116 HISTORY OF MECHANICS. 



ditions 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 ma- 

 thematical mechanics which remains to be consi- 

 dered, is that which is, we may venture to say, 

 hitherto incomparably the most incomplete of all, 

 Hydrodynamics. It may easily be imagined that 

 the mere hypothesis of absolute relative mobility in 

 the parts, combined with the laws of motion 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 hypo- 

 theses, often acknowledged 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 ves- 

 sel, and the Resistance which a solid body suffers in 

 moving in a fluid, have been the two main problems 

 on which mathematicians have employed them- 

 selves. We have already spoken of the manner in 

 which Newton attacked both these, and endeavoured 

 to connect them. The subject became a branch of 

 Analytical Mechanics by the labours of D.Bernoulli, 

 whose Hydrodynamwa was published in 1738. This 

 work rests upon the Huyghenian principle of which 

 we have already spoken in the history of the center 

 of oscillation ; namely, the equality of the actual 



