380 HISTORY OF MECHANICS. 



The reason of this peculiarity in the science of Hydrodynamics appears 

 to be, that its general principles were not discovered with reference tc 

 the science itself, but by extension from the sister science of the Me- 

 chanics of Solids; they were not obtained by ascending gradually 

 from particulars to truths more and more general, respecting the mo- 

 tions of fluids ; but were caught at once, by a perception that the 

 parts of fluids are included in that range of generality which we are 

 entitled to give to the supreme laws of motions of solids. Thus, 

 Solid Dynamics and Fluid Dynamics resemble two edifices which have 

 their highest apartment in common, and though we can explore 

 every part of the former building, we have not yet succeeded in trav- 

 ersing the staircase of the latter, either from the top or from the 

 bottom. If we had lived in a world in which there were no solid 

 bodies, we should probably not have yet discovered the laws of mo- 

 tion ; if we had lived in a world in which there were no fluids, we 

 should have no idea how insufficient a complete possession of the 

 general laws of motion may be, to give us a true knowledge of par- 

 ticular results. 



14. Various General Mechanical Principles. The generalized laws 

 of motion, the points to which I have endeavored to conduct my his- 

 tory, include in them all other laws by which the motions of bodies 

 can be regulated; and among such, several laws which had been dis 

 covered before the highest point of generalization was reached, and 

 which thus served as stepping-stones to the ultimate principles. Such 

 were, as we have seen, the Principles of the Conservation of vis viva, 

 the Principle of the Conservation of the Motion of the Centre of 

 Gravity, and the like. These principles may, of course, be deduced 

 from our elementary laws, and were finally established by mathema- 

 ticians on that footing. There are other principles which may be 

 similarly demonstrated; among the rest, I may mention the Principle 

 of the Conservation of areas, which extends to any number of bodies a 

 law analogous to that which Kepler had observed, and Newton demon- 

 strated, respecting the areas described by each planet round the sun. 

 I may mention also, the Principle of the Immobility of the plane of 

 maximum areas, a plane which is not disturbed by any mutual action 

 of the parts of any system. The former of these principles was pub- 

 lished about the same time by Euler, D. Bernoulli, and Darcy, under 

 different forms, in 1746 and 1747 ; the latter by Laplace. 



To these may be added a law, very celebrated in its time, and the 

 occasion of an angry controversy, the Principle of least action. Man- 



