, heard by day and by night, 135; area occupied by forests on, 243.

Orion, the Milky Way between Antinous and, 385, 386; position of, 390; variable star in, 393, 394; multiple system in, 395; nebula in, 408.

Oersted, Professor, discovery of, suggesting the theory of electro-magnetism, 312; science founding the reputation of, 316.

Oscillations, wide-spreading, produced by gravitation, 2; mechanical principle affecting small, 11; of the sines and cosines of circular arcs, 20; invariable plane whence they may be estimated, 24; of the pendulum retarded, 32; of the pendulum, experiments founded on, 50, 51; experiments testing the earth’s density, 57; a measure of time, 83; produced by tides, 95, 96; instruments measuring atmospheric, 113; barometer affected by periodic atmospheric, 120, 122; of ears of corn, 129, 130; producing musical notes, 140-142; instances of forced sympathetic, 148; causing vicissitudes in climates, 247; of the pendulum, disturbed by effects of temperature, 272; measuring variation of electrical intensity, 287.

Otto, M., motions of the heavenly bodies observed by, 405.

Oxidation of metals, electricity developed by, 298; by the Voltaic discharge on polished silver, 305.

Oxides decomposed by electricity, 307; alkalies resolved into metallic, 307.

Oxygen, in crystals, 109; proportion of, in water and carbonic oxide, 111; in the atmosphere, 117; chemical combination with, evolving light and heat, 270; action of electricity on, 284; electricity afforded by combination of metals with, 298; spectrum from, 303; separated from water by electricity, 307; paramagnetic, 344.

Ozone, produced by electricity, 284.

Pacific Ocean, mean depth of, 77; course of tidal waves down, 93; mean depth of, 96; currents, 100.

Paderborn, fulgorites from, 293.

Pallas, inclination of its orbit to the ecliptic, 10; diameter of, 21; astronomical tables, 63; ellipticity of its orbit compared with the terrestrial, 74; height of its atmosphere, 226; comet revolving between the orbits of Mercury and, 367.

Pan’s pipes, vibrations in the air passing over, 142.

Parabolic motion, ratio of forces procuring, 382.

Parallax of the sun, circumstance favourable to its correction, 21.

—— of an object defined, 43.

——, definition, mode of ascertaining, 52; distances computed from, 52-54; calculation from the moon’s horizontal, 55.

—— of fixed stars, 387-390.

—— of meteors, 421, 422.

Paramagnetic substances, 335, 336.

Paramagnetism defined, 335; substances it is resident in, 336; modes of imparting, ib.; a dual power, ib.; imparted by induction, 337; law of its intensity, 338; a property of oxygen, 344; in antithesis to diamagnetism, 347; neutral substances obtained by combinations of diamagnetism and, ib.; Dr. Tyndall’s experiments on polarity of, 348; dependent on arrangement of molecules, 350, 351; affected by compression, 351; truth establishing its identity with diamagnetism, 356, 357.

Parathermic rays, analyzed by Sir John Herschel, 217-219.

Paris, variation in length of the pendulum at, 51; mean annual temperature, 228; temperature of an Artesian well in, 230.

Paths of comets, 359, 360; secrets disclosed by their excentricities, 365.

Parry, Sir Edward, turned back by the Polar current, 101; mean temperature calculated from observations of, 245; thermometer at Melville Island marked by, 247.

Pauxis, the Straits of, ebb and flow of the sea in, 98.

Peel, Sir William, thunderstorm experienced by, 293, 294.

Pegasus, nebulous region of, 417.

Pendulum, the, principle equalizing its oscillations, 50; the earth’s figure calculated by, 50, 51; experiments ascertaining the earth’s density, 57; isochronous, a measure of time, 83; a standard of the measure of extension, 89; the, a connecting link between time and force, 94; inventions to neutralise the effects of temperature, 272.

Penumbra, in lunar eclipse, breadth of space occupied by, 40.

Perigee, of the lunar orbit, period of its revolution, 37, 38; cause of its rapid motion, 55.

——, solar, periods of its coincidence with the equinoxes, 86.

Perihelion of a planet’s path defined, 16.

—— of the earth’s orbit, its position regulating the length of seasons, 74.

Periodic inequalities of planets, 13, 14; law from which they are deduced, 24, 25; of Jupiter’s satellites, 28, 29; lunar, 35.

Perkins, Mr., experiments of, testing the laws of compression, 78.

Peron, M., specific diversity of marine animals asserted by, 254.

Perpendicular force, the source of periodic inequalities, 15; effects produced by, 18.

Perpetual motion, invariable proportion between heat and force precluding, 279.

Perseus, variable star in, 390, 391.

Peters, Mr., comet discovered by, 370; parallax of α Lyræ, 388, 389; distances of fixed stars calculated, 389; his theory of Sirius’ irregular motions, 392; sun’s motion proved by, 405.

Petit, M., observations of, on meteoric satellites, 423.

Peru, arcs of the meridian measured in, 48.

Phases of the moon, regulating returns of eclipses, 39.

Phenomena, of effects of light in eclipses, 41, 42; applied to computing longitudes, 43; caused by tidal oscillation, 96; from force of cohesion, 106, 107; of capillary attraction, 115; produced by refraction and reflection, 155-157; by polarization of light, 186-190; exhibited in fluorescence of light, 196, 197; resulting from interaction of rays and molecules, analogous to effects of photography, 219-222; phosphorescent, 295, 296; of galvanism, 310; of magnetism, 335, 345-348; magnecrystallic, 349, 350; exhibited by comets, 363, 364, 369, 370, 372-376; by the Milky Way, 385-387; by variable stars, 390-393; by double stars, 397-401; by nebulæ, 409-415, 417-419; by meteoric showers, 421, 422.

Phosphorescence, rays of the solar spectrum exciting, 216; cause of, in the solar spectrum, 217; excited by electricity, 294; fish possessing the property of, 295; the glow discharge, 295, 296; experiments investigating the nature of, 296.

Photo-galvanic engraving, 309.

Photography, first suggestions, 203; discoveries and improvements in, 204-207; conditions affecting the chemical properties of rays producing, 207, 208; images of the solar spectrum obtained by, 208-210; coloured copy of an engraving, 211; phenomena in, suggesting an absorptive action in the solar atmosphere, 212, 213; chemical energy producing, distinct from light and heat, 214; experiments by means of, testing the properties of rays, 218, 219; experiments on action of light, heat, electricity, producing results analogous to effects of, 219-223.

