the Particles of which are urged hy accelerating Forces. 323 



in applying it, every force which is introduced by a stratum 

 and is capableof moving the particles of A, must be carefully 

 ascertained and made ineffective. 



The method of Clairaut, as it has been explained and ex- 

 tended, will help us to form a just notion of Euler's theory. 

 A very little attention will show, that all the perplexities 

 that have ever attended this theory, originate in misconcep- 

 tion of the manner in which a particle of a fluid in equilibrium 

 is made immoveable by the pressures which act upon it. 

 If we conceive a particle placed on one of the interior sur- 

 faces in Clairaut's method, that is on a level surface, it is most 

 evident that all the pressure upon the particle is caused by 

 the action of the fluid above it, or on the outside of the level 

 surface. If the fluid without the level surface were removed, 

 there would be no pressure upon the particle, which would 

 only be subject to the action of the forces inherent in the sur- 

 face on which it is placed. Now pressures of equal intensity 

 are impressed at all the points of a level surface; these press- 

 ures are transmitted through the contained fluid to the par- 

 ticles on the surface ; so that every such particle is pressed 

 equally in all directions by the action of the fluid exterior to 

 the surface. It is therefore correct to say that a particle in 

 a level surface is not moved by the pressures caused by the 

 forces which urge all the fluid on the outside of that surface : 

 but this does not demonstrate that the particle is at rest by 

 the action of the whole mass. To complete the proof of an 

 equilibrium, it is further necessary to show, that the body of 

 fluid within the level surface is not liable to a change of its 

 form or position by the forces that act on its own particles. 

 The theory of Euler is therefore chargeable with mistaking 

 the action of a part only of the fluid, for the effect of the 

 forces that urge all the particles of the mass. If a canal be 

 drawn in any manner from a particle in a level surface to ter- 

 minate in the upper surface, it will invariably exert the same 

 pressure upon the particle: but the nature of a level surface 

 is such, that a part of any canal within it presses neither 

 way ; so that the pressure upon the particle is produced solely 

 by the action of the forces upon the part of a canal exterior 

 to the level surface. We may now safely affirm that the 

 great generality of Euler's theory arises from omitting what 

 is essential to an equilibrium ; and enough has been said to 

 show that, when the omission is supplied, we arrive at the 

 principles of Clairaut's method by a route which is different 

 indeed, but not so direct. 



One observation more it seems requisite to make. Euler 

 has investigated his theory in a memoir {Mem. de Berlin^ 



Y2 



