Part 17

SECTION FOURTH.

THE SOLAR SPOTS.

We have yet many phenomena to investigate by the aid of the theory, and we will develop them in that order which will best exhibit their mutual dependence. The solar spots have long troubled astronomers, and to this day no satisfactory solution of the question has been proposed; but we shall not examine theories. It is sufficient that we can explain them on the same general principles that we have applied to terrestrial phenomena. There can be but little doubt about the existence of a solar atmosphere, and, reasoning from analogy, the constituent elements of the sun must partake of the nature of other planetary matter. That there are bodies in our system possessing the same elements as our earth, is proved by the composition of meteoric masses, which, whether they are independent bodies of the system, or fragments of an exploded planet, or projected from lunar volcanoes, is of little consequence; they show that the same elements are distributed to other bodies of the system, although not necessarily in the same proportions. The gaseous matter of the sun's atmosphere may, therefore, be safely considered as vapors condensable by cold, and the formation of vortices over the surface of this atmosphere, brings down the ether, and causes it to intermingle with this atmosphere. But, from the immensely rapid motion of the polar current of the solar vortex, this ether may be considered to enter the atmosphere of the sun with the temperature of space.

Sir John Herschel, in commenting on the theory of Mr. Redfield before the British Association, convened at Newcastle in 1838, suggested an analogy to terrestrial hurricanes, from a suspected rotation and progressive motion in these spots. From their rapid formation, change of shape, and diameter, this view is allowable, and, taken in conjunction with the action of the ethereal currents, will account for all the phenomena. The nucleus of the spot is dense, like the nucleus of a storm on the earth, and surrounded by a penumbon precisely as our storms are fringed with lighter clouds, permitting the light of the sun to penetrate. And, it has been observed, that these spots seem to follow one another in lines on the same parallel of solar latitude (or nearly the same), exactly as we have determined the action of the vortices on the surface of the earth from observation. These spots are never found in very high latitudes--not much above 30d from the solar equator. If we consider this equator to be but slightly inclined to the plane of the vortex, this latitude would be the general position of the lateral solar vortices, and, in fact, be confined principally to a belt on each side of the equator, between 15d and 30d of solar latitude, rather than at the equator itself. This, it is needless to say, is actually the case. But, a more capital feature still has been more recently brought to light by observation, although previously familiar to the author, who, in endeavoring to verify the theory, seriously injured his sight, by observing with inadequate instrumental means. This is the periodicity of the spots.

We have already observed, that there is reason to suppose that the action of the inner vortex of the earth is probably greater than that of the outer vortex, on account of the conflicting currents by which it is caused. And the full development of this vortex requires, that the central vortex or mechanical axis of the system shall be nearly tangential to the surface. In this position, the action of the central vortex is itself at a maximum; and, when the planets of the system are so arranged as to produce this result, we may expect the greatest number of spots. If the axis or central vortex approaches to coincidence with the axis of the sun, the lateral vortices disappear, and the central vortex being then perpendicular to the surface, is rendered ineffective. Under these circumstances, there will be no spots on the sun's disc. When, on the other hand, all the planets conspire at the same side to force the sun out from the mechanical centre of the system, the surface is too distant to be acted on by the central vortex, and the lateral vortices are also thrown clear of the sun's surface, on account of the greater velocity of the parts of the vortex, in sweeping past the body of the sun. In this case, there will be but few spots. The case in which the axis of the vortex coincides with the axis of the sun, is much more transient than the first position, and hence, although the interval between the maxima will be tolerably uniform, there will be an irregularity between a particular maximum, and the preceding and subsequent minimum.

