2ti8 M. C« iSziK on the Mechanical Theory of Heat. 



Were the function S and the constant C^ known, the dura- 

 tion of an oscillation could be calculated from this formula. 

 In the case of the permanent gases we can readily determine 

 S ; for we know that with these 



dQ=M..c v .dt + M(c p -c v )(a + t) d ^ 



and, designating the ratio of the two specific heats by k, 



dv 



dQ=dT + (&-l)T-; 



therefore 



||.=<*s=i<nog(ft,*->). 



Hence, for permanent gases, 



k- 1 



e s = C 2 T% 2 , 



where C 2 denotes the constant occurring in this integration. 

 Substituting this value of S in the general formula of the os- 

 cillation-period, and putting C in the place of the product of 

 the constants C ± and C 2 , we get 



=V"t 



Let us now consider two gases whose molecules contain the 

 same number of atoms, at equal tension and equal tempera- 

 ture. Let p and pi be their densities under normal circum- 

 stances, i and ii their oscillation-periods ; then is 



If we refer the density to that of hydrogen as unit and take 

 the oscillation-period of hydrogen as the time-unit, then is 



Pi 



and 



_fc-i 

 i=d 2 . 



With gases whose molecules consist of two atoms each, 



£= 1-405, ^^ =0-2025; 



therefore 



log i= -0-2025 log d. 



