1902 - 3 .] Dr Muir on Axisymmetric Determinants . 571 
development, and that this will be equal to the former. For 
example, if a term have the quaternary cycle (1, 2, 3, 4), another 
term is obtainable by simply changing this into (4, 3, 2, 1), the 
effect on the original term being to change it from 
.... a 12 a 23 a 34 a 41 .... 
into 
.... a 43 a 32 a 21 « 14 .... 
which, in the circumstances, is equivalent to no substantial change 
at all. 
“ Pour fixer les idees ” he takes the case of the 6 th order, giving 
the following as the development of what we should nowadays 
denote by |^n« 2 2 a 33 a 44 a 55 a 66lrs = sr-5 v * z -’ 
^11^22^33^44^55^66 — 1^22*^33^44^5(5 4* ^^il^ 2 2^34%6 — ^^1^34 %(> 
+ 22Sa n a 22 a 33 « 45 a 56 a 64 — 22a 11 a| 3 a 45 a 56 a 64 + 4 2a 12 a 23 a 31 a 45 a 56 a 64 
— 22a 11 a 22 a 34 a 45 a 56 a 63 + 2^a%a B4 a^a^Qa &B + 2 ^a n a 23 a 34 a 45 a 56 a 62 
— 22a ]2 a 23 a 34 a 45 a 56 a 61 , 
where it will be seen that the first four types of terms correspond 
to the following partitions of 6, viz., 
1 , 1 , 1 , 1 , 1,1 1 , 1 , 1 , 1 , 2 1 , 1 , 2,2 2 , 2,2 
and the remaining types to the remaining partitions, 
1, 1, 1, 3 1,2,3 3,3 
1,1,4 2,4 1,5 
6 . 
(. Issued separately December 28 , 1903 .) 
