Mr. Ivorj's remark on a?i article hy M. Poisson. 275 



which expresses that the forces X, Y, Z are ineffective to dis- 

 place the particles in any direction upon the level surface, 

 their resultant being perpendicular to that surface. The sig- 

 nification of these equations being explicitly settled, it readily 

 follows that they are alone sufficient to determine the figure 

 of equilibrium, when there are no other causes tending to 

 displace a particle in a level surface, except the pressure of 

 the incumbent fluid caused by all the forces, of whatever de- 

 scription, that urge its particles. 



When the fluid consists of particles that attract one an- 

 other, M. Poisson admits that the matter exterior to a level 

 surface will attract the particles placed in that surface, or 

 within it. The effect of this attractive force is perfectly di- 

 stinct from the pressure of any canal passing between the 

 upper surface and the level surface. In neither of the equa- 

 tions (a) nor (i) is any account taken of an attraction which 

 the exterior fluid exerts upon a particle in a level surface. 

 But if the resultant of such attractions be not perpendicular 

 to the level surface at every point, the particles in that sur- 

 face will be displaced, and there will be no equilibrium. 

 Let P, Q, R, represent the partial attractions of the matter 

 exterior to a level surface, upon a particle in that surface, the 

 forces being respectively parallel to .r, j/, s, the coordinates of 

 the particle : then the condition that the attractive forces shall 

 be ineffective to move the particle in any direction upon the 

 level surface; or, which is the same thing, the condition that 

 the resultant of the attractions shall be perpendicular to that 

 surface, is thus expressed, 



/(Prf^ + Qr/j/ + R^;s= conSJ ^^'^ 



the coordinates varying in the level surface. Now these 

 equations are not less indispensable than the former ones (a) 

 and (b\ to the immobility of the particles of a level surface. 

 And thus it appears that, when all the forces in action are taken 

 into account, two independent conditions are necessary for 

 determining the figure of equilibrium of a fluid at liberty, 

 which consists of attracting particles; a conclusion that ac- 

 cords perfectly with the result deduced from analytical con- 

 siderations in this Journal for August last (p. 81). 



What has been proved is inconsistent with the argument 

 of M. Poisson in the article (No. 593) cited from his Meca- 

 7iiqjie. For, as it is here shown that the whole action of the 

 exterior matter, whether by attraction or by pressure, upon 

 the particles in a level surface, is directed perpendicularly to 

 that surface, it follows that the removal of the exterior matter 



T2 