The following table exhibits the solar spots, as determined by Schwabe, of Dessau:

Year of observation. Groups of spots observed. Number of days. 1826 118 277 1827 161 273 1828 225 282 1829 199 244 1830 190 217 1831 149 239 1832 84 270 1833 33 267 1834 51 273 1835 173 244 1836 272 200 1837 333 168 1838 282 202 1839 162 205 1840 152 263 1841 102 283 1842 68 307 1843 34 324

Previous to the publication of this table, the author had inferred the necessity of admitting the existence of another planet in the solar system, from the phenomenon of which we are speaking. He found a sufficient correspondence between the minima of spots to confirm the explanation given by the theory, and this was still more confirmed by the more exact determination of Schwabe; yet there was a little discrepancy in the synchronous values of the ordinates, when the theory was graphically compared with the table. Previous to the discovery of Neptune, the theory corresponded much better than afterwards, and as no doubt could be entertained that the anomalous movements of Uranus were caused by an exterior planet, he adopted the notion that there were two planets exterior to Uranus, whose positions at the time were such, that their mechanical affects on the system were about equal and contrary. Consequently, when Neptune became known, the existence of another planet seemed a conclusion necessary to adopt. Accordingly, he calculated the heliocentric longitudes and true anomalies, and the values of radius vector, for all the planets during the present century, but not having any planetary tables, he contented himself with computing for the nearest degree of true anomaly, and the nearest thousand miles of distance. Then by a composition and resolution of all the forces, he deduced the radius vector of the sun, and the longitude of his centre, for each past year of the century. It was in view of a little outstanding discrepancy in the times of the minima, as determined by theory and observation, that he was induced to consider as almost certain the existence of a theoretical planet, whose longitude, in 1828, was about 90d, and whose period is from the theory about double that of Neptune. And for convenience of computation and reference, he has been in the habit of symbolizing it by a volcano. The following table of the radii vectores of the sun, and the longitude of his centre, for the years designated in Schwabe's table, is calculated from the following data for each planet:

Long. of Planets. Masses. Mean distances. Eccentricities. Perihelion. [JUPITER] 1/1648 494.800.000 0.0481 11d [SATURN] 1/3310 907.162.000 0.0561 89 [URANUS] 1/23000 1824.290.000 0.0166 167 [NEPTUNE] 1/20000 2854.000.000 0.0088 0 [VOLCANO] 1/28000 4464.000.000

No. of spots in Dates. Rad. vector. Sun's long. Ordinates. Schwabe's table. Jan. 1, 1826 528,000 320d + 84 118 " 1827 480,000 339 + 36 161 " 1828 432,000 352 - 12 Max. 225 Max. " 1829 397,000 38 - 47 199 " 1830 858,000 71 - 86 190 " 1831 324,000 104 - 120 149 " 1832 311,000 144 - 133 84 " 1833 300,000 183 - 144 Min. 33 Min. " 1834 307,000 220 - 137 51 " 1835 338,000 263 - 106 173 " 1836 380,000 302 - 55 272 " 1837 419,000 337 + 25 Max. 333 Max. " 1838 488,000 3 + 44 282 " 1839 651,000 29 + 107 162 " 1840 632,000 51 + 188 152 " 1841 680,000 80 + 236 102 " 1842 730,000 105 + 286 68 " 1843 160,000 128 + 322 34 Min. " 1844 188,000 152 + 339 Min. 52 " 1845 772,000 174 + 328 114 " 1846 728,000 196 + 284 157 " 1847 660,000 218 + 216 " 1848 563,000 240 + 119 Observed. Max. " 1849 447,000 261 + 3 Max. " 1850 309,000 283 - 135 " 1851 170,000 323 - 274 " 1852 53,000 41 - 391 Min. " 1853 167,000 133 - 277 " 1854 315,000 160 - 129 " 1855 475,000 183 + 31 Max. " 1856 611,000 203 + 167 " 1857 720,000 225 + 276

It is necessary to observe here, that the values of the numbers in Schwabe's table are the numbers for the whole year, and, therefore, the 1st of July would have been a better date for the comparison; but, as the table was calculated before the author was cognizant of the fact, and being somewhat tedious to calculate, he has left it as it was, viz., for January 1st of each year. Hence, the minimum for 1843 appears as pertaining to 1844. The number of spots ought to be inversely as the ordinates approximately--these last being derived from the Radii Vectores minus, the semi-diameter of the sun = 444,000 miles.