Photosphere, the, of the sun described, 224.

Physical Sciences, the most extensive example of their connection, mode of its operation, 1.

Pi Herculis, direction of solar motion with regard to, 406.

Pisces, nebulous region of, 417.

Planetary motion, representation of, 14.

—— nebulæ, 409; appearance of, 412.

Planets, paths round the sun described by, 5; law determining their revolutions, ib.; forces adjusting their forms, 6; their motions in elliptical orbits, mean distance from the sun, 8; mode of obtaining the place of, in their orbits, 9; computations giving the place of, in space, 10; disturbances from reciprocal attraction affecting, compensations, 13-19; telescopic, 20, 21; perturbations in the mean motions of, 25, 26; influence of, on lunar motions, 36; eclipses and conjunctions of, 42; formula finding their masses, 55; their diameters, 56; mass of the telescopic, compared with the moon, ib.; comparative density, 58; method of computing their places, 58-64; discovery of, 61-63; exploded theory touching telescopic, 63; periods of their rotations, 66; variation and position of the plane of the ecliptic produced by, 79; its effect on the equinoctial points, 80; climates of, 225, 226; probably magnets, 346; constant velocity of their mean motions, 366.

Plants, distribution of known species over the globe, 249, 250.

Plates, vibrating, experiments by means of, 144-146.

Plateau, M., experiments of, on colour, 165, 166.

Platina, incandescent, used as a source of heat, 260.

Platinum, experiment producing spontaneous combustion of, 112, 113.

Playfair, Professor, quoted in reference to La Grange’s discovery, 23.

Pleiades, the, nebulous stars, 415.

Plücker, Professor, discoveries of, in the action of magnetism in crystals, 349.

Plumb-line, deviations of, from local attraction, 48; earth’s density calculated from a deviation of, 58.

Poinsot, M., La Place’s discovery extended by, 23; comparison by, 24.

Point, ready escape of electricity from a, 288.

Poisson, M., decisions of, on the phenomena of capillary attraction, 114.

Polar basin, probable temperature of, 245, 246.

—— star, change of position in the, 81, 82.

—— vegetation, contrasted with tropical, 248.

Polarity, produced by electricity, 282; of magnets defined, 336; induced in iron, 337; its antithetical manifestations of, 339; invariably dual, 341; of diamagnetic substances, 347, 348.

Polarization of light, definition of, 179; refracted by various substances, 180-183; by reflection, 184; angles of, 185; phenomena exhibited by transmission through analyzing media, 186-188; circular, 189-191; theory of circular and elliptical, 192, 193; substances producing, 193, 194; theory of coloured images formed by, 194; accidental, 195; discovery of, ib.; degraded light incapable of, 198; communicating electricity, 220; plane of motion of vibrations in, 223.

Polarization of heat, first attempts, 264; successful experiments, 265-267.

—— of electricity by induction, 286.

——, experiment showing the action of magnetism on, 319; affected by mechanical compression, 352.

Poldice mine, the, temperature of the water pumped from, 229.

Poles, the, cause of the flattening of a spheroidal mass at, 6; diameter of Jupiter at, 27; experiment determining the increase of gravitation towards, 49, 50; the, drifting of ice from, 100, 101; of maximum cold, centres of the isothermal lines, 245, 246; nature of magnetic force distinguished by, 332; four terrestrial, of maximum magnetic force, two magnetic, 343.

Pollux, an optically double star, 401.

Port Bowen Harbour, transmission of sound across, when frozen, 136.

Positive electricity, defined, 282; mode of exciting, 283.

—— impressions in photography, 204.

Pouillet, M., his estimate of the mean temperature of space, 119; quantity of solar heat received by the earth computed by, 238; data furnished by, to Professor Thomson, 279; development of electricity investigated by, 291.

Powell, Baden, substances producing elliptical polarization enumerated by, 193; dispersion of light accounted for by the undulatory theory, 200, 201; experiments in transmission of radiant heat, 262; attempts to polarise heat, 264.

Power, Mr., undulations producing fluorescent light computed by, 197; law of solar rays acting on media, 198.

Præsepe, the, in Cancer, 415.

Precession, a, in the equinoxes of planets, its cause, 66; mean, of the equinoctial points, defined and calculated, 80; influence of, on the pole of the equator, on longitudes, 81.

Pressure, electricity elicited by, 283, 284; law of electrical, 288.

Principato Citeriore, earthquake in, 234.

Prisms, solar spectrum formed by, 159; neutralizing effects of colour, 164; of brown tourmaline, light polarized by, 180; resolution of the pure white sunbeam by, 222; substance of, determining the point of maximum heat in the solar spectrum, 263, 264; electrical light analysed by, 288.

Problem determining the motions of translation of the celestial bodies, 11; of the three bodies, 58; the hardest astronomical, 92.

Procyon, light of, 402.

Proportion, definite, the law of, in mixing substances, 111, 112.

Protoxides of metals, their crystals, 109.

Prussia, Eastern, fulgorites from, 293.

Ptolemy, decrease in the inclination of Jupiter’s orbit since the age of, 19; discovery of the Evection by, 35; Indian lunar tables calculated in his time, 88; horoscope ascribed to the age of, 89; effects of refraction observed by, 155; colour of Sirius in his time, 401.

Quadratures, the equation of the centre in, 9; lunar orbit augmented in, 35; tides affected by the moon in, 96.

Quadrupeds, distribution of distinct species of, 255.

Quartz, crystallised, light polarized circularly by, 189, 190; varieties of polarization exhibited by, 193.

Quebec, extremes of temperature found in, 247.

Quinine, sulphate of, producing fluorescence of light, 197.

Radial force producing periodical changes in relative positions of the heavenly bodies, 15; effects produced by, 16, 17; principle neutralising its ultimate result, 19, 20.

Radiation of heat, laws regulating, 257; universal from substances, 268; natural phenomena resulting from, 269; slow decrease of the earth’s central heat from, 232; influence of, on temperature, 239; power of, in water compared with dry land, 242; of heat, a transfer of motion, 277.

Radii vectores, signification of, 8; areas described by, 10; force disturbing in the direction of, 14, 15.

Ragona-Scina, M., his theory of rayless lines in the spectrum, 163.

Rain, force shaping drops, 106; cause of periodic tropical, 123; region of, 124; theory of its formation, 270; an electric conductor, 292.

Rankine, Mr., his theory of the structure of matter, 104; his theory of the absorption of light, 177.

