Mr. R. H. M. Bosanquet on the Theory of Sound. 275 



well*: — The average vis viva along each of the three axes is 

 the same, and = average vis viva of rotation about each of the 

 three axes. 



If we applied these laws to the old value of ratio of speci- 

 fic heats (1*41), we got '(315 as the ratio of vis viva of transla- 

 tion : total vis viva ; and this was unintelligible. 



Kundt and Warburg f , starting from certain chemical con- 

 siderations as to the molecular constitution of mercury, were 

 led to investigate the ratio of specific heats in its vapour by 

 measuring the length of stationary sound-waves produced in 

 it. They found the ratio = 1*186 x that in air, whence, assu- 

 ming air =1*405, they got 1*666 for the ratio in mercury. 

 (If we put ratio in air =1*4, we get 1*660.) 



Their reasoning is then somewhat as follows : — If we regard 

 the atom of mercury as a perfectly smooth hard sphere, the 

 specific-heat-ratio of a gas composed of such atoms should be 

 If, or very nearly the value found. 



This well-known conclusion follows from the above princi- 

 ples by remarking that the vis viva of rotation is absent in the 

 supposed case, and consequently the ratio, vis viva of transla- 

 tion : total vis viva is unity ; whence, from Clausius's equation, 



c ~~ 3 ' 



The objection to the application of this reasoning to any 

 real gas such as mercury is that the spectroscope tells us that 

 vibrations go on inside the molecule (or atom), and in that 

 case the total vis viva would include that due to these 

 vibrations. 



All that can be said, then, is that the theory cannot at pre- 

 sent take count of these intramolecular (intraatomic) vibra- 

 tions. We have no theory about any of these matters that is 

 quite perfect ; but the gradual advance has consisted, and is 

 likely to consist, in the recognition of general correspondences, 

 as in the case of the dynamical theory of optics. From this 

 point of view we may admit the result of Kundt and Warburg 

 as one of interest and importance, while fully keeping in view 

 the incompleteness of the dynamical explanation it affords. 



Now it is but a step from the case of a smooth hard sphere 

 to the case of a smooth hard solid of revolution, which we may 

 conceive of as formed of two smooth hard spheres rigidly 

 joined up together, or as a cylinder, or having many other 

 forms. 



A gas constituted of such particles would have five equal 

 portions of vis viva, three of which would be due to translation, 



* Phil. Mag. [IV.] vol. xx. p. 36. 

 t Pogg. Ann. vol. clvii. p. 353. 

 T2 



