G. PLARR ON THE SOLUTION OF THE EQUATION Vp¢p= 0. 87 
from which we draw 
= A tSap, —B2 Rp) 20 = yy’, 
and as a= —aSaw—fBSBo—ySyo , 
po= —paSaa—pBSBa—pySyo , 
and remembering the definitions ya= Ap, &c., we get 
yo = tp2Sap’Sae , 
likewise 
b’a = tp’2SapSao , 
namely 
Yo = — tpSap’ 
v’o = — tp'Sap. 
Replacing ¢ by /@ : TpTp’, this gives 
| va = — Up JE Sap’ 
vo = — Up VE Sop. 
This shows that the tensors yw and w’e are variable with the direction of o, 
and that yw has its maximum tensor when o coincides, not with Up = Uy as 
one might have surmised, but with Up’; and the tensor of pw is minimum, 
namely zero, when w lies in a plane perpendicular, not to p, but perpendicular 
to p’. 
Similar remarks, mutatis mutandis, refer to the tensor of Wo. 
We may now let ourselves be guided by the principle, drawn from obser- 
vation, that when the expression of the tensor of a vector vanishes, the direction 
of the corresponding unit-vector will present a more or less marked degree of 
indetermination ; and we institute a discussion of the cases in which Tyo 
vanishes. 
We have 
Tho = Si ‘ TSaUp’ 5 
and we leave out of the question the second factor because its value depends 
on our own choice, and we discuss only the factor /€ . 
Originally we have defined @ by 
© = LT p'Tp”, 


