348 Proceedings of the Royal Society 
We determine n by treating the last expression by 
S( )<£> , 
sx being not coplanar with y and X. This gives 
ll$Po(f) f /x = Sy(^/A .(f)' /x . 
The first member becomes 
= nS/x.YyX — n^yX/x . 
The second member expresses, according to (10), the value of 
mfsyX/x . 
We have therefore 
n — m 
1 • 
We then generalise the relation 
#0 = ^7^ 
into 
( 20 ) (g, + g)p 0 =zY y\. 
From this we deduce, as above, 
(21) n s p 0 = Vy(<f>’ + g)\. 
This equation has now to serve for two purposes. 
First we treat both members by 
s ( + 
This gives for the first member 
+ 9)p = n g&{<t> + 9)po • P- = n g SyXfi . 
The second member of (21) treated likewise gives us then : 
Sy(<A' + g)H</>' + g)^ = nfiyXy . 
If we develop the first member according to the powers of p, we see 
that n g takes the form 
(22) n g = m 1 + m 2 g + g 2 , 
because the coefficient of g becomes m 2 according to the expression 
(10) of this coefficient. 
In the second place we treat the equation (21) by the operator 
(<f> + 9)- This g^es, by (20), 
n g YyX =(</> + g)Yy(y>’ + g)X . 
