Joule-Thomson Thermal Efect. 109 



(3) The result obtained in the foregoing- paragraph sug- 

 gested the advisability of making a similar calculation on the 

 basis of Clausius's characteristic equation 



which admittedly represents the behaviour of the easily con- 

 densible gases with greater accuracy than van der Waals's 

 equation does. 



Dividing throughout, as before, by v — ~B, and differentiating 

 with respect to T (assuming p = constant), we obtain 



A 2 A fiv\ R RT /By 



A 2A ,dv\ K 1IT f^v\ 



i. e. 



R 



+ 



,BrN , v-B T»(p + C)' 

 KdTJp R 2A 



{v-B} 2 T 2 (v + C)* 



_ r r _ B+ _A_p_z^\ 2 i /i-. 2A (»- B ) 2 r l 

 _ l t ^ktUo; si rt 2, t^+c) 3 / • 



Neglecting powers and products of the small quantities 

 A, B, and (J, this becomes 



T &),-•■ bf~ B; ■ • • (q -p° 



whence (by the same reasoning as in the previous discussion) 

 we obtain 



where y and S are constants — an expression which differs 

 from that given by Rose-Innes in that it involves the square 

 of the temperature instead of its first power. 



It may not be uninteresting to compare the results furnished 

 by this formula with the figures published by Rose-Innes 

 the comparison is here given for C0 2 only, seeing that the 

 behaviour of air and hydrogen is expressed about as well 

 by van der Waals's equation as by that of Clausius, and so 

 the calculation in their case is hardly worth making. 



Plotting the values of 6 and ^ for C0 2 as ordinates and 



abscissae we obtain a remarkably good straight line ; from it 



