58 Prof. H. L. Callendar on the Ther modi/ nam iced 



mometer, we take the differential equation in the form (5), 

 which may be written 



-^Q(dpldvh = e(dplde) c - ]} + (d(/n-)/dp)(dpldv) e . (21) 



In the small terms it is justifiable to make the approximations 

 (dp/dv) F =(d2?ldv)Q=—p/v. If we also put (dp/d0) v = ~Rlr, 

 which is only true at the point where dT/d6=l, we obtain 



0-T=S P QIR+(d(pv)ldp) e plR. . . (22) 



In order to evaluate this for C0 2 we may take SQ = 7*9 c.c. 

 as the proper mean value. We require in addition the value 

 of d(pv)/dp at or near 50° C, which may be taken as 2*4 c.c. 

 from Amagat's observations on C0 2 - The value of p is the 

 pressure in the gas-thermometer at the point considered. 

 Adopting Chappuis' value of the pressure-coefficient for COo 

 nt 100 cms. initial pressure, namely, '0037251, T = 2tf8 o '45, 

 we have /> = 119 cms. = l'58 X 10 6 c.G.s. at 50°. Taking 

 11=1-89 x 10 6 , we find the value of the correction 4°'55, 

 which gives # = 273°*0. This neglects the scale-correction 

 at 50°, which, however, is less than '05°. It is clear that the 

 correction depending on d(pv) cannot be neglected. If we 

 could replace Q by the cooling-effect in " free " expansion 

 (Y/E = 0), as in Joule's original experiment, this term would 

 not be required. 



6. The Equations of van der ^Yaals and Clausius. 



The above method of deducing the value of the absolute 

 zero from the cooling-effect may appear at first sight to be 

 wanting in precision ; but it assumes only that the effect is 

 small, and diminishes continuously with increase of tem- 

 perature, and the results to which it leads are really quite as 

 accurate as the available experimental data. By way of 

 contrast Ave may take a method which appears at first sight 

 to be unimpeachable, but which leads to results which are 

 obviously wrong. 



Van der Waals, in his celebrated essav "On the Con- 

 tinuity of State" (Phys. Soc. Translation, Cap. XI. p. 440), 

 was the first to interpret the cooling-etrect in terms of the 

 capillary pressure represented by the term a/v q in his well 

 known equation 



(p + alv 2 ){v-b) = ne (23) 



Taking this equation, he showed that, if the capillary pressure 

 varied inversely as the square of the volume, and the co- 

 volume b was constant, the foil of temperature in the Joule- 



