Dr. Schroder van der Kolk on the Velocity of Sound. 37 



Accordingly, for a displacement represented by 8 the force is 

 not e$, but it is this quantity increased by ehk, where k is a quan- 

 tity as yet unknown. The force is therefore = e8(l-t-k) } and the 

 above formula becomes* 



^^m=\/^m- . • • a) 



The theory of heat gives the formula 





Po 



for the case of a mass of air under the pressure^, of the volume 

 V , and at the temperature T , the latter reckoned from the ab- 

 solute zero, being compressed until these quantities become 

 respectively =p v Y v and T ( no heat being either communicated 



c 

 or withdrawn. 7 is here = -. In the case of sound, the con- 



c \ 



densations take place so quickly that this formula is certainly 



applicable. 



If H is the pressure read off upon the barometer, the pressure 

 at the crest of the wave will be greater. 



Let the compression be denoted by AV = V — V 1? we then 

 have 



as the expression for the height of the barometer at the crest of 

 the wave. 



This, however, is not the pressure which must be taken for the 



calculation. The formula \ / k. _ would be correct if the con- 



V b 



densation took place without development of heat; but even 

 then the pressure at the wave-crest would not be = H, but 



V 



z=hc, — H~- } in accordance with Mariotte's law. 



1 



Hence the additional pressure due to the evolution of heat is 



=^= h {(t:) v -v;} j 



and this pressure is equal to e§k or K$k, which also denotes the 

 increase of pressure caused by the heat. 



* Up to this point I have followed the statement of the theory of wave- 

 motion given by Dr.Wullner, in his Experimental-Physik, vol. i. pt. 1. pp. 

 386 et seq. and 4/0. 



