246 Mr. Ivory in reply to the Bulletin des Sciences, 



when the exponent of the attractive force is — 2 ; but on the 

 present occasion, the author brings forward the case when the 

 exponent of the attractive force is negative and greater than 2. 

 I have no inclination to enter the lists on this new ground ; 

 and I am persuaded that whoever will read attentively what is 

 written in the Bulletin, will not blame Laplace for departing 

 from the great generality aimed at in the third book of the 

 Mecanique Celeste, and in his later writings confining his theory 

 to the single case of an attraction inversely proportional to the 

 square of the distance. 



In p. 155, the author proceeds to animadvert on what he 

 calls my new principle of Hydrostatics, which he says has not 

 yet been refuted by any geometer " (Tune maniere vraiment sci- 

 entifique? Great was my astonishment on perusing what the 

 author has written, to find that it does not affect in any re- 

 spect what I have published concerning the equilibrium of a 

 planet in a fluid state. This part of the Bulletin is mostly 

 taken up with two demonstrations of the general equation of 

 the level surfaces, or the surfaces of equal pressure, in a fluid 

 mass in equilibrio. Now I have nothing to object to these de- 

 monstrations. Applied to the case of a homogeneous planet, 

 the meaning of the equation is this : The equilibrium of the 

 planet requires that it be possible to divide the whole fluid 

 mass into any number of strata separated by surfaces of equal 

 pressure, which, beginning at a point within the planet, extend 

 to the outer surface, and are included one within another*. 

 My solution of the problem h is so far from being inconsistent 

 with the general equation, or with the equivalent property of 

 the level surfaces, that it is the only general method that has 

 yet been found for rendering the existence of these surfaces 

 demonstrative and certain f . 



In the usual theory, and particularly in the theory delivered 

 in the Mecanique Celeste, it is affirmed that the perpendicu- 

 larity of gravity to the outer surface is all that is necessary to 

 insure the existence of the interior level surfaces, their gradual 

 decreasing, and final concurrence in a point. But of this no 

 sufficient demonstration is given ; and I contend that none 

 can be deduced from the single principle of equilibrium as- 

 sumed. I have done nothing more than add a condition which 

 is wanting, without which trie problem cannot be solved. 



In reference to some of the author's remarks, it is to be ob- 



* See Clairaut, Figure de la Terre, Part. i. § xxi. 



f In prop. 4th, p. 166 of this Journal for September 1827, it is shown 

 in what manner the general equation of the level surfaces is fulfilled in my 

 solution : and it is proved that, without the condition I have added, the 

 same equation could not be fulfilled, and there would be no equilibrium. 



served, 



