78 EQUILIBRIUM OF MUTUALLY ATTRACTIVE 



it is only by the transmitted pressures that it can be esta- 

 blished. 



Clairaut, as his views are represented by Mr Ivory, says 

 nothing of the transmission of pressure ; but it is impossible 

 to investigate fluid equilibrium without tacit or expressed re- 

 ference to some distinctive character of fluidity; and in the 

 principle he makes use of, the idea of the transmission of pres- 

 sure is essential. It appears, then, that the force at a surface 

 of equal pressure is normal to it; and this conclusion is little 

 else than a different way of putting the principles employed by 

 Clairaut. We are now enabled to dispense with any process of 

 constructing a fluid mass. 



On referring to the mathematical reasoning employed above, 

 we shall easily see that, substituting two infmitesimally near 

 surfaces of equal pressure for the consecutive free surfaces of 

 Clairaut, the result we arrive at is simply the symbolical ex- 

 pression of the principle just laid down, viz. that the force at 

 a surface of equal pressure is normal to it. A very little at- 

 tention will show, that (2) is true in every case of fluid equi- 

 librium, and that it is completely equivalent to the principle 

 which it represents. In translating, so to speak, his funda- 

 mental idea from the infinitesimal to the fluxionary conception, 

 that namely of successive generation, Clairaut has tacitly intro- 

 duced a new condition, namely, that a surface of equal pressure 

 will necessarily be a free surface of equilibrium, the superin- 

 cumbent part being removed. 



Mr Ivory remarks " The investigation of Clairaut is clear 

 and definite. It evidently assumes that there is no cause tend- 

 ing to disturb the equilibrium of A, except the action of the 

 forces at the surface of A upon the matter of $A. On this 

 account his method fails when there is a mutual attraction be- 

 tween the mass A and the stratum SA. If the mass A attract 

 the matter of the stratum 8 A, and cause it to press, it follows 

 necessarily that the matter of &A will react, and by its attrac- 

 tion will urge the particles of A to move from their places. In 

 this case, therefore, the equilibrium of A is disturbed by a force 

 which Clairaut has not attended to; and unless the effect of 

 this new force is counteracted, the body of fluid A + SA will not 

 be in equilibrium. The principle of the method suggests a 

 remedy for this omission, for it is easy to prove that the equi- 



