378 HISTORY OF MECHANICS. 



tion of each particle, though sensible when it acts upon another par- 

 ticle at an extremely small distance from it, becomes insensible and 

 vanishes the moment this distance assumes a perceptible magnitude. 

 It may easily be imagined that the analysis by which results are ob- 

 tained under conditions so general and so peculiar, is curious and 

 abstract ; the problem has been resolved in some very extensive cases. 

 13. Motion of Fluids. The only branch of mathematical mechan- 

 ics which remains to be considered, is that which is, we may venture 

 to say, hitherto incomparably the most incomplete of all, Hydro- 

 dynamics. It may easily be imagined that the mere hypothesis oi 

 absolute relative mobility in the parts, combined with the laws of mo- 

 tion and nothing more, are conditions too vague and general to lead to 

 definite conclusions. Yet such are the conditions of the problems 

 which relate to the motion of fluids. Accordingly, the mode of solving 

 them has been, to introduce certain other hypotheses, often acknowl 

 edged to be false, and almost always in some measure arbitrary, which 

 may assist in determining and obtaining the solution. The Velocity 

 of a fluid issuing from an orifice in a vessel, and the Resistance which 

 a solid body sutlers in moving in a fluid, have been the two main 

 problems on which mathematicians have employed themselves. We 

 have already spoken of the manner in which Newton attacked both 

 these, and endeavored to connect them. The subject became a branch 

 of Analytical Mechanics by the labors of D. Bernoulli, whose Hydro- 

 Jynamica was published in 1738. This work rests upon the Huy- 

 gheuiau principle of which we have already spoken in the history of 

 the centre of oscillation ; namely, the equality of the actual descent 

 of the particles and the potential ascent j or, in other words, the con- 

 servation of vis viva. This was the first analytical treatise ; and the 

 analysis is declared by Lagrange to be as elegant in its steps RS it is 

 simple in its results. Maclaurin also treated the subject ; but is ac- 

 cused of reasoning in such a way as to show that he had determined 

 upon his result beforehand ; and the method of John Bernoulli, who 

 likewise wrote upon it, has been strongly objected to by D'Alembert. 

 D'Alembert himself applied the principle which bears his name to this 

 subject; publishing a Treatise on the Equilibrium and Motion of 

 Fluids in 1744, and on the Res istance of Fluids in. 1753. His JRe- 

 fiexions sur la Cause Generale des Vents, printed in 1747, are also 

 a celebrated work, belonging to this part of mathematics. Euler, in 

 this as in other cases, was one of those who most contributed to give 

 analytical elegance to the subject. In addition to the questions which 



