130 NOTES TO BOOK VI. 



nical action. But something was subsequently done to 

 remove the ground of this complaint. In 1818, Gauss 

 pointed out that secular equations may be conceived to 

 result from the disturbing body being distributed along its 

 orbit so as to form a ring, and thus made the result con- 

 ceivable more distinctly than as a mere result of calcula- 

 tion And it appears to me that Professor Airy's treatise 

 entitled Gravitation, published at Cambridge in 1834, is 

 of great value in supplying similar modes of conception 

 with regard to the mechanical origin of many of the prin- 

 cipal inequalities of the solar system. 



Bessel in 1824, and Hansen in 1828, published works 

 which are considered as belonging, along with those of 

 Gauss, to a new sera in physical astronomy. (Abhand. 

 der Akad. d. Wissensch. zu Berlin, 1824; and Disquisi- 

 tiones Circa Theoriam Perturbationum. See Jahn. Gesch. 

 der Astron. p. 84.) Gauss's Theoria Motuum Corporum 

 Celestium, which had Lalande's medal assigned to it by 

 the French Institute, had already (1810) resolved all 

 problems concerning the determination of the place of a 

 planet or comet in its orbit in function of the elements. 

 The value of Hansels labours respecting the Perturba- 

 tions of the Planets was recognized by the Astronomical 

 Society of London, which awarded to them its gold medal. 



The investigations of M. Damoiseau, and of MM. 

 Plaria and Carlini, on the Problem of the Lunar Theory, 

 followed nearly the same course as those of their prede- 

 cessors. In these, as in the Mecaniqw Celeste, and in 

 preceding works on the same subject, the moon's co-or- 

 dinates (time, radius vector and latitude) were expressed 

 in function of her true longitude. The integrations were 

 effected in series, and then by reversion of the series, 



