G. PLARR ON THE SOLUTION OF THE EQUATION Vp¢p=0 , 69 
0= Sde[ — c G)+ Be (3)] 
By equation I’ = 0 there exists a relation between : and =. We will 
Therefore we have 
establish by definition 
(52) = = W?, W having the sign of Q. 
3 2 a 
Then G) + (3) =0 gives 
(52 bis) Ag G) = WwW, -2=W’. 
Thus the above scalar becomes : 
0 = Sde[—eW* + GeW"]. 
We now separate the factor W’, reserving it in case it becomes = zero, 
and we have 
0 = Sde[—eW + we]. 
Thus the vector v normal to the surface may be represented by 
(53) Hailes eo nies 
neglecting a scalar factor N, which we might suppose positive or negative when 
we wish v to be directed always towards the outside of the surface. For the 
present we content ourselves with taking v either towards the inside or towards 
the outside, as the formula will give it. 
In looking upon ¢ as a function of the parameter E, we get the expression 
poe _ in differentiating, P and Q under the form: 
P=P'4+é, Q=—CE+Q’ 
apa", dE, dQ=—(qpE+e ME, 
and substituting into 
o0=(4)aP+¥ aQ, 
this gives us, reserving the factor W*: 
dey. Gee, saris? 
(54) qe W-E” E-W° 


VOL. XXVIII. PART I, iS) 

