( 149 ) 



MRT db da 1 



(2) 



(u — b) 1 doc dx v* 

 and 



^L = ^ (3) 



(v—bf v % 



If now we make use of (2) and (3) for the elimination of MRT 



db v 



and of — , we get a simple form for — , viz. : 



dx b 



d*a /day 



da 2 f — J 



v __ dx z \dxj t 



b d'a fdaY* 



dx* \dxj 



v 

 We may also get a quadratic equation in — , but then it appears 



b 



v 

 that one of the values of — = 1, and that at T=0 the line v = 6 



b 



may be considered as coinciding with the branch of the volumes of 



/dp\ fdp\ 



( — 1 = 0, and also with [ — ] = 0. In the same way the line v = oo. 



\dvj x \dxj v 



/da^ d*a 



If we now write for the ratio of ( — and a — the quantity m, 



\dxj dx* 



\dx) 



so that m = then (4) becomes : 



d"a 



a 



da? 



v 3 — 2m 

 b 1 — m 



v 

 And drawing — as ordinate when m is laid out along the axis of 

 b 



v 

 the abscissae, we get fig. 32. For m = we have — = 3 and for 



b 



V V 



m = 1 we have — = oo. For m ]> 1 — is at first negative, but for 



b b 



v v 



m = •/ — = 0, and for greater values of m — is positive and stead- 

 b b 



v 

 ily increasing. The limiting value is — = 2. For negative value of 



V V V 



m — is always positive, descending from — = 3 to — = 2. The 

 b b b 



