Pfoceeclings of Royal Society of Edinburgh. 
196 
one term only of this ^ is admissible ; so that, as no origin was 
fixed, 
a being any constant versor. Thus we have the complete solution. 
It gives by (1) 
so that o- is merely -p i, multiplied by a constant and subjected to 
a definite rotation. 
But the following process is very much simpler. For we may get 
rid of the factor w, and so greatly simplify the investigation, by 
writing the equation of condition in the form 
Multiplying by y, and adding the three equations of this form, 
we have 
m 
From the three equations (5) we get also 
V («?) = 0 , 
so that 
^ = Up.a, 
dcr = m^a ^dpp 
— - nv^a ~ ^dp ~ 
d(T = ILqdpi} 
0) 
It gives at once 
0201O- = 02(K?a2) = 0i(Ks/3g) 
or 
V.y(v2-y035)2'‘ = O. 
(ffl) 
or 
V.^Tg = 0 . 
By the help of this we may write [a) as 