Rays, common nature and common properties of, 268.

—— of heat, existing independently of luminous, 257; laws of transmission of, 258; analogy between transmission of luminous rays and, 259; temperature of their source affecting transmission, 260; varying in nature with their origin, 261; transmitted through coloured glass, 262; traversing various media, ib.; subject to refraction and reflection, 263; polarized, 265-267; absorption and reflection of, 268; rotation of polarized, caused by magnetism, 319.

—— of light, bent by passing from rare into dense media, 153; partial and total reflection of, 156; loss of, by obliquity of incidence, 158; theory of their transmission and absorption, 159-161; comparative refrangibility of, 163; experiments on dispersion of, 164; principle determining their colour, 170, 171; transmission of, in glass or water, 177, 178; conditions of polarized, 179; double refraction, 181-183; polarized by reflection, 184, 185; coloured images produced by interference of, 194, 195; internal dispersion of, 195-198; heat, light, chemical action, independent properties of, 214, 215; undulations constituting, 223; conditions modifying the power of solar, to produce heat, 237; transmitted independently of calorific rays, 258; magnetizing of polarized, 318, 319.

Rays, solar, effect produced by their refraction in lunar eclipse, 40; passing between lunar mountains in solar eclipse, 41.

—— of the solar spectrum, their chemical properties, 203; varying chemical energy, 207, 208; varying nature of their action, 208; peculiar chemical action of the red, 209-211; deoxydating and oxydating action of, 211, 212; experiments detailed, 212-215; new, obscure, detected by Sir John Herschel, 217.

Red Sea, the, tide in, 98.

Reflection of waves of sound, 137, 138; of rays at surfaces of strata differing in density, phenomena occasioned by, 156, 157; affecting colour, 160; motion of a ray of light in, 177; light polarized by, 184, 185; elliptical polarization produced by, 193; heat polarized by, 266; of radiant heat from surfaces, 268.

Refraction of the sun’s rays in lunar eclipses, 40; of waves of sound, 138; of light by the atmosphere, 153, 154; mode of estimating, in case of celestial bodies, 155; formulæ obtaining in case of terrestrial objects, ib.; phenomena occasioned by, 155, 156; colours decomposed by, 159, 160; produced without colour, 164, 165; power of, in media affecting the elasticity of the luminous ether, 177; of a polarized ray, 180; double, 181, 182; Fresnel’s theory of, 183; diminished capability of producing fluorescence, 196; capability of, in rays, affecting their chemical action, 209-212; effect of, on the lunar atmosphere, 226; influence of, on transmission of heat, 258; of rays of heat, 261-264; heat polarized by, 266.

Refrangibility, substances diminishing, of light, 196; affecting the chemical action of rays, 209-212; affecting radiation of heat, 257; affecting transmission of radiant heat, 261-263.

Reich, Professor, temperature of mines observed by, 228; mean increase calculated by, 230.

Reptiles, distribution of distinct species of, 254.

Repulsion of electricities, 283; experiments determining the laws of electrical, 286, 287; modes of, in static and in Voltaic electricity, 317; developing comets’ tails, 375-377.

Resistance, a cause of accelerated motion, 367.

Retina, the, action of, in receiving impressions, 166; comparative sensibility of its fibres to light, 178.

Retrograde motion of comets, 359, 368, 373, 379.

Rhodiola rosea, identical species of, found in Tartary and in Scotland, 251.

Rhombohedrons of carbonate of lime, 109.

Richman, Professor, killed by lightning, 293.

Richter, variation in length of the pendulum observed by, 51.

Rings of Saturn, 66-68; Saturn’s, diamagnetic, 347; luminous, surrounding comets, 374, 375; surrounding Donati’s, 379.

Ritchie, Professor, electrical experiments of, 314.

Ritter, M., chemical properties of the solar spectrum observed by, 203; oxydizing effect of red rays, 209.

Rive, M. Auguste de la, rate of increase of temperature in wells observed by, 230.

Rivers, curvature of the land proved by, 46; influence of, on the earth’s rotation, 71; rising of tides in, 98; effect of, in cooling the atmosphere, 243.

Roget, Dr., phenomena of electro-magnetism explained by, 313.

Rome, observations on lunar mountains made at, 70; era fixed at, 85; comet discovered from, 370.

Ross, Sir James, stratum in the ocean discovered by, 101; depressure of the barometer observed by, 120; volcanic region discovered, 232.

Rosse, Lord, nebulæ resolved by his telescope, 407, 408; spiral nebula, 409, 410; annular nebulæ discovered by, 410; nebulous star, 411; planetary nebulæ, 412; nebulæ resolved by, 415.

Rotation affecting winds, 122-127; of winds, 124, 125; of hurricanes, 125, 126; produced by the Voltaic current acting on iron, 305; of stratifications of electrical light, 307; caused by electricity, 313, 314; of light caused by an electric current, 319; of magnets producing electricity, 330-332; changes produced in comets by, 376.

Rotations of the solar system, 7; of the sun, 65; of the planets, 66; of satellites, 68; of Jupiter’s satellites, 70; of the earth, a measure of time, 71; influence of temperature on, 72; axis of, invariable, 76, 77.

Rotatory motion, form indicating, 65; of Donati’s comet, 379.

Roux, M. le, observations on magnetic action in crystals, 350.

Rudberg, M., refrangibility of substances ascertained by, 201, 202.

Ruhmkorff, M., improvements on his electro-inductive apparatus, 328.

Russell, Scott, Mr., velocity of the tidal wave estimated by, 95.

Russia, arc of the meridian measured in, 48; climates of, 244.

Sabine, General, variations in the magnetic elements investigated by, 343, 344.

Sagittarius, comet traversing the constellation of, 379; the Milky Way in, 386; nebula, 414.

Sahara, the, causing monsoons, 124.

—— desert, extent, influence of, on the atmosphere, 243.

Salt, Mr., papyrus sent from Egypt by, 89.

Sand, tubes in, formed by lightning, 293.

Sandy deserts influencing temperature, 243.

Sandwich Land, excess of cold in, over corresponding latitudes, 241.

Sargassa, or grassy sea, found in the Atlantic, 253.

Satellites, intensified action of attraction upon, 7; intimate union of, with their primaries, 26; exceptions to a general law of the solar system, 65, note; rotations equal to the times of their revolutions, 68; comet passing through, 69.

