( 191 ) 



PQ will have to lie between x = and x = 1 for the condition 



(da\- 2 (Pa 



— I = — a — — to be fultilled in the diagram. 

 \dxj 3 dx 3 



According to the result arrived at in Contribution VII with regard 



to the point in which f- =0 touches the line f — 1 = 0, the 



W» \dv) x 



/da\ 3 2 d?a 

 value of x in which [ — J = — a — - must lie not very far from 

 \dxj 3 aar J 



this point of contact. 



But whether it might not even lie to the right of that value of x, 



a x 

 for which — has a minimum value, can only appear from a direct 



o x 



investigation. Then it may appear at the same time whether in case 



dp d*p 



of contact of the two curves — = and = the temperature 



dv dvdx 



has maximum value or minimum value. 



Let us eliminate the value of v from the equations of the two 



curves. Among others we may do this by substituting the value of 



db 

 2 — 

 dx 1 da d"p 



v from = — in = 0. Let us write : 



v — a dx dv dx 



1 db 



v — b b dx 



— = 2 = 2«, 



b 1 da 



or 



and 



and 



a dx 



y = 1 + 2 '' 



b 1 

 Tl-f-2* 



b 



v \+2z 



From -4- = follows : 

 dvdx 





\X- 



db 



MRT — 



_V dx 



v da 



dx 