In passing judgment on this relation, it must also be borne in mind, that the recognized masses of the planets cannot be the true masses, if the theory be true. Both sun and planets are under-estimated, yet, as they are, probably, all to a certain degree proportionally undervalued, it will not vitiate the above calculation much.

The spots being considered as solar storms, they ought also to vary in number at different times of the year, according to the longitude of the earth and sun, and from their transient character, and the slow rotation of the sun, they ought, ceteris paribus, to be more numerous when the producing vortex is over a visible portion of the sun's surface.

The difficulty of reconciling the solar spots, and their periodicity to any known principle of physics, ought to produce a more tolerant spirit amongst the scientific for speculations even which may afford the slightest promise of a solution, although emanating from the humblest inquirer after truth. The hypothesis of an undiscovered planet, exterior to Neptune, is of a nature to startle the cautions timidity of many; but, if the general theory be true, this hypothesis becomes extremely probable. We may not have located it exactly. There may be even two such planets, whose joint effect shall be equivalent to one in the position we have assigned. There may even be a comet of great mass, capable of producing an effect on the position of the sun's centre (although it follows from the theory that comets have very little mass). Yet, in view of all these suppositions, there can be but little doubt that the solar spots are caused by the solar vortices, and these last made effective on the sun by the positions of the great planets, and, therefore, we have indicated a new method of determining the existence and position of all the planets exterior to Neptune. On the supposition that there is only one more in the system, from its deduced distance and mass, it will appear only as a star of the eleventh magnitude, and, consequently, will only be recognizable by its motion, which, at the greatest, will only be ten or eleven seconds per day.

MASSES OF THE SUN AND PLANETS.

We have alluded to the fact of the radial stream of the sun necessarily diminishing the sun's power, and, consequently, diminishing his apparent mass. The radial stream of all the planets will do the same, so that each planet whose mass is derived from the periodic times of the satellites, will also appear too small. But, there is also a great probability that some modification must be made in the wording of the Newtonian law. The experiments of Newton on the pendulum, with every variety of substance, was sufficient justification to entitle him to infer, that inertia was as the weight of matter universally. But, there was one condition which could not be observed in experimenting on these substances, viz., the difference of temperature existing between the interior and surface of a planet.

We have already expressed the idea, that the cause of gravity has no such mysterious origin as to transcend the power of man to determine it. But that, on the contrary, we are taught by every analogy around us, as well as by divine precept, to use the visible things of creation as stepping stones to the attainment of what is not so apparent. That we have the volume of nature spread out in tempting characters, inviting us to read, and, assuredly, it is not so spread in mockery of man's limited powers. As science advances, strange things, it is true, are brought to light, but the more rational the queries we propound, in every case the more satisfactory are the answers. It is only when man consults the oracle in irrational terms that the response is ambiguous. Alchemy, with its unnatural transmutations, has long since vanished before the increasing light. Why should not attraction also? Experience and experiment, if men would only follow their indications, are consistently enforcing the necessity of erasing these antiquated chimeras from the book of knowledge; and inculcating the great truth, that the physical universe owes all its endless variety to differences in the form, size, and density of planetary atoms in motion, according to simple mechanical principles. These, combined with the existence of an all-pervading medium filling space, between which and planetary matter no bond of union subsists, other than that which arises from a continual interchange of motion, are the materials from which the gems of nature are elaborated. But, simplicity of means is what philosophy has ever been reluctant to admit, preferring rather the occult and obscure.

