CHAP. II., 2.] 



PHYSICAL ASTRONOMY LAPLACE. 



17 



(63.) 

 Earth's 

 ellipticity 

 and solar 

 parallax 

 deduced 

 from the 

 moon's 

 motion. 



I 



been also slowly increasing. The result is that the 

 moon's motion has been continually accelerated. 

 Now, we have in the last section referred by anti- 

 cipation to this acceleration as having led to the 

 belief that the moon must at last fall to the earth. 

 Laplace's discovery, however, shows that the acce- 

 leration has a limit, depending on that of the ex- 

 centricity of the earth's orbit, which having reached 

 its minimum, the lunar mean motion will begin to 

 be retarded, and will continue so through a vast 

 cycle of ages, and so on alternately. Theory enables 

 us to assign, with considerable accuracy, the amount 

 of the acceleration, which is now about 10" of lon- 

 gitude in a century. 1 



Besides this very satisfactory discovery, Laplace 

 investigated three of the lunar inequalities in a man- 

 ner leading to curious and unexpected results. Two 

 of these depend on the spheroidal figure of the earth. 

 The nutation of the earth's axis, which is due to the 

 attraction of the moon on the protuberant equatoreal 

 parts of the earth, is exactly reproduced by the equi- 

 valence of action and reaction in the movements of 

 the lunar orbit, only less perceptible in degree on 

 account of the length of the leverage at which they 

 are effected. The inequality of the moon's motion 

 in latitude may be used to determine the degree of 

 compression of our globe at the poles. Laplace de- 

 duced from the Greenwich observations of the moon 



the fraction ^~, and, from a relative inequality in 

 longitude, ^-. ; a coincidence really astonishing, not 



only as between themselves, but also when compared 

 with the mean result of laborious investigations by 

 actual measurement of the earth's surface. The other 

 result we referred to was the determination from the 

 lunar theory of the solar parallax, in other words, 

 the distance of the earth from the sun, which enters 

 into the expression of a certain inequality of the 

 moon's motion in longitude. From the observed 

 amount of this inequality, Laplace obtained a value 

 of the solar parallax exactly coincident with that 

 obtained with so much labour on occasion of the 

 transit of Venus in 1769. Strange and admirable 

 result (as Laplace himself remarks), that the astro- 

 nomer, immured in his observatory, and watching our 

 satellite through his telescopes, and reading the re- 

 sult by the aid of mathematical analysis and the 

 theory of gravitation, should be able to determine the 

 figure of our earth, and its distance from the sun, 

 with perhaps quite as great accuracy as by any direct 

 measurements. Truly the wonders of fact exceed 

 those of fiction, and the divinations of true science 

 may match the pretensions of her counterfeit, astro- 

 logy. 



In conclusion of this subject, I regret that space ( 64 -) 

 does not allow me to advert particularly to Laplace's Ju p?[J r , 

 remarkable success in accounting for some singular satellites. 

 peculiarities in the system of Jupiter's satellites, 

 arising from, and partly occasioning, an exact com- 

 mensurability in the periods of some of them (which 

 Sir John Herschel has lately observed to hold also 

 in the Saturnian system in a somewhat different 

 manner), a case which we have seen to be especially 

 excluded in the instance of the planets, and which 

 has been pronounced by a very competent judge (Mr 

 Airy) to be " the most curious and complicated sys- 

 tem that has ever been reduced to calculation." It 

 ought to be stated, however, that Laplace's dis- 

 coveries were based upon a previous and highly 

 original investigation of Lagrange. 



II. In the second place, we shall briefly state the (65.) 

 nature of Laplace's happy explanation of a great in- Lon S 1 - 

 equality of the solar system, tc which, like the fact O f j u pi te r 

 of the lunar acceleration, especial attention had been and Sa- 

 called by the sagacity of Halley, and which, like it, turn - 

 resisting all the efforts of geometers to interpret, 

 threatened the credibility of the Newtonian theory of 

 gravity. We are therefore to look upon this step as 

 something more than a solution of a difficult problem; 

 it was a new, peculiar, and unsuspected combination 

 of circumstances on which it depended, and the solu- 

 tion afforded a key in all time coming to difficulties 

 depending upon a like cause. 



Halley had ascertained, that by comparing mo- (66.) 

 dern with the most ancient observations of Jupiter and^ 1 . 

 Saturn, the mean motion of the former planet had been qualities ; 

 accelerated, and that of the latter retarded. Lambert 

 remarked subsequently that, if we confine ourselves 

 to modern observations alone, an opposite change 

 would appear to be in progress. The amount of the 

 error of the tables was so considerable (amounting to 

 20' or more in the middle of the eighteenth century, 

 and capable, in fact, of becoming much larger), as to 

 have been (along with the apsidal motion of the lunar 

 orbit) one of the first subjects of anxiety and specu- 

 lation to geometers, when the Newtonian theory came 

 fairly into discussion. For nearly forty years this 

 stubborn inequality was vainly attempted to be ac- 

 counted for by Euler, Clairaut, D' Alembert, Lagrange, 

 and by Laplace himself, before the latter hit upon 

 the true cause of the anomaly. It was long, and 

 naturally, believed to be a properly secular inequa- 

 lity, arising from the average mutual effects of the 

 planets Jupiter and Saturn, though Lamberts re- 

 mark rendered this less probable. It was in the course 

 of the consequent research that Laplace proved that 

 the mutual action of the two planets could produce 





1 We here add that very recently Mr Adams has discovered that Laplace, and also his followers, in confining their at- 

 tention to the radial effect of the sun's interference with the lunar motions, as affected by the excentricity of the earth's orbit, 

 have unwarrantably assumed that the area described by the moon a unit of time is invariable. He finds, on the contrary, tan- 

 gential perturbations depending on the same cause, and sensibly modifying the amount of secular mean motion deduced from 

 theory. (Philosophical Transactions, 1853.) 



