( 207 ) 



problem; and as soon as k^>n we have only to occupy ourselves 

 with a single branch for the section. This is also immediately seen 

 from the quadratic equation in v — b of p. 201, which has then one 

 negative, and one positive root, So if h }> n, we may say that the 

 two surfaces intersect in a curve which has only one branch. For 

 x = and x = l the value of v is always equal to b, and that of 

 T always equal to 0. From this follows already that there will be 

 question of a maximum value of T for the section. For this value 



of T the two curves will touch at given value of T, viz. I - '- ) — 



KjWJcT 



and ( — ) = 0. We have also met with such a contact in the case 

 \dasJoT 



k < n, and we then concluded that the contact took place as is 



represented in fig. 24 r (Contribution V p. 134). 



But another contact is possible, namely such a contact for which 



fd*ty\ fdp\ 



the curve — — = lies in the region where ( — | is positive 



\d**J,T \dxJoT 



everywhere except at the point of contact, or as we might also 



express it, outside ( — ] = 0. This would imply for the intersection 

 \d<cj r 



of the two surfaces, that the common curve which runs upwards 



from as = 0, and x = 1 and T = 0, passes round the top of 



77 I = 0, or that it remains entirely on the side of the small 



volumes, as was the case up to now. 



In the gradual transformation of the common line of intersection 

 which is due to the increase of k above n, it must, therefore, have 



cPx\> 

 passed through the top of - — = for certain value of k. And we 



ax* 



shall now treat the condition for this circumstance. Properly speaking 



I have already tried to solve this problem in Contribution III p. 834, 



to which I refer for the meaning of the following formula. The 



circumstance that the curve of intersection passes through the top 



is given by : 



cPa da 



— (1-2.,,) = - 

 a x* dx 



But I shall adapt the discussion of this formula to the systematic 

 treatment of this paper. 



(1—2^)» 

 If we put the value for y g l (see Cont. Ill p. 832) this 



4A V v 1 — x g) 



