502 
MAJOR MACMAHON ON SYMMETRIC FUNCTIONS 
For the purpose of this portion of the memoir alone it would have been expedient 
to use the word bipart in lieu of the word part in the foregoing definition, but I have 
retained the word part for the reason that the definition remains valid whatever be 
the order of multiplicity of the parts. 
Of a partition Ps,%) product (pi<7i a separation composed 
of the separates 2hPi) iPzP:)- 
Definition. 
“ A partition qua its separations is termed a separable partition.” 
Definition. 
“ If the successive biweights of the separates of a separation be 
the separation is said to have the specification 
Observe that the biweights of the separation and of its specification are necessarily 
the same, and identical with the biweight of the separable partition. 
Observation. 
The separable partition is counted as one amongst its own separations. 
34. To take a concrete example of these definitions, consider a separable partition 
To bl). 
We have 
Separations. 
Specifications. 
(2bIbbT) 
{^), 
(2b Ib) (bl) 
(3b bl), 
(M bl) (To) 
(2lTb), 
(Tbbl) 
(IT 2b), 
{w) (Ib) (bl) 
(bb ibbi). 
35. I will discuss the law of symmetry that has been established in the light of 
these definitions. 
I recall the relations 
