76 G. PLARR ON THE SOLUTION OF THE EQUATION Vp¢p=0. 
This shows that p” can be real only when 
fet he . Bn 
Sep >0, angle ep’ > 90°, 
and consequently the surface [=0 extends not in all directions round the 
direction of «’, but only on one side of a certain plane passing through ¢ and 
Vea’, where eS. 90°. 
As we have W,,=0, the normal is directed parallel to 
(63) U,, = WE. 
4s — 
This accounts for Sp’we’ being of a smaller order than the order of p’, 
because p” must be nearly directed in the tangent plane at the point ¢,,e. 
We need not show that the directions of p’, which alone can take place, 
are those which render E greater than E, (not smaller), because we have 
shown already that it is only when E is comprised between E, and /, (supposing 
always here 4, > 0) that there are three real roots for ¢ given by ['=0. 
The double sign of the value of Sp’awe’ shows that there are two sheets 
beginning at E=E,, e=e,,, the conic so determined forms therefore an edge- 
like termination of the surface in this region. 
If we were to examine the section perpendicularly made to this edge, and 
call p’=20,,+yae the vector of a point of the section beginning at ¢,,<, 0,, 
being a unit-vector in the plane of ¢< and we’, perpendicular to we’, we would 
find 

2 
8 * , , 3 
Yec= — . T(Vewe )az?, 

ul 
which gives the approximate expression for the beginning of the section of the 
surface at the point ¢,,€. 
We have for W,=0 
