76 Prof. H. L. Calleiular on the Thermoc) 'ynamical 



because the direct measurement of s by experiment is gene- 

 rally impracticable ; but it serves to trace the probable 

 variations of the ratio of the specific heats S/s=#\ 



In the special case in which n = s Q /'R the formulae may be 

 somewhat simplified, since R = S — s , and may be written as 

 follows : — 



S = S (1 + nc/V), (55) 



s = s (l+nc/Y){l-c/Y), .... (56) 



9 =^/s=y /(l-ciY) (57) 



r hence 



This appears to be the case for steam (Proc. R. S. vol. lxvii. 

 p. 266, 1900), but is not true generally. 



In the case of a diatomic gas, if we assume the limiting 

 ratio of the specific heats to be <7 = 1*400, as indicated by 

 theory, we have S = o*5R, ^ = 2*5R, if the limiting values of 

 the specific heats are constant. The ratio of the specific 

 heats, if n = 2'5, would be g = 1*400(1 + c/Y). If n = 2, as in 

 Rankine's equation, we should have <?= 1*400(1 + *92c/V) 

 approximately. Inserting c = 0*90 c. c, V=784 c. c. for air 

 at 0° C. and 75 cms. pressure, we should find g = 1*4015, 

 which illustrates the smallness of the variation with pressure 

 for the permanent gases. Taking the density of air as 

 1*2930 gm. per litre at 0° C. and 760 mm. in lat. 45°, and 

 assuming the value of c — b at 0° to be 0*50 c. c. from 

 Amagat's observations, we should find R = 2*8725 X 10 6 C.G.s., 

 which would give B = 3*5R=1'0055 joules per gramme- 

 degree; or 0*2405 calories at 20° C, if the calorie at 20° C. is 

 taken as 4*180 joules. This is about 1 per cent, larger than 

 the value found by Regnault, namely S = *2375. The obser- 

 vations of Joly at constant volume give s = *1721 cals. at 

 60° C. and ^• = 49 c. c, when reduced to the same unit. The 

 theoretical value at this pressure, assuming c = 0'61 c. c. at 

 60° C.j would be 0*1736 calories, which is also nearly 

 1 per cent, larger than that observed. It should be remarked, 

 however, that even apart from the difficulty of the expe- 

 riments, there is considerable uncertainty in the units of heat 

 employed. Joly used Regnault' s value for the latent heat of 

 steam at 100°, namely 536*7; but his own experiments with 

 the steam calorimeter give 540*2 in terms of the calorie at 20°. 

 The difference is nearly sufficient to account for the dis- 

 crepancy in the observed and calculated values. Considering 

 the difficulty of experiments on the specific heats of gases, we 

 are probably justified in the assumption that the limiting 

 values of the specific heats are constant for the more permanent 



