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SYLVESTEE'S AXISYMMETEIC UNISIGNANT. 
By Thomas Muir, LL.D., F.E.S. 
(Eead May 24, 1911.) 
1. In a previous paper* it was suggested that the multihnear 
unisignant functions 
which are the final developments of the axisymmetric determinants 
a^ + b. —b. 
— b. a^ + b-. 
o 3 o 
— ^3 + 63 + 
- 
a, + 6, 4- b 
3 
might with advantage be viewed apart altogether from the theory of 
determinants. In support of this it was shown that, the numbers of the 
variables being 2 + 1, 3 + 2 + 1, the functions could be much more 
appropriately denoted by 
1(22 a. 
b. 
^3 bM 
and that with this notation a recurrent law of formation could be readily 
formulated, namely, 
\\a,\\ = a,, jia^ a.]^ (a^ + a.) [ ] &3 1- 1 + a.a., 
J ^3 
bl b. 
{a, + a. + a^.\b. b^) 
+ a^a^\^i^b^ + c,[] + a^a^^^i^b^ + c^^^. 
+ a^a^ ! I ^3 + ^4 1- ! + ^^2^3^4, 
* Muir, T. " Borchardt's Form of the Eliminant of Two Equations of the nth 
Degree. Trmis. R. Soc. S. Africa, I., pp 447-452. 
