G. PLARR ON THE SOLUTION OF THE EQUATION Vpgp=0 : 75 
and so this curve belongs to another sheet of the surface than that which we 
have followed as yet. : 
But this new sheet is the beginning of a double sheet which does not 
extend to values of E smaller than E,; namely: 
Let us consider a point on the curve E,, ¢,,, and let ¢,,<’ be its vector ; 
and let us consider another point on the surface, whose vector we shall 
represent for the moment by 
e= é,€ a p’ ; 
p’ being treated here as infinitesimal, of which we shall neglect the 2d order. 
Then we have 
e = — é, + 2¢,Sep” + Ty7?A’ 
Se@e = @ Se We’ + 2¢,,Sp we Hi Ts?B’ : 
Then, as P and Q are annulled as to their terms independent of p”, we get 
P= — 2¢,Sép" + Ty’A” 
Q = 2¢,,Sp"ae + Ty’B" . 
Then we must have: 
, ray 2 2 QO? m7 4a 
O= —8e5S*'p’ i 462 S°p”awe' + Tp4C 

the additional term Tp*C’ being of at least the (3+4)™ order because we have 
to suppose 
S’p’ we’ to be of the order S*e'p” , 
Spe’ namely of the ($)* order. Thus we get 
N=! 2 FE 1 WINS 
Spa = +/ 5 (Sep )#. 