——, Jupiter’s, proportion of their mass to that of their primary, 27; disturbing force of attraction affecting their orbits, 28; periodic and secular inequalities, 28, 29; eclipses, 30; rotation, 70; passage of a comet through, 359; comet nearly approaching, 370.

—— of Saturn, 32; of Uranus and Neptune, 33.

——, mode of computing their masses, 55; comparative density of, 58.

—— of Neptune, 63.

—— of the earth, shooting stars, 423.

Saturn, unequally occurring compensations of disturbance in its motions, 15; disturbing influence of, on Jupiter, excentricity of its orbit compared with Jupiter’s, 17; retarding the revolution of Jupiter’s nodes, 19; invariable plane passing between Jupiter and, 24; observations on the mean motions of Jupiter and, 25, 26; eclipse of, 42; internal structure, 58; astronomical tables of, 60; period of his year, 66; the rings of, described, 66-68; his ring probably diamagnetic, 347; action of, on Halley’s comet, 362, 363; comets having their perihelia in his orbit, 381.

Saurian reptiles, distinct tribes of, 254.

Saussure, M., temperature of mines observed by, 228, 229; lichen discovered by, 249.

Savart, M., his researches and experiments in acoustics, 132, 133; experiments on vibrations of glass rulers, 145-147; experiments showing sympathetic undulations, 148, 149; discoveries on the nature of voice, 152.

Savary, M., orbital elements of a double star determined by, 396; his mode of ascertaining the actual distances of fixed stars, 402, 403.

Scheele, M., chemical changes effected by the solar spectrum observed by, 203.

Schroëter, height of planetary atmospheres calculated by, 226.

Schwabe, M., periodic variation in the solar spots observed by, 344.

Science, its value regarded as the pursuit of truth, 1; errors of the senses corrected by, 32; evidence of its antiquity, 87.

Sciences, mutual relations of forces proving the connexion between, 319-321; analysis proving the whole circle of, kin, 427, 428.

Scoresby, Captain, phenomenon occasioned by refraction observed by, 156.

Scorpio, vacant patch of the Milky Way in, 386; position of, 390; a double star in, 395; nebula in, 414.

Scotland, progress of the tidal wave round, 94.

Sea, the, inappreciable influence of, on the direction of gravity, 77; mean height of snow-line above the level of, 241; comparative extent of, 242.

Seasons, conditions determining the duration of, 74; cause of their unequal periods, 87; theory of the tropical dry and rainy, 123.

Seaweeds, photographic impressions of, 205, 206; luxuriance, deep colours of, 253.

Secchi, Professor, mountains of the moon observed by, 70; photographic image of the moon obtained, 214; temperatures of the sun’s surface estimated, 225; experiments of, in photographing the moon and Jupiter, 226, 227.

Secular inequalities of planets, 13, 14; means of discovering, 24, 25; effect of, on the mean motion of the moon, 36, 37.

—— variations in mean values of the magnetic elements, 343.

Seebeck, point of maximum heat in solar spectrum fixed by, 263; discovery of, 264; relations of heat to electricity discovered by, 332, 333.

Seed-lobes, proportion in the distribution of plants having one or two, 252.

Seleniate of zinc, crystals of, 107.

Senarmont, M., experiments of, in expansion of crystals, 273.

Senses, necessarily inaccurate testimony of the, 281.

September, times coinciding in, 84.

Serpentarius, star in, vanishing, 392.

Shell-fish, their mode of clinging to rocks, 117.

Shield, the, clusters of the Milky Way between Ophiuchus and, 387.

Shooting stars, phenomena of, described, 421, 422; theories of, 423.

Siberia, Eastern, depression of the barometer observed in, 120.

Sidereal times, mean, periods of, 83; measurement of apparent, ib.

Sigma Eridani, period of revolution in, 400.

Silesia, fulgorites from, 293.

Silver iodized, its sensitiveness to impressions, 221.

Sirius, the Egyptian year estimated from, 85; comet’s tail extending from the Hare to, 373; rank of, 384; comparative magnitude, 385; parallax, 389; cause of his irregular motion, 392; change in colour, 401; light, 402; extent of surface, 404.

Smyth, Admiral, his measurement of Etna compared with Sir John Herschel’s, 120; eclipse of a double star observed by, 397; its periodic time determined, 398.

——, Piazzi, heat of the moon felt by, 227.

Snow, cause of perpetual, on summits of alpine chains, 119; causes modifying the height of the line of perpetual, 241; protecting vegetation, 249; radiation of heat by, 257.

Soda, sulphate of, change of form in its crystals, 107; crystals of the neutral phosphate and the arseniate of, 109.

Soil, the, dependence of temperature on the nature of its products, 243.

Solar gravitation, 424, 425.

—— magnetism, its connexion with terrestrial, 344.

—— spectrum, cause of the point of maximum heat varying in, 263, 264.

—— system, the, gravitation of the bodies composing, 5; conditions securing the stability of, 11, 12; proof of its stability, 20; equilibrium of, underanged by the ethereal medium, 22; invariable plane, forming the equator of, 23, 24; question of its revolution round a common centre, 24; properties of its medium, 32; masses of bodies composing, 55, 56; their diameters, 56; uniform direction of rotation in, 65; comparative apparent importance of, in creation, 226; probably magnetic throughout, 346; comets forming part of, 365; possible ultimate destruction of, 372; computations of comets revolving within, 381, 382; paths described by heavenly bodies in, 382, 383; position of, relative to the Milky Way, 385; direction of its motion, 405.

Soleil, M., crystals compressed by, 189.

Solids, conditions reducing molecular particles to, 104, 105; distinctive forms taken by matter in, 106; velocity of sound passing through, 135; change of shape in, accompanying ringing sound, 147; expansion of, by heat, 271.

Solstices, the, solar motion at, affecting the duration of time, 84; the year estimated from the winter, 85; periodical coincidence of the solar perigee and apogee with, 86, 87.

Sothaic period, the, of the Egyptians, 85.

Sound, medium conveying, 129; its propagation by undulations illustrated, 129, 130; conditions modifying the intensity of, musical notes, 131; experiments testing the compass of audible, 132, 133; media modifying the velocity of, 133-137; laws of its reflection from surfaces, 137, 138; undulations of, subject to the laws of interference, 138, 139; laws of the foundation of musical science, 140-143; reinforced by resonance of cavities, 150, 151; repeated vibrations required to produce, 178; different modes of action in undulations producing light and, 199, 200; identical nature of heat and, 280, 281; measuring velocity, 290, 291.

