THE 



PHILOSOPHICAL MAGAZINE 



AND 



ANNALS OF PHILOSOPHY. 



[NEW SERIES.] 



SEP T E MB E R 1827. 



XXX. On the Figure of Equilibrium of a Homogeneous 

 Planet in a Fluid State ; in reply to the Observations of 

 M. Poisson, published in this Journal for July last. By 

 J. I?oRY, Esq. M.A. F.R.S.* 



THE two letters which I have addressed to Professor Airy 

 in the last Numbers of this Journal, fully ascertain the 

 nature and extent of the analytical method employed by La- 

 place in the investigation of the figure of the planets. I now 

 proceed to the conditions which I have found to be necessary 

 for solving the problem of a homogeneous mass of fluid re- 

 volvino- upon an axis, to which M. Poisson objects. The sub- 

 ject is one of considerable importance ; it involves a capital 

 question in the system of Newton, towards the solution of 

 which nothing has in reality been added since the time of 

 Maclaurin and Clairaut. This is the more unaccountable, be- 

 cause, in the long interval elapsed, the problem has continued 

 to occupy the attention of all the great mathematicians ; the 

 difficulties attending the computation of the attractive forces, 

 which embarrassed the first inquirers, have been overcome by 

 the progress of mathematical science ; and we are in posses- 

 sion of a theory of the equilibrium of fluids, which is sup- 

 posed to be exact and complete. Yet these accessions to our 

 knowledge have been made not only without advancing the 

 problem of the figure of the planets, but even without reaching 

 what had jireviously been investigated by a more simple geo- 

 metry. What reasons can be assigned for this total ineffi- 

 ciency ? Any attempt to elucidate this matter, and to detect 



* Conimtinicatcil by the Author. 

 iVcTjoiJmVs. Vol. 2. No. 9. %>/. 1827. Y any 



