Thermodynamic Properties of Air. 21 



Waals, &c. It is most advantageous to perform the differen- 

 tiations upon that quantity which has been directly measured, 

 and the variations of which are most marked, i. e. upon the 

 coefficient a. Differentiating twice equation (6) we obtain 



B^ _ B^y _ 2r7o^a %.B^ . 



d* 2 ~~ B^ 2 ~ p ~d0 p dO 2 ' ' ' ' { } 



To obtain ^— ; and ^— ^ I constructed on a large scale a diagram 



of values of « arranged in curves of equal pressure, abscissae 

 representing temperatures ; it is in fact the diagram alluded 

 to in § 14 (Part I.). These curves were divided in short 

 pieces, approaching to straight lines ; the differences of 



ordinates of their ends gave ^ ; the values so obtained 



were considered as corresponding to the middle point of each 

 piece. 



Another diagram was then constructed with ^ as ordinates. 



The curves were carefully smoothed, care being taken to keep 

 the whole of them in sight in doing so. The process of 



B 2 ^ 

 differentiation repeated furnished the values of^— -^*. 



d 2 w 

 Using these values ^ can be now calculated by equa- 



tion (7). It would be superfluous to reproduce here the 

 vast number of values thus obtained ; some of them will be 

 given later on. An idea of the curious shape of the curves 



7s 2 v 



^-jcan be obtained by inspection of PL L. where the values of 



ot 



Vv 



B* 5 



^-j have been collected on isothermals, from — 100° to — 144°. 



* It might be objected that this method of calculation is not capable of 

 yielding results of any high accuracy. Indeed, it cannot be denied that 

 in drawing long- curves along a comparatively small number of observed 

 points, the success depends in a large measure on the firmness of eye 

 and steadiness of the drawer's hand. Yet on the other hand it is to be 

 remarked that the curves control one another, gross errors are thus easily 

 avoided. 



Although graphical differentiation, if accurately done, is a very tedious 

 process, it is unfortunately not possible to perform it by mechanical 

 means, since, as far as I know, mechanical differentiators (working in 

 a similar manner to the numerous integrators) do not exist. If I am 

 right they are even impossible on dynamical grounds. 



(o^5S 



