312 A Short History of Astronomy [CH. xi. 



importance ; whereas the periodic inequalities of the planets 

 are generally small and the secular inequalities are the most 

 interesting. 



The method of treating the elements of the elliptic orbits 

 as variable is specially suitable for secular inequalities ; but 

 for periodic inequalities it is generally better to treat the 

 body as being disturbed from an elliptic path, and to study 

 these deviations. 



"The simplest way of regarding these various perturbations 

 consists in imagining a planet moving in accordance with the laws 

 of elliptic motion, on an ellipse the elements of which vary by 

 insensible degrees ; and to conceive at the same time that the 

 true planet oscillates round this fictitious planet in a very small 

 orbit the nature of which depends on its periodic perturbations." * 



The former method, due as we have seen in great measure 

 to Euler, was perfected and very generally used by Lagrange, 

 and often bears his name. 



243. It was at first naturally supposed that the slow 

 alteration in the rates of the motions of Jupiter and Saturn 

 ( 2 35 2 36, and chapter x., 204) was a secular inequality ; 

 Lagrange in 1766 made an attempt to explain it on this 

 basis which, though still unsuccessful, represented the 

 observations better than Euler's work. Laplace in his first 

 paper on secular inequalities (1773) found by the use cf 

 a more complete analysis that the secular alterations in 

 the rates of motions of Jupiter and Saturn appeared to 

 vanish entirely, and attempted to explain the motions by the 

 hypothesis, so often used by astronomers when in difficulties, 

 that a comet had been the cause. 



In 1773 John Henry Lambert (1728-1777) discovered 

 from a study of observations that, whereas HalJey had found 

 Saturn to be moving more slowly than in ancient times, it 

 was now moving faster than in Halley's time a conclusion 

 which pointed to a fluctuating or periodic cause of some 

 kind. 



Finally in 1784 Laplace arrived at the true explanation. 

 Lagrange had observed in 1776 that if the times of revo- 

 lution of two planets are exactly proportional to two whole 



* Laplace, Systeme du Monde, 