If action be equal to reaction, and all nature be vibrating with motion, these motions must necessarily interfere, and some effect should be produced. A body radiating its motion on every side into a physical medium, produces waves. These waves are a mechanical effect, and the body parts with some of its motion in producing them; but, should another body be placed in juxtaposition, having the same motion, the opposing waves neutralize each other, and the bodies lose no motion from their contiguous sides, and, therefore, the reaction from the opposite sides acts as a propelling power, and the bodies approach, or tend to approach each other. If one body be of double the inertia, it moves only half as far as the first; then, seeing that this atomic motion is radiated, the law of force must be directly as the mass, and inversely as the squares of the distances. There may be other atomic vibrations besides those which we call light, heat, and chemical action, yet the joint effect of all is infinitesimally small, when we disregard the united attraction of all the atoms of which the earth is composed. The attraction of the whole earth at the surface causes bodies to fall 16 feet the first second of time; but, if two spheres of ice of one foot diameter, were placed in an infinite space, uninfluenced by other matter, and only 16 feet apart, they would require nearly 10,000 years to fall together by virtue of their mutual attraction. Our conceptions, or, rather, our misconceptions, concerning the force of gravity, arises from our forgetting that every pound of matter on the earth contributes its share of the force which, in the aggregate, is so powerful. Hence, the cause we have suggested, is fully adequate to account for the phenomena. Whether the harmony of vibrations between two bodies may not have an influence in determining the amount of interference, and, consequently, produce some difference between the gravitating mass and its inertia, is a question which, no doubt, will ultimately be solved; but this harmony of vibrations must depend, in some degree, on the atomic weight, temperature, and intensity of atomic motion.

That a part of the mass of the earth is latent may be inferred from certain considerations: 1st, from the discrepancies existing in the results obtained for the earth's compression by the pendulum and by actual measurement; and, 2d, from the irregularity of that compression in particular latitudes and longitudes. The same may also be deduced from the different values of the moon's mass as derived from different phenomena, dependent on the law of gravitation. Astronomers have hitherto covered themselves with the very convenient shield of errors of observation; but, the perfection of modern instruments now demand a better account of all outstanding discrepancies. The world requires it of them.

The mass of the moon comes out much greater by our theory than nutation gives. The mass deduced from the theory is only dependent on the relative inertiae of the earth and moon. That given by nutation depends on gravity. If, then, a part of the mass be latent, nutation will give too small a value. But, in addition to this, we are justified in doubting the strict wording of the Newtonian law, deriving our authority from the very foundation stone of the Newtonian theory.

It is well known that Newton suspected that the moon was retained in her orbit by the same force which is usually called weight upon the surface, sixteen years before the fact was confirmed, by finding a correspondence in the fall of the moon and the fall of bodies on the earth. Usually, in all elementary works, this problem is considered accurately solved. Having formed a different idea of the mechanism of nature, this fact presented itself as a barrier beyond which it was impossible to pass, until suspicions, derived from other sources, induced the author to inquire: Whether the phenomenon did exactly accord with the theory? We are aware that it is easy to place the moon at such a distance, that the result shall strictly correspond with the fact; but, from the parallax, as derived from observation (and if this cannot be depended on certainly, no magnitudes in astronomy can), we find, that the moon does not fall from the tangent of her orbit, as much as the theory requires. As this is of vital importance to the integrity of the theory we are advocating, we have made the computation on Newton's own data, except such as were necessarily inaccurate at the time he wrote; and we have done it arithmetically, without logarithmic tables, that, if possible, no error should creep in to vitiate the result. We take the moon's elements from no less an authority than Sir John Herschel, as well as the value of the earth's diameter.

