the received principles of Hydrodynamics. 165 



and Physics/ pp. 101-107.) In certain cases the law admits of 

 being verified directly by experiment ; but generally the verifi- 

 cation is effected by comparisons of results obtained mathemati- 

 cally, on the hypothesis of the truth of the law, with observed 

 facts. Also for the case of fluid in motion an a priori demon- 

 stration of the same law may be given on principles which are 

 indicated in pp. 172 and 173 of the work just cited. But in 

 this case experiment cannot be directly employed for its verifica- 

 tion ; and on this account some mathematicians have thought 

 that the law was not as certainly established for fluid in motion 

 as for fluid in equilibrium. It may, however, be asserted that, 

 although for fluid in motion the demonstration can only be 

 effected by the combination of reasoning with the results of ex- 

 periment, both the a priori proof of the law, and its verification 

 a posteriori by comparison of calculated results with observation, 

 are equally valid whether the fluid is in motion or at rest. 



(3) Assuming that Boyle's law has been proved by experi- 

 ment to be true for air of given temperature at rest, what evi- 

 dence is there that it is true for air in motion ? This question, 

 to which, as far as I am aware, a satisfactory answer has not 

 hitherto been given, I propose to answer as follows : — Since it 

 does not appear practicable to verify the law for fluid in motion 

 by direct experiment, the only course that can be adopted is to 

 justify the assumption of the law for that case by a priori rea- 

 soning. This having been done, the truth of the assumption 

 has to be confirmed, as in all like instances, by comparison of 

 results mathematically deduced from it with experiment. The 

 chain of the reasoning is therefore incomplete unless it is shown 

 by an a priori argument that the equation p = a 2 p is not excluded 

 by the state of motion. Now this link is supplied by Mr. Moon's 

 equation p= funct. (p and v), the investigation of which rests 

 on the general principle that all physical relations expressible by 

 functions of space and time are comprehended by the rules of 

 abstract calculation. Thus that equation is quite general, inclu- 

 ding every supposable relation between p and v ; and accordingly 

 we may assume that v vanishes from the equation, or that v is a 

 function of p. In either case^> becomes a function of p only. 

 Now, since in the original investigation p was assumed to be a 

 function of space and time, this relation between p and p } inclu- 

 ding as a particular case p — a z p, must apply to fluid in motion. 

 Hence Boyle's law may be assumed as a basis of reasoning in 

 hydrodynamics. 



