74 
Mr. Knight on the Expansion 
4- c x 4* c x% +* 
1,0 2,0 3,0 
+ c y + c x y + c x 'y -f 
0,2 1, 1 2,1 
+ +cxjr + 
0,2 1,2 
*4“ c y % + 
°»3 
►into the form 
B -|- B .r B a:* -4 B a; 3 -j- 
1,0 2,0 3,0 
+ B y + Bxy -f Bx'y + 
0,1 1, 1 2,1 
+ By +Bxy + 
0,2 1,2 
+ b y + 
0,3 
Equation (») is in this case reduced to B =£. / B x p,v which 
m,n m — p ,7 i—r 
expanded is 
00 
■B =/ B ,‘ i0 +/ B 2 ‘ 0 + 
7M,K ^ 171 — I ;tt W2 — 2,« 
+/ b 0 :, +/ b + 
771)11— I ^ m—l)?l— I 
+ / B 
wz,M — 2 
0,2 
4 * 
+ 
By this formula, we find the first terms of the expansion to be 
9 (e) + 9 (<0 ,% * + 9 (c) l 0 r -f 
+ 9 (0 o!, y + 9 ( c ) (,!<>)’ 
+ f ( e ) 1^1 
+ 9 M 
+ 
*y + 
Let it be required to find B. We have, after neglecting the 
terms specified, 
2,2 
