348 M. Bessel's Examination of the Divisions 



obtained the true conditions necessary to the equilibrium of a 

 homogeneous fluid, there is no longer any difficulty in de- 

 ducing from them what was proved synthetically by Maclau- 

 rin. The peculiar analysis of Legendre and Laplace is no 

 more than a modification of the exact equations of the equili- 

 brium, when we neglect the square and higher powers of the 

 oblateness of the spheroid. 



In those remarkable propositions, which never can be too 

 much admired, where Newton treats of the attractions of 

 spheres and spheroids, he proves that a particle placed any 

 ■where within a hollow spherical shell uniformly dense, will 

 be in equilibrio, or will be attracted equally in opposite direc- 

 tions. The same conclusion has been extended to a hollow 

 shell of homogeneous matter bounded by any two elliptical 

 surfaces similar to one another. This curious property is 

 noticed by all the writers on attraction; but it seems to be 

 viewed as belonging accidentally to elliptical spheroids. The 

 new theory shows its connection with the equilibrium ; for the 

 hollow shell is no other than a level stratum of a homoge- 

 neous fluid in equilibrio* 



The paper above alluded to treats only of homogeneous 

 fluids. But the same principles likewise apply when the mass 

 is composed of strata of variable densities, as I shall be able 

 to show on another occasion. A great advantage arises from 

 knowing the true equations of equilibrium, in shortening the 

 demonstrations, and in clearness and precision. When the 

 equations can be solved, the exact figures of equilibrium are 

 obtained, as in the case of a homogeneous fluid ; otherwise, 

 the analytical method of approximate solution must be em- 

 ployed. James Ivory. 

 May 5, 1854. 



LVII. Examination of the Divisions o/TIeichenbach's Circle 

 at the Obsa-vatory of Konigsberg. By M. Bessel.* 



f HAVE applied to this instrument the same method by 

 * which I have formerly determined the errors of the divi- 

 sions of Cary's circle, with such changes only as the nature of 

 its construction required. Cary's circle is read off by micro- 

 scopes, and one of them, together with another expressly con- 

 structed for the purpose ot examination, is sufficient for in- 

 vestigating the errors of division. Reichenbach's circle has 



* Translated from the viith section of M. Bessel's Astronomical Obser- 

 vations. 



no 



