1 .' AN ESSAY OS THE MATHEMATICAL PRINCIPLES OF PHYSICS. 



On both theories, too, the preservation of the universe is effected only by the 



unceasing expenditure of enormous quantities of work, so that the conservation 



energy in physical operations, which has been the subject of so many 



. ... . ; ;.. , ; iy of itiaA li:i- \>-<\ to so many disfovi-r'n-s, is 



apparent only, and is merely a kind of "moveable equilibrium" between supply 

 nnd destruction. 



It may seem a sort of anticlimax to descend from these highest heavens 

 invention down to the "equations of condition" of fluid motion. But it 

 would not be right to pass by the fact that the fluids treated of in this Essay 

 ore not in all respects similar to those met with elsewhere. In all their motions 

 they obey a law, which our author was the first to lay down, in addition 

 or perhaps in some cases in opposition to those prescribed for them by Lagrange, 

 Poisson, &c. 



It is true that a perfect fluid, originally at rest, and afterwards acted on 

 only by such forces as occur in nature, will freely obey this law, and that not 

 only in the form laid down by Professor Challis, in which its rigour is partially 

 relaxed by the introduction of an arbitrary factor, but in its original severe 

 Minplifity, as the condition of the existence of a velocity-potential. 



But, on the one hand, problems in which the motion is assumed to violate 

 this condition have been solved by Helmholtz and Sir W. Thomson, who tell 

 us what the fluid will then do; and, on the other hand, Professor ChallisV 

 fluid is able, in virtue of the new equation, to transmit plane waves consisting 

 of transverse displacements. As this is what takes place in the luminiferous 

 sether, other physicists refuse to regard that aether as a fluid, because, according 

 to their definition, the action between any contiguous portions of a fluid is 

 entirely normal to the surface which separates them. 



It is not necessary, however, for us to say any more on this subject, as 

 the Essay before us does not contain, in an explicit form, the equation referred 

 to, but is devoted rather to the exposition of those wider theories of the 

 constitution of matter and the phenomena of nature, some of which we have 

 endeavoured to describe. 



