MR. J. H. BRINKWORTH ON SPECIFIC HEAT OF STEAM. 387 



were lacking, and the necessity of fresh equipment caused inevitable delays. The 

 experimental part of the work was still incomplete when the appearance of 

 GRINDLEY'S paper, " On the Cooling of Saturated Steam by Free Expansion " (' Phil 

 Trans.' A, 1900) made it necessary to publish a preliminary account of the theory, 

 which appeared in ' Roy. Soc. Proc.' for June, 1900. 



GRINDLEY'S observations of the cooling effect agreed remarkably well over the 

 whole range with those given by the differential throttling calorimeter, although his 

 experimental method was very different. But he deduced the values of the specific 

 heat by assuming REGNAULT'S formula dH/dT = 0'305, for the rate of variation of the 

 total heat of saturated steam, and obtained results for the specific heat at atmospheric 

 pressure increasing from 0'387 at 100 C. to 0'665 at 160 C., which could not be 

 reconciled with direct experiment. Owing to the uncertainty of REGNAULT'S formula 

 for the total heat, it seemed better to deduce the variation of the total heat from the 

 measurements of the specific heat as already explained. 



The theory of the relation between the total heat and the specific heat was worked 

 out by assuming a modified form of the characteristic equation employed by RANKINE 

 and by JOULE and THOMSON for a similar purpose. This equation was put in the 



form, 



V-/; = RT/P-c, .......... (5) 



where b is the molecular volume of HIRN, a small constant of the same order of 

 magnitude as the volume of the liquid, and c represents the diminution of volume of 

 the vapour due to coaggregation or pairing of the molecules. JOULE and THOMSON 

 deduced the values of c from their empirical expression C = A/T 3 for the cooling effect 

 by integrating equation (4) on the assumption that S was constant. This method was 

 shown to give unsatisfactory results in the case of CO 2 , and was quite inadmissible in 

 the case of steam. The opposite procedure was accordingly adopted ; an expression 

 was assumed for c, and the resulting equation for SC, namely, 



-b, .......... (G) 



(7) 



was compared with the experimental values obtained for S and G. 

 The complete variation of S with pressure was directly given by 



where S is a function of the temperature only, which appears from experiment to be 

 very nearly constant over the experimental range for steam. The value of the index 

 n was taken as being S /R 1, because it had been found by experiments with a 

 sensitive platinum thermometer on the adiabatic compression of steam that the 

 pressure temperature relation was of the form P/T n+1 = constant, with n constant, 

 which was shown to be thermodynamically exact in spite of variation of S, provided 

 that S /R = n+l. 



