Professor Airy in reply to Mr. Ivory- 4*5 



Whatever may be the meaning of the expression " similar 

 forces," I am quite unable to discover in the sentence begin- 

 nino- at line 22, any grounds for the inference in line 25. 

 Perliaps I may place the question in a clearer point of view, 

 in the following manner. If a fluid mass in equilibrium, acted 

 on by any external forces, and by the mutual attraction of its 

 particles, were inclosed in a thin shell of the same shape, there 

 would be no pressure on the shell. Or, if a pressure were 

 communicated to the fluid (by slightly contracting the shell, 

 suppose, or by a force acting on a small piston), the pressure 

 on a unit of surface would be the same in every part of the 

 shell. Now suppose some more of the fluid to be spread on 

 the shell, and (from the action of the external forces, the at- 

 traction of the inclosed fluid, and the mutual attraction of its 

 own particles) to receive the form of equilibrium. I do not 

 see the slightest reason to believe that the pressure on the shell, 

 produced by this superincumbent matter, would be every where 

 equal. Though the whole force which acted on every particle 

 in the original external surface must have been perpendicular 

 to that surface, and consequently the whole force arising from 

 the external forces and the attraction of the original fluid 

 acts in a direction perpendicular to the shell upon the ex- 

 terior particles in contact with the shell: yet there is an- 

 other force not considered ; namely, the attraction of the new 

 stratum on its own lowest particles ; and if this can be re- 

 solved into a perpendicular and a tangential force, the pres- 

 sure on different parts of the shell 7nust be unequal (from the 

 property of equal transmission of pressure in all directions). 

 Yet the whole fluid would still be in equilibrium, without 

 owing its equilibrium to the existence of the shell, if the va- 

 riations of the internal pressure on the shell, produced by the 

 attraction of the external fluid on the internal, corresponded 

 exactly to the variations of the external pressure. 



Now I need not point out to Mr. Ivory that this is the case 

 when the equation of integrability is satisfied ; which holds 

 with all the forces with which we have to do. The fluid 

 therefore may be in equilibrium, and yet the surface which 

 was the external surface may, for all that we can discover, be 

 a surface of unequal pressure ; and if this be admitted, the 

 question is ended. I may remark, that even if Mr. Ivory had 

 proved every thing which he has stated as far as line 41, the 

 inference in the next sentence would have been unjust. " If 

 the action of the exterior stratum does not disturb the equili- 

 brium of the interior fluid body, this can happen only because 

 the lesultant of the attractions of the exterior matter u[)on any 

 particle within the stratum is evanescent." It will be enough 



