Dr. Schroder van der Kolk on the Velocity of Sound, 41 



331 



is thus ■?-—-„ = 12-04 metres. Now at the muzzle of the gun 



half a wave-crest is formed, as indicated in the annexed figure, 



the length of which is about 3 

 metres, and the volume of a 

 sphere with this radius is 113*1 

 cubic metres. If 2*961 cubic 

 metres of gas are evolved in 

 this space, the condensation 



W1 H be = nM =gg nearly. 



We have, further, It = 3, r in Moll and Van Beek's experiments 

 17669 metres, \ 2 =0'2857 x i. =0-00752 'and \=0-0872. 



do 



The formulae above mentioned then give 



^ = 52-974 and * 2 =53'371. 



The second term is 0*0000687, and therefore negligible. 



The result is therefore in this case that the difference in the 

 time required by sound to traverse the given distance in a tube 

 and in open space is 0*4 second, or that the distance through 

 which it travels in this time is 132*4 metres. 



It is interesting to observe that the second term in the expres- 

 sion for t<2 has an inappreciable value. Disregarding it, we have 



r— It 



t 2 = , that is to say, the ordinary formula. Hence it fol- 



lows that, in free space, the intensity of the report of a cannon- 

 shot has no perceptible effect on its velocity of transmission. 



I had at first supposed that the formula would have afforded 

 an explanation of the observation of Ross, spoken of above. 

 This, however, is not the case, for the difference of velocity is 

 much too slight. On the contrary, this observation seems to be 

 as yet entirely unexplained; and even Le Conte, in his Memoir 

 on Sound (Phil. Mag. S. 4. vol. xxvii. p. 1) treats it as only a 

 completely isolated observation which is not sufficiently esta- 

 blished. In the Fortschritte der Physik (Berlin, 1860, p. 167) 

 it is explained as a psychological illusion*. 



The result we have arrived at of the unequal velocities does 

 not in any way contradict Poisson's theory. It is true that he 

 found the velocity to be independent of the intensity • but in 

 his investigation he neglected the velocity of vibration, which is 

 precisely the point in question, in order to be able to integrate 

 the partial differential equations. 



* [See, however, Earnshaw, Phil. Mag. S. 4. vol. xx. p. 37, and vol, xxvii. 

 p. 98.— Transl.] 



