Mr. J. J. Waterston on the Theory of Sound. 491 



Mr. Herapath unfortunately as&umed heat or temperature to 

 be represented by the simple ratio of the velocity instead of the 

 square of the velocity — being in this apparently led astray by 

 the definition of motion generally received — and thus was baffled 

 in his attempts to reconcile his theory with observation. If we 

 make this change in Mr. Herapath's definition of heat or tempe- 

 rature, viz. that it is proportional to the vis viva or square velocity 

 of the moving particle, not to the momentum or simple ratio of 

 the velocity, we can without much difficulty deduce, not only the 

 primary laws of elastic fluids, but also the other physical pi'oper- 

 ties of gases enumerated above in the third objection to Newton's 

 hypothesis. In the Archives of the Royal Society for 1845-46, 

 there is a paper " On the Physics of Media that consists of per- 

 fectly Elastic Molecules in a state of Motion," which contains 

 the synthetical reasoning upon which the demonstration of these 

 matters rests. The velocity of sound is therein deduced to be 

 equal to the velocity acquired in falling thi-ough three-fourths 

 of a uniform atmosphere. This theory does not take account 

 of the size of the molecules. It assumes that no time is lost at 

 the impact ; and that if the impacts produce rotatory motion, the 

 vis viva thus invested bears a constant ratio to the rectilineal vis 

 viva, so as not to require separate consideration. It also does not 

 take account of the probable internal motion of composite mole- 

 cules ; yet the results so closely accord with observation in every 

 part of the subject, as to leave no doubt that Mr. Herapath's 

 idea of the physical constitution of gases approximates closely 

 to the truth. M. Krouig appears to have entered upon the sub- 

 ject in an independent manner, and arrived at the same result; 

 M. Clausius, too, as we learn from his paper "On the Nature 

 of the Motion we call Heat" (Phil. Mag. vol. xiv. p. 108). 



The physics of such media is a study that must be ungenial, 

 perhaps repulsive, to mathematicians brought up in the statical 

 school. The fundamental hypothesis does not permit us at once 

 to transfer the subject to the domain of pure mathematics, as 

 Newton's hypothesis converted physical astronomy into a purely 

 mathematical study. The mode of action by which certain phte- 

 nomena make their appearance must be realized at each step in 

 conformity with the conservation of force : the causal relation 

 must be ever present to the mind, or no true progress can be 

 made. On the other hand, the mathematics required is simple, 

 and almost every one of the applications of the theory admits of 

 popular illustration. An attempt of this kind 1 have given above 

 in reference to the conveyance of sonorous unpulses, introducing 

 a dynamic theory of sound. The strict demonstration of the 

 velocity is given in the memoir above referred to. A few fnrtlier 

 illustrations may here be added to show in brief the capabilities 



