Part 39

That Jupiter in a higher orbit than Mars is likewise revolved about the sun with a motion nearly equable as well in distance as in the areas described, I infer from Mr. Flamsted's observations of the eclipses of the innermost satellite; and the same thing may be concluded of Saturn from his satellite by the observations of Mr. Huyghens and Mr. Halley.

If Jupiter was viewed from the sun it would never appear retrograde or stationary, as it is seen sometimes from the earth, but always to go forward with a motion nearly uniform. And from the very great inequality of its apparent geocentric motion we infer--as it has been previously shown that we may infer--that the force by which Jupiter is turned out of a rectilinear course and made to revolve in an orbit is not directed to the centre of the earth. And the same argument holds good in Mars and in Saturn. Another centre of these forces is, therefore, to be looked for, about which the areas described by radii intervening may be equable; and that this is the sun, we have proved already in Mars and Saturn nearly, but accurately enough in Jupiter.

The distances of the planets from the sun come out the same whether, with Tycho, we place the earth in the centre of the system, or the sun with Copernicus; and we have already proved that, these distances are true in Jupiter. Kepler and Bullialdus have with great care determined the distances of the planets from the sun, and hence it is that their tables agree best with the heavens. And in all the planets, in Jupiter and Mars, in Saturn and the earth, as well as in Venus and Mercury, the cubes of their distances are as the squares of their periodic times; and, therefore, the centripetal circum-solar force throughout all the planetary regions decreases in the duplicate proportion of the distances from the sun. Neglecting those little fractions which may have arisen from insensible errors of observation, we shall always find the said proportion to hold exactly; for the distances of Saturn, Jupiter, Mars, the Earth, Venus, and Mercury from the sun, drawn from the observations of astronomers, are (Kepler) as the numbers 951,000, 519,650, 152,350, 100,000, 70,000, 38,806; or (Bullialdus) as the numbers 954,198, 522,520, 152,350, 100,000, 72,398, 38,585; and from the periodic times they come out 953,806, 520,116, 152,399, 100,000, 72,333, 38,710. Their distances, according to Kepler and Bullialdus, scarcely differ by any sensible quantity, and where they differ most the differences drawn from the periodic times fall in between them.

Earth as a Centre

That the circum-terrestrial force likewise decreases in the duplicate proportion of the distances, I infer thus:

The mean distance of the moon from the centre of the earth is, we may assume, sixty semi-diameters of the earth; and its periodic time in respect of the fixed stars 27 days 7 hr. 43 min. Now, it has been shown in a previous book that a body revolved in our air, near the surface of the earth supposed at rest, by means of a centripetal force which should be to the same force at the distance of the moon in the reciprocal duplicate proportion of the distances from the centre of the earth, that is, as 3,600 to 1, would (secluding the resistance of the air) complete a revolution in 1 hr. 24 min. 27 sec.

Suppose the circumference of the earth to be 123,249,600 Paris feet, then the same body deprived of its circular motion and falling by the impulse of the same centripetal force as before would in one second of time describe 15-1/12 Paris feet. This we infer by a calculus formed upon Prop. xxxvi. ("To determine the times of the descent of a body falling from a given place"), and it agrees with the results of Mr. Huyghens's experiments of pendulums, by which he demonstrated that bodies falling by all the centripetal force with which (of whatever nature it is) they are impelled near the surface of the earth do in one second of time describe 15-1/12 Paris feet.

But if the earth is supposed to move, the earth and moon together will be revolved about their common centre of gravity. And the moon (by Prop, lx.) will in the same periodic time, 27 days 7 hr. 43 min., with the same circum-terrestrial force diminished in the duplicate proportion of the distance, describe an orbit whose semi-diameter is to the semi-diameter of the former orbit, that is, to the sixty semi-diameters of the earth, as the sum of both the bodies of the earth and moon to the first of two mean proportionals between this sum and the body of the earth; that is, if we suppose the moon (on account of its mean apparent diameter 31-1/2 min.) to be about 1/42 of the earth, as 43 to (42 + 42^2)^1/3 or as about 128 to 127. And, therefore, the semi-diameter of the orbit--that is, the distance of the centres of the moon and earth--will in this case be 60-1/2 semi-diameters of the earth, almost the same with that assigned by Copernicus; and, therefore, the duplicate proportion of the decrement of the force holds good in this distance. (The action of the sun is here disregarded as inconsiderable.)

This proportion of the decrement of the forces is confirmed from the eccentricity of the planets, and the very slow motion of their apsides; for in no other proportion, it has been established, could the circum-solar planets once in every revolution descend to their least, and once ascend to their greatest distance from the sun, and the places of those distances remain immovable. A small error from the duplicate proportion would produce a motion of the apsides considerable in every revolution, but in many enormous.

The Tides

While the planets are thus revolved in orbits about remote centres, in the meantime they make their several rotations about their proper axes: the sun in 26 days, Jupiter in 9 hr. 56 min., Mars in 24-2/3 hr., Venus in 23 hr., and in like manner is the moon revolved about its axis in 27 days 7 hr. 43 min.; so that this diurnal motion is equal to the mean motion of the moon in its orbit; upon which account the same face of the moon always respects the centre about which this mean motion is performed--that is, the exterior focus of the moon's orbit nearly.

