180 
PROF. H. F. BAKER ON CERTAIN. LINEAR 
and 
C 2 
+x 2 * 1 2 (K-‘-fr 2 +-K 
•i-tf). 
Picking out the coefficients of r in these, and putting therein f = 1, we have 
— X/g — ““X ^9, 
a 2 = ^\ 2 h 2 + §\ 2 Jc 2 , 
and hence, to X 3 , 
u 2> 
n-i ) 72— — X7r—f-X 2 /^ + 2X-&C, 
= ( a i + a -i) 2 ~~ (71 + 7a) 2 = 
X 2 
-[x 2 ( )] 3 , 
= \ 2 h 2 -\ 3 h{h 2 +%Jc 2 ). 
This agrees with a result previously found (§ 6), but fails to give the first term in 
q- if h — 0. When this is so it is necessary to take account of the terms in X 3 . By 
taking terms in X 3 in a 1} c u we only obtain terms in <p (— c^ + ^Cj) which involve X 4 . 
But the terms in X 2 in a x , c x which are written down give terms in X 3 in <p ( — a 1 + ^ 2 c 1 ), 
which are 
x 2 M a (ir 2 + T r 2 -i+K 2 -K 4 )+\%** ( 
■ 3 +K _1 - 
4 
■ 3 ■ 
r^-rf+K 3 - 
-r-K 4 ), 
and hence the additional terms 
m a 
x 3 M 2 (-M- 2 -tr 2 -|T+i+K 2 -K 4 ) 
+ X'^jp, (;V«f tr 1 —3 t +T3t' 
■3-n 3 - 
' 3t 4 + 3 )> 
and the additional terms in c 2 
^(-i-r 4 -K- 4 +ir 2 +tr H- 
c2 
4 l>3Z. X. /1JP-5 7 m , 13? ? 2y 2 _C>4\ 
+ A hb l(id — T2& +3t + T2a + T t +"4"t —v(, — 3 <, —X5/- 
In finding the terms in X 3 in 
This gives for <p ( — a 2 +£ 2 c 2 ), 
J 1 , 2 3. 1 1 Hi 
f— 2 T — ^ 4 + 4t ~2" T S J 
a 
3) u 3> 
it is sufficient to retain the terms X 2 in a., and c„. 
+xWMf->(-!i ? -^+*)-l+f(-i* , -iT-4)+£’(-$T+¥)+F(-iT+*)} 
,\W + (-Jr+V)-W+f (-Jr + V)-*?} 
+XV{-K- , -J- , (|r+«)+» + f(|T-|f);W+f(2r-«-«*}. 
