44 ANNUAL OF SCIENTIFIC DISCOVERY. 



odical variation of orbits, which secures the stability of the system by pre- 

 scribing a maximum and & minimum amount of deviation ; and this is not a 

 contingent, but a necessary truth, by rigorous demonstration, the inevitable 

 rcsiilt of undoubted data in point of fact, the eccentricities of the orbits, the 

 directions of the motions, and the movement in one plane of a certain posi- 

 tion. That wonderful proposition of Newton, which, with his corollaries, 

 may be said to give the whole doctrine of disturbing forces, has been little 

 more than applied and extended by the labors of succeeding geometricians. 

 Indeed, La Place, struck with wonder at one of his comprehensive general 

 statements on disturbing forces in another proposition, has not hesitated to 

 assert that it contains the germ of La Grange's celebrated inquiry exactly a 

 century after the " Principia " was given to the world. The wonderful pow- 

 ers of generalization, combined with the boldness of never shrinking from a 

 conclusion that seemed the legitimate result of his investigations, how new 

 and even startling soever it might appear, was strikingly shown in that 

 memorable inference which he drew from optical phenomena, that the dia- 

 mond is " an unctuous substance coagulated; " subsequent discoveries having 

 proved both that such substances are carbonaceous, and that the diamond is 

 crystallized carbon ; and the foundations of mechanical chemistry were laid 

 by him with the boldest induction and most felicitous anticipations of what 

 lias since been effected. The solution of the inverse problem of disturbing 

 forces has led Le Terrier and Adams to the discovery of a new planet, merely 

 by deductions from the manner in which the notions of an old one are 

 affected, and its orbit has been so calculated that observers could find it 

 nay, its disc, as measured by them, only varies 1-1,200 of a degree from the 

 amount given by the theory. Moreover, when Newton gave his estimate of 

 the earth's density, he wrote a century before Maskelyne, and by measuring 

 the force of gravitation in the Scotch mountains, gave the proportion to water 

 as 4'71G to 1 ; and, many years after, by experiments with mechanical appa- 

 ratus, Cavendish (1798) corrected this to 5'48, and Baily, more recently (1842), 

 to 5*66, Newton having given the proportion as between five and six times. 

 In these instances he only showed the way, and anticipated the result of 

 future inquiry by his followers. But the oblate figure of the earth affoi'ds an 

 example of the same kind, with this difference, that here he has himself per- 

 fected the discovery, and nearly completed the demonstration. From the 

 mutual gravitation of the particles which form its mass, combined with their 

 motion round its axis, he deduced the proposition that it must be flattened at 

 the poles ; and he calculated the proportion of its polar to its equatorial diam- 

 eter. By a most refined process he gave this proportion upon the supposition 

 of the mass being homogeneous. That the proportion is different in conse- 

 quence of the mass being heterogeneous does not in the least affect the sound- 

 ness of his conclusion. Accurate measurements of a degree of latitude in 

 the equatorial and polar regions, with experiments on the force of gravitation 

 in those regions, by the different lengths of a pendulum vibrating seconds, 

 have shown that the excess of the equatorial diameter is about eleven miles 

 less than he had deduced it from the theory; and thus that the globe is not 

 homogeneous. But on the assumption of a fluid mass, the ground of his 

 hydrostatical investigation, his proportion of 229 to 230 remains unshaken, 

 and is precisely the one adopted and reasoned from by La Place, after all the 

 improvements and all the discoveries of later times. Surely at this we may 

 well stand amazed, if not awe-struck. A century of study, of improvement, 

 of discovery has passed away, and we find La Place, master of all the new 



