Note on Double Alternants. 
179 
or, still more interestingly as regards the right-hand members, 
- 1.2.1 { a.a^ + iSa^.Sft + /3,/3, } , 
- 1.3.3.1 { a^a^a^ + ^^a.a^.'E.j^, + l2a,.S/3,/33 + /3,/3,/33 } , 
+ 1.4.6.4.1 I a^a^a-^a^ + l^a^a^a^.^j^, + ^^a.a^.^f^.ji^ + l^a,.^fi,fi^pD^ + (^.P^i^-^fi^ \ , 
Further, we observe that the determinant quotients are unisignant, the 
common sign being + when n is of the form or 4m + l, and — when 
of the form 4m + 2 or 4m + 3. (II.) 
5. An interesting verificatory proof is reached by taking the asserted 
result and multiplying it row-wise by ^i, and thereafter multiplying the 
product column-wise by Thus, if we multiply 
row-wise by in the form 
1 
1 
1 
1 
1 
/3. ft] -ft\ /3| 
iX ftl -ft] fti 
ft, ftl -ftl ftt 
ft 4 ftl -ftl ftt 
fts ftl -ftl ftt 
we obtain 
aja2a^a^a^ + ftl 
^a.a^a^ + lOftl 
Sttict^ - 10/3^ 
aia2a3a4a5 + ftl 
^a^^a^a^a^ — 5ftj 
lla.a^a^ + 10 ftl 
2a I - 10 ftl 
2ai -h5/3i 
Stti + 5ft^ 
and the multiplication of this column-wise by in the form 