Sounding boards, intensifying musical vibrations, 149; action of, in musical instruments, 150.

South, Sir James, positions of stellar systems measured by, 396.

South pole, the, excess of cold at, 241.

—— Sea islands, height of tides at, 98.

Southern Ocean, rise of the tidal wave in, 93; velocity of the wave, 94.

Spain, meteoric showers off the coast of, 421.

Specific heat defined, 275.

Spectra of gases and flames, their characteristic peculiarities, 163, 164; three superposed, of the pure white sunbeam, 222.

Spectrum, the solar, decomposed into seven colours, 159; colours of, modified by thickness of the medium absorbing, 160; decomposed into three colours, 161; rayless lines in, 162; observations and experiments on rayless lines, 163, 164; experiment of fluorescent light, 197; obtained independently of prismatic refraction, 201; energetic action of, on matter, 203; photographic coloured images of, 208-210; analysis, properties of, experiments, 211-219; complex nature of, 222; produced from diffracted light, 223.

—— of an electric spark, 289.

—— of the Voltaic arc, 303.

Spheres, mode of attraction in hollow and solid, 4; planets partaking the nature of, 7; impulses regulating rotations, ib.; conditions procuring the figure of, 44; formula finding the density, 56; force giving the form of, 106; power of retaining electricity, 288.

Spherical form, the result of cohesion, 106.

Spheroids, influencing attraction differently from spheres, 4; force disturbing attraction in, 27; compression of the terrestrial and of Jupiter’s, computed, 38, 39; of elliptical strata, quantities invariable in, 46; of the sun, 65; effect produced by the attraction of an external body on, 79; power of retaining electricity, 288.

Spiral nebula, 409, 410.

Spots on the sun’s surface, periods of their vicissitudes, 224; amount of heat varying with, 225.

Spring tides, 96-99.

Springs, hot, rising in mines, 229; mean heat of the earth determined from, 238.

Standards of weights and measures, whence derived, 89, 90.

Stars, fixed, the, the solar system probably not independent of, 24; velocity of light deduced from aberration of, 31; vast distances of, 54; precession affecting their longitudes, 80; computations of their positions furnishing historical data, 88, 89; made visible by refraction, 154; peculiar law of light demonstrated by the aberration of, 202; magnitude of the solar system seen from, 226; numbers, classification of, 384; positions, 385; the Milky Way, 385-387; parallaxes and distances of, 387-389; variable, 390-395; missing, 395; systems of multiple, classified, ib.; binary, 395-406 (see Double stars); nebulous, 406-419 (see Nebulæ); seemingly innumerable, 420; meteors, 420-423.

Static electricity, 282: see Electricity.

Steam, formation of, 269; force converting liquids into, 277; measure of its elasticity, 278; question of its being superseded by electricity, 328.

Steel, paramagnetism induced in, 336; conditions of magnetic power remaining permanently in, 337, 338; its elasticity affected by magnetism, 352.

Stephenson, George, quotation from, 279-280.

Stokes, Professor, remarks of, on gradation of colours, 161; experiments on fluorescence of light, 197; his decision with regard to vibrations of polarised light, 223.

Storms, magnetic, 344; varying with latitude, 345, 346.

Strata of the earth, position and comparative density of, 77.

Stratifications, experiments showing, in electric light, 306, 307.

Struve, M., measurement by, 48; his observations on Saturn’s rings, 68; occultation by a comet observed by, 364; comet’s nucleus described, ib.; distance of a fixed star measured by, 388, 389; catalogue of double stars, 396; remarks on colour and light of double stars, 401; sun’s motion proved by, 405.

Stutgardt, natural hot springs used in manufactories near, 231.

Submarine telegraph, 325-327.

Sulphate of magnesia, its crystals boiled in alcohol, 108.

—— of nickel, effect of exposure to the sun, on its crystals, 107.

—— of soda, its crystals, 107.

—— of zinc, experiment on its crystals, 108.

Sulphuretted hydrogen gas, its constituent parts, 111.

Sumbawa, volcanic eruption of, 233.

Summer, mean temperature of, varying in the same latitude, 246, 247; atmospheric electricity in, 291.

Sun, the, law regulating his attraction of heavenly bodies, 5; effect of his attraction on planetary orbits, mean distance of planets from, 8; importance of his magnitude in the solar system, 12; disturbances in the relative positions of planets and, 14; force modifying his intensity of attraction, 16; resistance offered by, to the power of disturbing forces, 20; periods of conjunctions of Jupiter, Saturn, and, 25; influence of, on lunar motions, 34, 35; action of the planets reflected by, 37; eclipses of, 40, 41; supposed constitution of, 41; his atmosphere, 42; mode of finding his parallax, 52, 53; mean distance from the earth, 53; mass of, 55; diameter, 56; comparative density, attractive force, 56, 57; astronomical tables of, 63; deductions from his rotation about an axis, period of, 65; attraction of, producing a precession of the equinoxes, 79, 81; returns of, a measure of time, 83-85; divisions of time, dependent on revolutions of the major axis of his orbit, 86, 87; action on tides, 92, 97; disturbing the equilibrium of the atmosphere, 121; dry and rainy seasons regulated by, 123; cause of decreased light and heat in horizontal rays, 157, 158; distance of, falsely estimated, 158; light polarized by, 195; indications of an absorptive atmosphere surrounding, 212, 213; his diameter, 224; appearance of, through his atmospheres, ib.; variations in heat and light emitted from, 225, 226; amount of heat annually received by the earth from, 238; effect of his brilliancy on the heat emitted by, 259; his position affecting variations in the magnetic elements, 343, 344; connexion between periodic variation in his spots and in the magnetic elements, 344; vast sweep of his gravitating force, 365; increased attraction of, for comets, 372; gulfs separating stars from, 390; possibility of change in his lustre, 394; spot on, measured by Sir John Herschel, 394, 395; proportion of his light to the moon’s, 404; rate and orbit of motion with his system, 405, 406; a nebulous star, 412; meteoric nebula revolving round, 422; gravitating force of, 424, 425.

Sunbeams, resolved into their component colours, 159-162; law prevailing in the phenomena of, 198; light a distinct property of, 214; resolved into three spectra, 222; undulations constituting, 223; their influence on vegetation, 249.

Swan, the, vanishing star in, 393.

Switzerland, meteors falling in, 421.

Syene, arc of the meridian measured between Alexandria and, 49.

