( 206 ) 



B 1 (w-f3)(3n+l) , 1 v—b 1 n — 1 



and so \- x = , while = -, it is at 



C 8 n' -1 2 db 8 n-f-1 



dx 

 once evident that the sign is certainly positive. 



We can now get an insight into the way in which increase of 



a i — rt n 

 the value of influences the intersection of the two surfaces 



d*ifc dp 



= and — = 0. If this quantity, which I shall represent by k, 



dx* dx 



n' — 1 

 is smaller than 14-8 . no intersection is possible. In this 



consideration we shall leave n and C invariable, and so keep = 



dx" 1 



dp 

 unchanged. If we now make k increase, — = will vary and 



dx 



d*\p 



intersect the surface = 0. When k <^ n, this intersection takes 



dx* 



place in a closed curve. As well in the ^-projection as in the 



7Vr-projection and in the v, 7-projection we may speak of a lower 



and an upper branch. But these branches do not extend over the 



whole width from x = to a? = l. With approach of k to n the 



width of this section becomes larger, but the lower branch descends 



continually, and the upper branch ascends. In the v,#-prqjection this 



implies that the branch with the lower value of v approaches b, and 



that the upper branch assumes a higher value of v. In the T,x-pro- 



jection this means that T verges to zero for the lower branch, and 



increases for the upper branch, but still remains very far below 



the value of T q (See Contribution III These Proc. IX p. 830). And 



finally when k has become equal to n, the closed curve of the 



section extends from x = to x = I , but the lower branch coincides 



with the line v = b, and the value of T for this branch is the 



absolute zero-point. For the upper branch v and T have constantly 



increased. And the question rises whether then the whole section 



is still found on what I shall call the back side for the surface 



= 0; i.e. the points with the smaller value of v. We shall 



presently revert to this question. But already now it is to be seen 

 what will be the consequence of increase of k above n. 



The process we described above, goes on. The lower branch does 

 not become imaginary, but has values of v <^ b and values of T 

 which are again positive. So they are of no importance for the real 



