Memoirs presented to the Cambridge philosophical society on the occasion of the jubilee of Sir George Gabriel Stokes, bart., Hon. LL. D., Hon. SC. D., Lucasian professor.

28 MAJOR MACMAHON, APPLICATION 0F THE PARTITION ANALYSIS TO
which (putting =xbcf(12111), y=bcf(ll), z =b1, w= -f N2N brings it to
nQ b2f3 (131)
~~ I
>1- N34. -f(12211). 1- bf3 (131). 1 - bf (11)
bcf
+ b2f3 (14211)
1
1- N3 V4. 1-f/(12211). 1 - bf3 (1:31). 1 - bcf (1). 1 - bcf(12111)
bcf
Q b4f6 (28422)
i - - NN. 1 -f (12211). 1 - b2f3 (131). 1 - bf (12111). 1 - b2f3 (14211)
b2f4 (121)2
1
1 - b-fN 4 1-f(12211). 1 - b2(131). 1 bcf(ll). 1 -f(lll)
(131)
1 - (11).1 - (11).1 - (131). 1 - (12211)
+ (1421{(14211) {1- (11) (12221)}
+ 1- 1.1 - (1111). 1 - (131). 1 -(12111). 1 - (12211). 1 - (12221)
(14211)2
- (131). 1 - (12111). 1 - (12211). 1 - (12221). 1 -(14211)
+1 -(11). î. __(121)2
- (11). 1 - (111). 1 - (1111). 1 - (131).1 - (12211)'
yielding the single new ground product
(14211).
For D2 we require the result
p
Qi e2
1 - ex. 1 -ey.1- -z.1 -
e e
__p _ 2y x2 + x3w + y32z
1-xz.1-yw 1 -y 1 -y 1 -. 1-y 1-.1 w 1 -. -yz
and putting p = n23N32, x=bcf(12111), y=bcf(ll),
anbc N22N3,
bo o~~