()0 Prof. H. L. Callendar on the Thermodynamical 



(which is approximately given by the expression — (a^R6 — b) ) 

 positive and equal to about +0'4 c.c, i. e. the gas would 

 appear " pluperfect," like hydrogen, whereas it is very much 

 the reverse. If on the other hand we take the values of the 

 constants given by van der Waals, which would be equi- 

 valent to the following, 



«/Rft = -l*42 c.c, &=l\L6c.c, . . (27) 



the compressibility at 0° C. is well represented, but the value 

 of the cooling-effect is much too small. At higher tern- 

 peratures the formula gives values of the cooling-effect which 

 are more nearly correct, but the value of d{pv)ldp at 200° C. 

 is found to be — 1*40 c.c, which is nearly twice as large as 

 the value given by Amagat's observations. The formula 

 would also make the scale- correction of the constant- volume 

 thermometer vanish at all temperatures, whereas the obser- 

 vations of Chappuis (see below) prove that it is quite large 

 in the case of C0 2 . 



On these and similar grounds we are justified in concluding 

 that the formula of van der Waals does not represent the 

 behaviour of C0 2 at moderate pressures with sufficient 

 accuracy to be of practical value. Clausius, however, has 

 shown (Phil. Mag. June 1880) that the agreement is greatly 

 improved if we suppose the coefficient a in the capillary 

 pressure to vary inversely as 6, which leads to a formula of 

 the same type as that proposed by Rankine, but with the 

 addition of the covolume b. For the purposes of gas- 

 thermometry, or for calculations at moderate pressures, we 

 may neglect quantities of the second order, and may write 

 the equation of Clausius in the form 



v = B.dlp-a/R$* + b {28) 



Love (Phil. Mag. July 1899) has shown that a formula of this 

 type represents all the observations on the cooling-effect very 

 well, but he has not applied it to the calculation of the 

 absolute zero, or the scale-correction of the gas-thermometer. 



7. Expression in Terms of the Co-aggregation- Volume c. 



In the application of this or similar equations to represent 

 the behaviour of imperfect gases at moderate pressures, 1 

 have found it very convenient to employ the single letter c 

 to represent the term a/Rd 2 . The quantity e represents 

 a volume, expressible in cubic centimetres, which is to a first 

 approximation a function of the temperature only, and which 

 may be called the " co-aggregation-volume/' as it denotes the 

 diminution of volume caused bv the formation of molecular 



