of Edinburgh , Session 1881-82. 
533 
This gives 
(17) S/<^' = S^/. 
By the use of this equality the value (13) of m l becomes 
= sfcbfQi^i' - sy^'Sz>y , 
the last term being now a square in virtue of (17). We also 
observe that 
</>'&'= -i'&i'<j>'k' 
= -i'&k'ty' . 
Introducing these values, and that of m 2 into the sum 
nd - < lm l — (fik') 2 , 
the result will be 
namely, 
We put 
(18) 
sv</>i'+sy<K + s%'<K 
+SH'<kj' +sy<t>j' +s%'<£/' , 
-WY-Wf. 
j i 2 =tv+t w, 
1 m,=pvw, 
and the relation will be 
(19) 4-2m 1 -(^') 2 = M 2 . 
Further, by (7) we get 
(<£'&') 2 = p 2 + w 2 . 
Substituting this into (19), and adding and subtracting 2 m 2 u -1- u 2 , 
we get 
( 20 ) 
Hence also 
(m 2 + M )2-2— “- p 2 = M 2 . 
(m 2 + M )V + ('^) -(^ + p>) +M^. 
