Prof. Challis on the Principles of Theoretical Physics. 321 



tained by the impact of minute bodies whose existence even is 

 not ascertained ; and to account for the elongation of comets' 

 tails, it might be equally unnecessary to invent pro hdc vice a 

 new kind of repulsive force emanating from the sun. 



I take this opportunity of adverting to an assertion which has 

 been made and reiterated respecting the science of hydro- 

 dynamics, to the effect that, compared with other departments 

 of natural philosophy, it is of minor importance, and has pro- 

 duced "meagre" results. As this assertion is probably only 

 the expression of an opinion, entertained by those who have 

 made it, respecting the course which physical research may 

 most profitably take, I claim the right in the interests of science 

 to state an opposite opinion, formed after having long made 

 hydrodynamics a special subject of inquiry, viz. that it is pre- 

 cisely the determination, by the application and solution of partial 

 differential equations, of the motion and pressure of fluids, which 

 is required for the theoretical explanation of the present large 

 accumulation of experimental facts, and that the discovery and 

 successful solution of the hydrodynamical problems proper for 

 this purpose hold the same place with respect to actual theore- 

 tical physics as the solution which Newton first effected of ap- 

 propriate dynamical problems held with respect to physical 

 astronomy. 



I beg permission to close this communication by referring to 

 a fact of observation which appears to be a singular confirma- 

 tion of the new principles which I have applied in hydrodyna- 

 mical research. It will be unnecessary to indicate here the pro- 

 cess by which the velocity of sound has been determined on those 

 principles, as it is given at length in a communication to the 

 Philosophical Magazine for December 1852. For the present 

 purpose it will suffice to state that the velocity {a Y ) of the pro- 

 pagation of sound is there given by the equation 



in which v is the maximum velocity of the propagated wave, and 

 the value of -g is — 2 . Hence, substituting V for a\ / \ _j_ __, 

 it will readily be found that 



fl, = V.(l + 1-0308 ~). 



It thus appears, as a theoretical result, that the rate of propa- 

 gation depends in some degree on the loudness of the sound, the 

 louder being propagated with the greater velocity. I was not 

 aware that such had been observed to be the fact, till my atten- 