Sykes, Colonel, extensive range of cultivation of wheat observed by, 250.

Sympathetic vibrations in musical instruments, 147-149.

Syren, the, an instrument ascertaining the number of musical pulsations in a second, 143.

Syzygies, tides increased in the, 96.

Table-lands, high, influence of, on the atmosphere, 241.

Tahiti, transit of Venus observed at, 53.

Tail of comets, sudden development of, 372; forces producing, 375; unequal illumination of, 375, 376; change in position of, 376; divided, ib.; constitution of, 377.

Talbot, Fox, his inventions in photography, 204.

Tangent, a, to planetary orbits, planets impelled in the direction of, 8; force, disturbing, in the direction of, 14, 15; deflection from, a measurement of centrifugal force, 49.

Tangential force, occasioning secular inequalities, 14; effects produced by, 15; producing the variation of the moon, 35; force acting on the sea, 100.

—— velocity, effects produced by modifications of, 16; undiminished by the ethereal medium, 22.

Telegraph, the electric, discovery leading to the invention of, 323, 324; the Atlantic, 325; principles of its construction, 326, 327; date of its completion, 327.

Telegraphs, land, principle of their construction, 328.

Telescope, the achromatic, principle of its construction, 164.

——, the differential, differences in illumination determined by, 227.

——, Lord Rosse’s, nebulæ resolved by, 407, 415.

Telescopium, comet traversing the constellation of, 379; nebula in, 414.

Temperature, a decrease in, affecting the earth’s rotation, 72; excentricity of the terrestrial orbit, a cause of decreasing, 73; law equalising, 74; geological changes affecting, 75.

——, varying in the terrestrial atmosphere, zone of constant, 119; affecting atmospheric undulations, 121; modifying the velocity of sound, 134; chemical action of light affected by, 218-222; of the ethereal medium, 227, 228; underground stratum of constant, 228; rate of increase in, below the earth’s crust, 228, 231; of the ocean, 231; mode of finding annual average, 239; causes of disturbance in regular variation of, 240-245; variations in the same latitude, 246, 247; influence of, on vegetation, 248; affecting transmission of heat, 259, 260; of solid bodies, caused by absorption of rays, 268; affecting the length of the pendulum, 272; causes of perpetual variations in, 274; transmission of electricity affected by, 284; affecting magnetism, 352.

Teneriffe, the Peak of, prevailing winds on, 124; lunar heat on, 227; zones of vegetation, 250; character of its flora, 252.

Terrestrial globe, the, a magnet, 336.

—— magnetism, 341-343; the three elements and their variations, 343, 344; storms, period of their variation, 344; its connexion with solar magnetism, ib.; effect of atmospheric magnetism on, 345; probable cause of, 346; effect of planetary magnetism on, 346, 347.

—— meridian, a, defined, 46.

Tessular system of crystallization, 108.

Texas, monsoons occasioned by its deserts, 124.

Thames, the, period occupied by the tidal wave in reaching, 94.

Thaw, cause of the sensible chilliness of, 276.

Theory of probabilities, use of, in determining astronomical data, 60.

Thermo-electric currents, discovery of, 332; phenomena exhibited by, 333; principle of, applied to measuring heat, 333, 334.

Thermography, examples of, 219-221.

Thermometer, the, principles applied to the construction of, 113; consulted in determining mountain heights, 119, 120; refraction varying with, 154; heat measured by motion in, 274.

Thermomultiplier, use of, in experiments, 264; principle of its construction, 333, 334.

Theta Orionis, the multiple system of, 395.

Thomas, St., the island of, hurricane with pauses at, 127.

Thomson, W., Professor, experiments of, in freezing water, 271; dynamical theory of heat maintained by, 275 note; his calculation of the force exerted in vibrations of light, 279; investigation into the relations of light and magnetism, 320; density of the ethereal medium computed by, 356; magnetic property of the ethereal medium pleaded for, 357.

Thunder, theory of prolonged peals of, 138.

Tibet, wheat ripening in, 250.

Tidal wave, theory of, 92; its birthplace, 93; course of, 93, 94; velocity, 94; effect of depth on its motion, 95.

Tides, calculation from the moon’s action on, 55; theory of forces producing, 91, 92; circumstances occasioning irregularities, 93; rising, progress of, 93, 94; three kinds of oscillations in, 95, 96; variations in, from lunar and solar influence, 96-98; effect of interference of waves on, 99; the sea’s equilibrium underanged by, 100.

——, lunar and diurnal, of the terrestrial atmosphere, 121; examples of sympathetic undulation, 148.

Time, a measure of motion, 58; a measure of angular motion, 83; difference between mean and apparent solar, 84; mean equinoctial, mode of computing its object, 86; estimation of, corrected by means of laws of unequal expansion, 272.

Timocharis, comparison of his observations with Hipparchus, 80.

Tomboro, submerged in a volcanic eruption, 233.

Toronto, observations on magnetic storms at, 346.

Torpedo, the, electrical action of, 310, 311.

Torricellian vacuum, experiment on the electric discharge in the, 306; lines of magnetic force passing through, 344.

Toucan, comet approaching the constellation of, 379; a nebula in, 414.

Toucani, 47; globular nebulous cluster, 414.

Tourmaline, brown, light polarized by prisms of, 180; property qualifying it to analyze polarized light, 182; coloured images produced by, 186, 187; changed by compression, 189; heat polarized by, 265; electricity communicated to, 284.

Trade winds, friction of, not affecting the earth’s velocity, 72; action on the general motion of the sea, 100; system of, accounting for atmospheric anomalies, 120; theory of their origin, phenomena connected with, 122, 123; becoming monsoons, 124.

Transits of Venus, 52, 53.

——, two consecutive, of any star, a measure of time, 83.

Transmission of radiant heat, 258, 262; of electricity, 284, 285; of voltaic electricity, 298; molecular structure affecting, 303; method of, determining the influence of electric currents, 317; of gravity, an unsolved question, 355; probable agent, 356; medium of, in space, 424.

Transparent bodies, temperature of, unaffected by the sun’s rays, 227.

Trees, number of species of forest, found in America and Europe, 252.

Tribes, apparently distinct, of the human race, 255.

Triple stars, 395; periods of revolution in, 400.

Tropical year, change in its length, 80; period of, 83; difficulty of adjusting its estimation, 85.

—— revolution of the major axis of the solar ellipse, its period, 86.

—— vegetation, the luxuriance of, 248.

