218 Mr. William Sutherland on the 



Andrews makes ~dj?fdT a little larger than Amagat ; and this 

 being so, it is not worth while to seek for closer agreement 

 than that in Table IV., at least at present. 



We have, however, a sensitive means of determining whether 

 the form and the values of the constants adopted truly repre- 

 sent the behaviour of C0 2 closely enough at high volumes, — 

 namely, Thomson and Joule's and Regnault's experiments on 

 the cooling of C0 2 when it escapes through a porous plug 

 from under pressure (Phil. Trans. 1854-1862; Mem. de V Acad. 

 xxxvii.). Natanson (Wied. Ann. xxxi.) has repeated the Joule 

 and Thomson experiments on C0 2 under the more favourable 

 conditions afforded by the commercial sale of the fluid in 

 large quantity and great purity, so that he has been able to 

 measure not only the cooling effect for a given pressure excess, 

 but also its variation with pressure. Taking all these experi- 

 ments together, we have a delicate test for the equation at 

 high volumes. 



The most convenient expression for the cooling effect for 

 our present purpose is 



^ d8 a dv 



where 8 is the cooling effect, K p is the specific heat at constant 

 pressure, and 6 is temperature on the absolute thermo- 

 dynamic scale. In previous papers I took from Joule and 

 Thomson's original investigation = T + '1°, not then aware 

 that SirW. Thomson, in his article "Heat" (Encyc. Brit.), 

 had by a fuller discussion of all the experimental data proved 

 = T, and so removed the difficulty that the term *7 opposed 

 to the harmony of the thermodynamic and molecular kinetic 

 conceptions of temperature. 



With our characteristic equation the cooling effect is, after 

 the appropriate reductions, given by 



K p ~ = 2(l/m-k) +p\m/RT-k)(l/B.T-2k) 



- 2k(lfRT - 2k) - lk/m }/RT. 



Within Joule and Thomson's range of pressure this can be 

 reduced to 



K,g=2(//BT-*); 



and dB can be made to stand for the integral cooling effect if 

 dp stands for the integral excess of 2 '54 metres of mercury, 

 to which they reduced their results. The term in p will be 



