54 Prof. H. L. Callendar on the Thermodynamical 



account of Regnault's data in addition to those of Joule and 

 Thomson, he arrives at an empirical equation of the form 



0/0 o = (1 + -003654 1 ' 00029 , . . . (1*2) 



in which t is the temperature on the centigrade scale. The 

 Tallies of the corrections calculated by this method are much 

 smaller than those in the original table of Joule and Thomson, 

 .and are of the right order of magnitude between 0° and 100°, 

 but it does not appear that an equation of this type correctly 

 represents the phenomena. 



4. JRanlcine's Equation for C0 2 . 



In the same paper (Phil. Trans. 1854, p. 337) Joule and 

 Thomson quoted another empirical formula for C0 2 contained 

 in a letter from Rankine, namely, 



pv = ^e-aR0^l0v, .... (13) 



in which the value of the constant a (in degrees of tem- 

 perature) was given as 1/9, and was deduced solely from 

 Regnault's observations of the pressure-coefficient of C0 2 at 

 various constant densities. In a previous paper (Trans. Roy. 

 Soc. Edinb. xx. p. 561) Rankine had given an estimate of 

 # , the absolute zero, obtained by plotting Regnault's values 

 of the pressure-coefficients of air and C0 2 , which led to the 

 value O = 274°*6, but in the formula quoted he employed 

 ,# = 274 c -0. This formula agreed very well with Regnault's 

 coefficients of expansion for C0 2 , and also with his observa- 

 tions on the compressibility. Joule and Thomson further 

 showed that it satisfied their own observations on the 

 cooling-effect at that time available, employing the expression 

 Q = 3Ra# o 2 /S0 2 , deduced from Rankine's formula. Taking 

 Rankine's value for a, and putting R = 1*89 x 10 6 , S = 8'4 x 10 6 

 c.G.s. we find Q at 0° C. = l°'28 per atmo., which is in fair 

 agreement with the value actually observed. 



At a later date (Phil. Trans" 1862) Joule and Thomson 

 succeeded in obtaining more accurate measurements of the 

 cooling-effect over a range of temperature extending from 4 C 

 to 96° C, and found that the cooling-effect for air and C0 2 

 varied nearly as 1/0 2 , and could therefore be represented by 

 Rankine's formula. By adopting the expression Q = A/# 2 for 

 the cooling-effect, and integrating equation (4), neglecting 

 the variations of 8, and assuming that the equation must 

 approximate indefinitely to v=Il0/p at high temperatures, 

 they obtained the following type of characteristic equation, 



v = m/p-AS/3d\ .... (14) 