Tuileries, clock in the, showing decimal time, 84.

Twilight, caused by refraction, 154; effect of reflection, 158.

Tyndall, Professor, his experiments proving diamagnetic polarity, 348; on magnetic action in crystals, 349.

Undulations, theory of, 99; of the atmosphere, 121, 122; of the waves of sound, 129, 130; intervals produced by interference, 139; giving musical notes, 142, 143; sympathetic, 147, 149; of the luminous ether, 169, 170; in refraction and reflection, 177; producing fluorescence, 197; different, in light and sound, 199, 200; constituting a sunbeam, 223; heat propagated by, 267; of light, evolution of latent force in extinguished, 279, 280; of natural forces identical, 281.

Undulatory theory of light, 168-170; law of motion affecting, 176, 177; phenomena proving, 198; objection, from the different action of light and sound, refuted, 199; proving the existence of the ethereal medium, 358; acceleration in comet’s motion proving, 367.

—— theory, experiments determining in favour of, 200, 201; final and decisive experiment, 202; of heat, 267.

Unison, note in, 142.

United States, astronomical observations made in, 371, 373.

Uranium, phosphorescent property of, 296; peculiar luminous properties of, 296.

Uranus, effect of reciprocal attraction between Neptune and, 22; periods of the revolutions of his satellites, 33; distance from the sun, 54; astronomical tables of, 60; discovery suggested by his perturbations, 61; observations on, leading to Neptune’s discovery, 62; sun’s influence in, 225; action of, on Halley’s comet, 363; appearance of the sun to, 380, 381; comets in his orbit, 381, 382.

Ursa Major, periodic time of a double star in, 398; nebulous region of, 417.

Utah, deserts of, causing monsoons, 124.

Vacuum produced by shell-fish, 117; existing in the air, 118.

Valz, M., telescopic planet discovered by, 21; comet observed by, 358; observations on a comet’s approach to the sun, 364; cause assigned by, for contraction in diameter of comets, 377, 378.

Vapour, formation and dispersion of, 269, 270; force developing, 277.

Variable stars, periodic fluctuation of lustre in, 390, 391; new, appearing and vanishing, 392, 394; missing, 395.

Variables, region of the, 122.

Vegetation, effect of, in lowering temperature, 243; the two requisites for, 248; strength and vitality of, 249; chemical action of light influencing, ib.; laws of its distribution, 249-252; distribution of marine, 252, 253; theories of specific diversity of original distribution of, 253, 254.

Venus, zone of instability between the sun and, 21; perturbation in the mean motion of the earth and, 26; eclipsing Mercury, 42; transits of, parallaxes calculated from, 52, 53; astronomical tables of, 63; climate, 226.

Vernal equinox, planetary motions estimated from, 9.

Vesta, astronomical tables of, 63; no atmosphere surrounding, 226.

Vesuvius, revived volcanic action of, 234.

Vibrating plates used in experiments on musical sound, 144, 147.

Vibrations of the air producing sound, 129; in music, 131; number made by the human voice in a second, 132.

—— of the ether in natural and polarized light, 193; in fluorescence of light, 196; plane of, in polarized light, 223.

Vico, Padre de, comet discovered by, 370.

Vienna, observations on comets from, 370.

Vietch, James, comet with luminous rings discovered by, 374, 375.

Vincent, St., revival of an extinct volcano in, 234.

Virginia, daguerreotyped spectral image obtained in, 213.

Virgo, planetary conjunction between Libra and, 42; variable star in, 392; star vanished from, 395; nebulous zone passing, 416, 417.

Viviers, transit of a comet across the sun observed from, 374.

Volcanic regions of the globe, 232; annual number of eruptions, 233; celebrated eruptions, ib.; earthquakes caused by, 234; supposed causes of action, 235; Sir John Herschel’s theory, 235-237.

Volta, Professor, electricity rendered manageable by, 297; the world’s debt to, 328.

Voltaic electricity, first suggestions of, 297; theory of the transmission of, 298; construction of the battery, 298, 299; theory of its production, 300; characteristic properties, 300, 301; action of, generating heat and light, 301-303; arc, experiments, 303-305; the, discharge oxidizing silver, 305, 306; stratified light, 306, 307; chemical decomposition effected by agency of, 307, 308; crystallization, 308; an agent in the fine arts, 309; conductors of, ib.; relations of heat and, 310; fish producing effects of, 310, 311; science suggested by its influence on a magnetized needle, 312; rotation effected by, 313, 314; inducing magnetism, 314, 315; distinction between static electricity and, 317; unvarying dual force of, 334.

Voltaic pile, the, invention of, 297; perfected, 298-300.

Vortices, molecular, theory of, 104.

Vosges mountains, temperature of mines in the, 228.

Vulpecula, nebula in, 409.

Wardhus, transit of Venus observed at, 53.

Watches, irregular action of, corrected by the laws of unequal expansion, 272.

Water, constituent parts of, 111; boiling point of, an estimate of mountain heights, 120; as a medium for sound, 135; light polarized circularly by, 194; experiment deciding the velocity of light in, 202; law of expansion of, 271; process of congelation, 276; boiling points of, 277; decomposed by electric agency, 307; as an electric conductor, 309; rotating by electricity, 314.

Waterspouts, origin and cause of, 128.

Waterstone, Mr., magnetic property of the ethereal medium maintained by, 357.

Waves neutralized by interference, 99.

——, atmospheric, over local districts, periods, dimensions of, 121, 122.

—— of sound, 131; furnishing an illustration of reflections of sound and light, 137; interference of, producing calm, 139.

Wedgwood, Dr., attempts of, to trace objects by means of light, 203, 204.

Week, the, of seven days, the most ancient and universal division of time, 85.

Wells, increase of temperature in, 230, 231.

Welsh, Mr., observations made by, in a balloon ascent, 119.

West Indies, the, cause of hurricanes in, 126.

Wheels invented to test intensity of sound, 132, 133.

Wheat, range of its cultivation, 250.

Wheatstone, Professor, experiments in acoustics of, 132; musical instruments invented by, 143; paper on musical vibrations read by, 145; experiments on sounding boards of, 150; experiments on sound reinforced by resonance, 151; instrument measuring velocities of electricity and light invented by, 202; spectrum of an electric spark observed, 289; speed of electricity measured, 289, 290; experiments on the spectrum of Voltaic flame, 303.

Willis, Mr., articulating machine invented by, 151; investigations of, into the mechanism of the larynx, 152.