Mass of the moon 1/80 Mean distance in equatorial radii 59.96435 Sidereal period in seconds 2360591

The vibrations of the pendulum give the force of gravity at the surface of the earth, and it is found to vary in different latitudes. The intensity in any place being as the squares of the number of vibrations in a given time. This inequality depends on the centrifugal force of rotation, and on the spheroidal figure of the earth due to that rotation. At the equator the fall of a heavy body is found to be 16.045223 feet, per second, and in that latitude the squares of whose sine is 1/3, it is 16.0697 feet. The effect in this last-named latitude is the same as if the earth were a perfect sphere. This does not, however, express the whole force of gravity, as the rotation of the earth causes a centrifugal tendency which is a maximum at the equator, and there amounts to 1/289 of the whole gravitating force. In other latitudes it is diminished in the ratio of the squares of the cosines of the latitude; it therefore becomes 1/434 in that latitude the square of whose sine is 1/3. Hence the fall per second becomes 16.1067 feet for the true gravitating force of the earth, or for that force which retains the moon in her orbit.

The moon's mean distance is 59.96435 equatorial radii of the earth, which radius is, according to Sir John Herschel, 20.923.713 feet. Her mean distance as derived from the parallax is not to be considered the radius vector of the orbit, inasmuch as the earth also describes a small orbit around the common centre of gravity of the earth and moon; neither is radius vector to be considered as her distance from this common centre; for the attracting power is in the centre of the earth. But the mean distance of the moon moving around a movable centre, is to the same mean distance when the centre of attraction is fixed, as the sum of the masses of the two bodies, to the first of two mean proportionals between this sum and the largest of the two bodies inversely. (Vid. Prin. Prop. 60 Lib. Prim.) The ratio of the masses being as above 80 to 1 the mean proportional sought is 80.666 and in this ratio must the moon's mean distance be diminished to get the force of gravity at the moon. Therefore as 81 is to 80.666, so is 59.96435 to 59.71657 for the moon's distance in equatorial radii of the earth. Multiply this last by 20.923,713 to bring the semi-diameter of the lunar orbit into feet = 1.249.492.373, and this by 6.283185, the ratio of the circumference to the radius, gives 7.850.791.736 feet, for the mean circumference of the lunar orbit.

Further, the mean sidereal period of the moon is 2360591 seconds and the 1/2360591th part of 7.850.791.736 is the arc the moon describes in one second = 3325.77381 feet, the square of which divided by the diameter of the orbit, gives the fall of the moon from the tangent or versed size of that arc.

1106771.36876644 = ---------------- = 0.004426106 feet. 2498984746

This fraction is, however, too small, as the ablatitious action of the sun diminishes the attraction of the earth on the moon, in the ratio of 178 29/40 to 177 29/40. So that we must increase the fall of the moon in the ratio of 711 to 715, and hence the true fall of the moon from the tangent of her orbit becomes 0.00451 feet per second.

We have found the fall of a body at the surface of the earth, considered as a sphere, 16.1067 feet per second, and the force of gravity diminishes as the squares of the distances increases. The polar diameter of the earth is set down as 7899.170 miles, and the equatorial diameter 7925.648 miles; therefore, the mean diameter is 7916.189 miles. So that, reckoning in mean radii of the earth, the moon's distance is 59.787925, which squared, is equal to 3574.595975805625. At one mean radius distance, that is, at the surface, the force of gravity, or fall per second, is as above, 16.1067 feet. Divide this by the square of the distance, it is 16.1067/3574.595975805625 = 0.0045058 feet for the force of gravity at the moon. But, from the preceding calculation, it appears, that the moon only falls 0.0044510 feet in a second, showing a deficiency of 1/82d part of the principal force that retains the moon in her orbit, being more than double the whole disturbing power of the sun, which is only 1/178th of the earth's gravity at the moon; yet, on this 1/178th depends the revolution of the lunar apogee and nodes, and all those variations which clothe the lunar theory with such formidable difficulties. The moon's mass cannot be less than 1/80, and if we consider it greater, as it no doubt is, the results obtained will be still more discrepant. Much of this discrepancy is owing to the expulsive power of the radial stream of the terral vortex; yet, it may be suspected that the effect is too great to be attributed to this, and, for this reason, we have suggested that the fused matter of the moon's centre may not gravitate with the same force as the exterior parts, and thus contribute to increase the discrepancy.