Equations of Motion of a Viscous Liquid. iili 



fluid. " When generalizing James Bernoulli's theory of 

 pendulums he discovered a principle of dynamics so simple 

 and general that it reduced the laws of motion of bodies to 

 that of their equilibrium. He applied this principle to the 

 motion of fluids, and gave a specimen of its application at 

 the end of his Djjnamique in 1743. It was more fully developed 

 in his Trait<- Des Fluides, which was published in 1744, 

 where he resolves, in the most simple and elegant manner, 

 all problems which relate to the equilibrium and motion of 

 fluids. He makes use of the very same suppositions as Daniel 

 Bernoulli, though his calculus is established in a very ditfer- 

 ent manner. He considers, at every instant, the actual motion 

 of a stratum as composed of a motion which it had in the 

 preceding instant and of a motion which it has lost. The 

 laws of ecjuilibrium between the motions lost furnish him 

 with the equations which represent the motion of the fluid. 

 Although the science of hydrodynamics had then made con- 

 siderable progress, yet it was chiefly founded on hypothesis. 

 It remained a desideratum to express by equations the motion 

 of a particle of fluid in any assigned direction. These equa- 

 tions were found by D 'Alembert from two principles: first, 

 that a rectangular canal, taken in a mass of fluid in equi- 

 librium, is itself in equilibrium; second, and that a portion of 

 fluid, in passing from one place to another, preserves the same 

 volume when the fluid is incompressible, or dilates itself accord- 

 ing toagiven law when the fluid is elastic. His very ingenious 

 method was published in 1752, in his Essai Siir la Ixesistdiice 

 Dcs Fluides. It was brought to perfection in his Opuscules 

 Mdlhemaiiques, and was adopted by Euler." Philosophers 

 had attempted in vain to determine the laws of fluid motion 

 independent of all hypotheses. However, the method of 

 fluxions proved inadetjuate to the purpose, and it was only 

 after Euler had contributed to science his calculus of partial 

 ditferences that the object was reached. D'Alembert first 

 applied the new calculus to the motion of water, and he and 

 Euler both succeeded in obtaining equations of motion for a 

 perfect fluid restricted by no particular hypothesis. 



Chevalier Dubuat, a French engineer, published in 1786 

 a very satisfactory theory of the motion of a fluid, based upon 

 the experiments of himself and others. '' He considered that 

 if water were a perfect fluid, and the channels in which it 



