(Leibnitz, &c.) Nor does it appear that in Germany mathematicians had attained this point of view. Leibnitz, as we have seen, did not assent to the opinions of Descartes, as containing the complete truth; and yet his own views of the physics of the universe do not seem to have any great advantage over these. In 1671 he published A new physical hypothesis, by which the causes of most phenomena are deduced from a certain single universal motion supposed in our globe;—not to be despised either by the Tychonians or the Copernicans. He supposes [393] the particles of the earth to have separate motions, which produce collisions, and thus propagate[15] an “agitation of the ether,” radiating in all directions; and,[16] “by the rotation of the sun on its axis, concurring with its rectilinear action on the earth, arises the motion of the earth about the sun.” The other motions of the solar system are, as we might expect, accounted for in a similar manner; but it appears difficult to invest such an hypothesis with any mechanical consistency.
[15] Art. 5.
[16] Ib. 8.
John Bernoulli maintained to the last the Cartesian hypothesis, though with several modifications of his own, and even pretended to apply mathematical calculation to his principles. This, however, belongs to a later period of our history; to the reception, not to the prelude, of the Newtonian theory.
(Borelli.) In Italy, Holland, and England, mathematicians appear to have looked much more steadily at the problem of the celestial motions, by the light which the discovery of the real laws of motion threw upon it. In Borelli’s Theories of the Medicean Planets, printed at Florence in 1666, we have already a conception of the nature of central action, in which true notions begin to appear. The attraction of a body upon another which revolves about it is spoken of and likened to magnetic action; not converting the attracting force into a transverse force, according to the erroneous views of Kepler, but taking it as a tendency of the bodies to meet. “It is manifest,” says he,[17] “that every planet and satellite revolves round some principal globe of the universe as a fountain of virtue, which so draws and holds them that they cannot by any means be separated from it, but are compelled to follow it wherever it goes, in constant and continuous revolutions.” And, further on, he describes[18] the nature of the action, as a matter of conjecture indeed, but with remarkable correctness.[19] “We shall account for these motions by supposing, that which can hardly be denied, that the planets have a certain natural appetite for uniting themselves with the globe round which they revolve, and that they really tend, with all their efforts, to approach to such globe; the planets, for instance, to the sun, the Medicean Stars to Jupiter. It is certain, also, that circular motion gives a body a tendency to recede from the centre of such revolution, as we find in a wheel, or a stone whirled in a sling. Let us suppose, then, the planet to endeavor to approach the sun; since, in the mean time, it requires, by the circular motion, a force to recede from the same central body, it comes to pass, that when [394] those two opposite forces are equal, each compensates the other, and the planet cannot go nearer to the sun nor further from him than a certain determinate space, and thus appears balanced and floating about him.”
[17] Cap. 2.
[18] Ib. 11.
[19] P. 47.
This is a very remarkable passage; but it will be observed, at the same time, that the author has no distinct conception of the manner in which the change of direction of the planet’s motion is regulated from one instant to another; still less do his views lead to any mode of calculating the distance from the central body at which the planet would be thus balanced, or the space through which it might approach to the centre and recede from it. There is a great interval from Borelli’s guesses, even to Huyghens’ theorems and a much greater to the beginning of Newton’s discoveries.
(England.) It is peculiarly interesting to us to trace the gradual approach towards these discoveries which took place in the minds of English mathematicians and this we can do with tolerable distinctness. Gilbert, in his work, De Magnete, printed in 1600, has only some vague notions that the magnetic virtue of the earth in some way determines the direction of the earth’s axis, the rate of its diurnal rotation, and that of the revolution of the moon about it.[20] He died in 1603, and, in his posthumous work, already [mentioned] (De Mundo nostro Sublunari Philosophia nova, 1651), we have already a more distinct statement of the attraction of one body by another.[21] “The force which emanates from the moon reaches to the earth, and, in like manner, the magnetic virtue of the earth pervades the region of the moon: both correspond and conspire by the joint action of both, according to a proportion and conformity of motions; but the earth has more effect, in consequence of its superior mass; the earth attracts and repels the moon, and the moon, within certain limits, the earth; not so as to make the bodies come together, as magnetic bodies do, but so that they may go on in a continuous course.” Though this phraseology is capable of representing a good deal of the truth, it does not appear to have been connected, in the author’s mind, with any very definite notions of mechanical action in detail. We may probably say the same of Milton’s language: