294 
MR. G. T. WALKER OK REPULSION AND ROTATION 
On substituting in the latter equation from the equations connecting (3, y with 
F', G', H', and remembering that F' = 0, we get 
_a 
06 
= 0, 
and this is to hold for all values of G', H' consistent with 
| (CAG') + | (ABH') = 0. 
This condition is replaced by taking 
CAG'= f 
oc 
ABH'=-f» 
CD 
and the former relation becomes 
or 
d_ 
"C 0^ 
P 3/V 
0 
~ B 0 
p e/q 
db 
AB 0a 
1<AC dc)_ 
dc 
_AC 0a 
\AB 6/y_ 
_a 
db 
'*Lfl( 2 L\ + — 
Jo a.. \ A n I l 
AB JC da VAC/ ‘ A 2 
fat 
0 
dc 
b d_ 
AC da 
C 
AB 
+ A?J 
ab 
= 0. 
therefore 
r_c_ 0 ^ / b _\ _ b _ _0 /_c_\ 
* bc [AB da \ AC ) AC 05 \AB/_ 
+ /c 06 
■_c a_/B_ 
AB 0a \ AC 
’A 1 /AY 
AC 0a VAB/ 
“^0c 
c db (a 2 ^ 
IS 
= o. 
Now jf being arbitrary the coefficients of fi c , &c. must vanish, therefore 
C 0 
/B\ 
B 0 
A \ 
AB 0a 1 
[AC 
AC 0a ^ 
Iab) 
and 
A 2 
= function of a (or constant) 
On differentiation, the relation 
A1 /JL\ _ A A /A\ 
AB 0a VAC/ ~ AC 0a \AB/ 
becomes 
Therefore 
_c_ 0_ /b\ i d_ /r \_b_ 0_ /c\ i_ d_ n\ _ 
A‘ 2 B 0a \C/ A0a\A/ A 2 C0a\B/ A0a\A/ 
C 0_ /B\ _ B 0_ /C\ _ 
B da \Cj C 0a \B/ ~ °* 
(iii.). 
Therefore 