By reason of the diurnal revolutions of the planets the matter which they contain endeavours to recede from the axis of this motion; and hence the fluid parts, rising higher towards the equator than about the poles, would lay the solid parts about the equator under water if those parts did not rise also; upon which account the planets are something thicker about the equator than about the poles.

And from the diurnal motion and the attractions of the sun and moon our sea ought twice to rise and twice to fall every day, as well lunar as solar. But the two motions which the two luminaries raise will not appear distinguished but will make a certain mixed motion. In the conjunction or opposition of the luminaries their forces will be conjoined and bring on the greatest flood and ebb. In the quadratures the sun will raise the waters which the moon depresseth and depress the waters which the moon raiseth; and from the difference of their forces the smallest of all tides will follow.

But the effects of the lumniaries depend upon their distances from the earth, for when they are less distant their effects are greater and when more distant their effects are less, and that in the triplicate proportion of their apparent diameters. Therefore it is that the sun in winter time, being then in its perigee, has a greater effect, whether added to or subtracted from that of the moon, than in the summer season, and every month the moon, while in the perigee raiseth higher tides than at the distance of fifteen days before or after when it is in its apogee.

The fixed stars being at such vast distances from one another, can neither attract each other sensibly nor be attracted by our sun.

Comets

There are three hypotheses about comets. For some will have it that they are generated and perish as often as they appear and vanish; others that they come from the regions of the fixed stars, and are near by us in their passage through the sytem of our planets; and, lastly, others that they are bodies perpetually revolving about the sun in very eccentric orbits.

In the first case, the comets, according to their different velocities, will move in conic sections of all sorts; in the second they will describe hyperbolas; and in either of the two will frequent indifferently all quarters of the heavens, as well those about the poles as those towards the ecliptic; in the third their motions will be performed in eclipses very eccentric and very nearly approaching to parabolas. But (if the law of the planets is observed) their orbits will not much decline from the plane of the ecliptic; and, so far as I could hitherto observe, the third case obtains; for the comets do indeed chiefly frequent the zodiac, and scarcely ever attain to a heliocentric latitude of 40 degrees. And that they move in orbits very nearly parabolical, I infer from their velocity; for the velocity with which a parabola is described is everywhere to the velocity with which a comet or planet may be revolved about the sun in a circle at the same distance in the subduplicate ratio of 2 to 1; and, by my computation, the velocity of comets is found to be much about the same. I examined the thing by inferring nearly the velocities from the distances, and the distances both from the parallaxes and the phenomena of the tails, and never found the errors of excess or defect in the velocities greater than what might have arisen from the errors in the distances collected after that manner.

SIR RICHARD OWEN

Anatomy of Vertebrates

Sir Richard Owen, the great naturalist, was born July 20, 1804, at Lancaster, England, and received his early education at the grammar school of that town. Thence he went to Edinburgh University. In 1826 he was admitted a member of the English College of Surgeons, and in 1829 was lecturing at St. Bartholomew's Hospital, London, where he had completed his studies. His "Memoir on the Pearly Nautillus," published in 1832, placed him, says Huxley, "at a bound in the front rank of anatomical monographers," and for sixty-two years the flow of his contributions to scientific literature never ceased. In 1856 he was appointed to take charge of the natural history departments of the British Museum, and before long set forth views as to the inadequacy of the existing accommodation, which led ultimately to the foundation of the buildings now devoted to this purpose in South Kensington. Owen died on December 18, 1892. His great book, "Comparative Anatomy and Physiology of the Vertebrates," was completed in 1868, and since Cuvier's "Comparative Anatomy," is the most monumental treatise on the subject by any one man. Although much of the classification adopted by Owen has not been accepted by other zoologists, yet the work contains an immense amount of information, most of which was gained from Owen's own personal observations and dissections.

I.--Biological Questions of 1830

At the close of my studies at the Jardin des Plantes, Paris, in 1831, I returned strongly moved to lines of research bearing upon the then prevailing phases of thought on some biological questions.

The great master in whose dissecting rooms I was privileged to work held that species were not permanent as a fact established inductively on a wide basis of observation, by which comparative osteology had been created. Camper and Hunter suspected the species might be transitory; but Cuvier, in defining the characters of his anaplotherium and palæotherium, etc., proved the fact. Of the relation of past to present species, Cuvier had not an adequate basis for a decided opinion. Observation of changes in the relative position of land and sea suggested to him one condition of the advent of new species on an island or continent where old species had died out. This view he illustrates by a hypothetical case of such succession, but expressly states: "I do not assert that a new creation was necessary to produce the species now existing, but only that they did not exist in the same regions, and must have come from elsewhere." Geoffrey Saint Hilaire opposed to Cuvier's inductive treatment of the question the following expression of belief: "I have no doubt that existing animals are directly descended from the animals of the antediluvian world," but added, "it is my belief that the season has not yet arrived for a really satisfying knowledge of geology."

The main collateral questions argued in their debates appeared to me to be the following:

Unity of plan or final purpose, as a governing condition of organic development?

Series of species, uninterrupted or broken by intervals?

Extinction, cataclysmal or regulated?