( 188 ) 



tote for that value of x, for which in rarefied gas state, the deviation 



db da 

 from the law of Boyle is maximum, viz. for which MRi — = — . 



dx dx 



da 



db dx 

 It has minimum volume on the line v — b = 3 — — -, whereas the 



dx da 



dx~* 



da 



dp ^ . . . . , , db dx 



line — = has such a minimum volume on the line v — 6 = 2 — . 



dx dx d*a 



dx* 



d*p dp 



The points of intersection of = and — =0 indicate the 



dv dx dx 



dp 



points in which — = has a tangent parallel to the X-axis, as follows 

 dv 



d°p dv d*p 



from 1 = 0. For such a point of intersection we have 



dv* dx dx dv 



db da 

 MET — — 

 MET 2a dx dx 



at Ihe same time — = — and— ——:= — ; and so 



(v— by v 3 {v—b) s v s 



which last equation represents the locus of these points of intersection. 



db a" 

 Differentiating this locus "v — b = 2 we find: 



dx da 

 dx 



d*a 

 3 — — 2a — 

 dv db \dx J dx* 



/da\' 

 [d^J 



dx dx 



fda\* 

 [dx^J 



If in the diagram we think all the values of x present, e.g. 



ascending from the value of ,v for which — = 0, this locus is a curve 



dx 



da 

 with an asymptote for the value of x, for which — = 0, and it has 



dx 



fda\* 2 d*a 

 a minimum volume for the value of x, for which I — J = — - a — . 



\dxj 3 dx* 



For greater values of x the volume increases. 



db da 



dx dx 1 db 1 da 

 It in — = — the value 6b is put tor v, we tind - — = . 



t' — b 2a b dx a dx 