Winds, trade, 122, 123; monsoons, 124; extra-tropical, in the North Atlantic, ib.; currents above the trade winds, 124, 125; phenomena of rotatory motion, 125; hurricanes, 125, 128; agency of, influencing temperature, 244, 245.

Wines, range of cultivation of the best, 250.

Winter, atmospheric electricity in, 291.

——, mean temperature of, varying in the same latitude, 246, 247.

Wolf, Professor, periods of variation in solar heat computed by, 225.

Wollaston, Dr., experiments of, on sensitiveness to sound, quotation from, 132; experiment of, to show the effect of variable media on refraction, 156; discovery of rayless lines in the solar spectrum, 162; observations of, on the chemical properties of the solar spectrum, 203, 209; magnetic rotation suggested by, 313; light emitted by the heavenly bodies calculated, 404.

Xi Ursæ Majoris, periodic time of, 398; velocity of the revolving star, 400.

Year, a, in Jupiter and Saturn, 66; tropical change in its length, 80; length of the sidereal, ib.; period of the mean, 83; estimation of the Egyptian, 85; first of our era, 86; length of the, affected by a comet’s passage, 359.

Young, Dr., his calculation of the possible compression of solids, 78; date of a horoscope determined by, 89; density of a liquid column estimated by, 114; exception adduced by, to a general law in acoustics, 137; his theory of the pleasures of harmony, 142; undulatory theory established by, 169; data used by, to test his theory of light, 175; illustration of, proving sound and heat kindred forces, 280, 281.

Zeta Cancri, a triple star, 395; periodic time of, 398; revolution, 400; colours, 401.

Zeta Herculis, periodic time, eclipse of, 398; light, 402.

Zinc, seleniate of, effect of temperature on its crystals, 107; sulphate of, its crystals boiled in alcohol, 108.

——, electricity communicated to plates of, 220.

Zodiac, the, signs of, change in their positions, 80.

Zone of constant temperature in the atmosphere, 119; laws of storms in the temperate and torrid, 127, 128; of spots on the sun’s surface, its breadth, 224; of constant temperature below the earth’s crust, 228; comparative unequal distribution of land in temperate and torrid, 244; of fixed stars, 385; of stars nearest the sun, 390; nebulous, 416; of nebulous patches, 417; of meteoric nebulæ, 423.

Zones of instability of planetary orbits, 21.

—— of temperature in the ocean, 101.

—— of vegetation on the Peak of Teneriffe, 250.

Zoophytes, specific distribution of, 254.

THE END.

LONDON: PRINTED BY W. CLOWES AND SONS, STAMFORD STREET, AND CHARING CROSS.

These correspond to No. 1, 6, and 7 of Faraday’s plate in his 29th Series of Experimental Researches in Electricity.

Fig. 1. Spiral nebulæ of 51 Messier, as seen by Lord Rosse.

Fig. 2. Great nebula of Orion. ]

Footnotes

Footnote 1:

The mean distance of the earth from the sun is 95,000,000 miles, but to avoid the inconvenience of large numbers, it is assumed to be the unit of distance; hence the mean distance of Mars is 1·52369, or 1·5 nearly, that of the earth being = 1.

Footnote 2:

The obliquity given in the text is for the year 1858.

Footnote 3:

Sir John Herschel remarks that there are just as many thousands of feet in a degree of the meridian in our latitude as there are days in the year, viz. 365,000.

The Greenwich Observatory is in N. lat. 51° 28ʹ40ʺ.

Footnote 4:

Or more correctly 3422ʺ·325 and 238,793 miles, as deduced from Mr. Adams’ more accurate calculations.

Footnote 5:

Neptune was discovered in the year 1846.

Footnote 6:

The satellites of the two great planets on the farthest verge of the solar system form a singular exception to this law.

Footnote 7:

See the chapter on the Tides and Currents in the ‘Physical Geography,’ by the author, 4th edition.

Footnote 8:

Sir John Herschel on Meteorology.

Footnote 9:

Bakerian Lecture, by Michael Faraday, Esq. Phil. Trans. 1857.

Footnote 10:

See page 104.

Footnote 11:

M. Marbach of Breslau.

Footnote 12:

‘Meteorology,’ by Sir J. Herschel.

Footnote 13:

This theory of heat and motion originated with Mr. Joule, of Manchester, who has maintained it with the greatest talent, both by experiment and analysis; and it has had an able advocate in Professor W. Thomson, of Glasgow.

Footnote 14:

To this remarkable man the world is indebted for the locomotive railway system, which is rapidly advancing the civilization of mankind. Britain may well be proud of its working classes, which can produce such men; and Mr. George Stephenson is not the only one; there are many others; but no man has ever had greater influence by his labours and discoveries on human affairs.

Footnote 15:

‘Correlation of the Physical Forces, by W. R. Grove, Esq.,’ one of the most remarkable and talented works that has appeared, to which the author with pleasure acknowledges her obligations.

Footnote 16:

“Eripuit fulmen Cœlo, sceptrumque tyrannis,” is the inscription on a medal struck in honour of Franklin.

Footnote 17:

Faraday.

Footnote 18:

Professor Matteucci still expresses doubts on this subject, but has not yet finished his experiments.

Footnote 19:

Babbage.

Footnote 20:

Phil. Mag. for May 1858.

Transcriber's Notes

Some corrections were made to the original text. In particular, punctuation was corrected without further note. Inconsistent spelling and hyphenation was retained unless noted otherwise. There were two Notes 189 in the original; this was retained as printed. Spelling of Index entries was changed to reflect the body text where inconsistencies were found. Index page numbers were corrected where errors were found. Further corrections are noted below:

p. 50 0·005·1449 -> 0·0051449 p. 61 24,000 -> 240,000 p. 62 M. Leverrier -> M. Le Verrier p. 84 in mean solar day -> in a mean solar day p. 96 syzigies -> syzygies p. 115 arrising -> arising p. 120 Herchel -> Herschel p. 123 generally know -> generally known p. 159 Fraunhoffer’s -> Fraunhofer’s p. 168 contaary -> contrary p. 214 oxyde -> oxide p. 216 aperature -> aperture p. 296 M Niepce -> M. Niepcé p. 306 torrecelian -> Torricellian p. 307 potass -> potash p. 350 de Roux -> le Roux p. 423 Β -> β p. 447 areal -> aërial p. 456 perigree -> perigee p. 471 108° -> 180° p. 478 Meissier -> Messier