466 WAVES OF EXPANSION. [CHAP. X 



256. With the value of K given in Art. 254, we find for water 



at 15 C. 



c = 1490 metres per second. 



The number obtained directly by Colladon and Sturm in their 

 experiments on the lake of Geneva was 1437, at a temperature 

 ofSC* 



In the case of a gas, if we assume that the temperature is 

 constant, the value of K is determined by Boyle's Law 



viz. K=p<> .............................. (2), 



so that c = (PO/PQ)* ........................ (3). 



This is known as the ' Newtonian ' velocity of sound f. If we 

 denote by H the height of a 'homogeneous atmosphere* of the 

 gas, we have p Q = #/> H, and therefore 



c = (H)i ........................... (4), 



which may be compared with the formula (8) of Art. 167 for 

 the velocity of ' long ' gravity-waves in liquids. For air at C. 

 we have as corresponding values { 



p = 76 x 13-60 x 981, p = '001 29, 

 in absolute C.G.S. units; whence 



c = 280 metres per second. 

 This is considerably below the value found by direct observation. 



The reconciliation of theory and fact is due to Laplace . 

 When a gas is suddenly compressed, its temperature rises, so 

 that the pressure is increased more than in proportion to the 

 diminution of volume ; and a similar statement applies of course 

 to the case of a sudden expansion. The formula (1) is appro- 

 priate only to the case where the expansions and rarefactions are 

 so gradual that there is ample time for equalization of temperature 

 by thermal conduction and radiation. In most cases of interest, 

 the alternations of density are exceedingly rapid ; the flow of heat 



* Ann. de Chim. et de Phys., t. xxxvi. (1827). 

 t Principia, Lib. ii., Sect, viii., Prop. 48. 

 J Everett, Units and Physical Constants. 



"Sur la vitesse du son dans Fair et dans 1'eau, Ann. de Chim. et de Phys., 

 t. iii. (1816); Mecanique Celeste, Livre 12 me , c. iii. (1823). 



