128 
MAJOR P. A. MACMAHOR OX A CERTAIX CLASS OF 
introducing tlie undetermined quantities 
“12> 
“l8J “23» 
write 
= “i22i25 
— “is'Zisj 
^23 — “23723’ 
«21 = 
1 
^12 
(Xgi 
1 
*13 
1 
^32 — ’ 
*23 
and thence by substitution 
Pi 
“122'i2 
“is^Zis 
1 
^\2 
P^ 
“23^/23 
— i^l23’ 
1 
«13 
1 
*23 
P& 
which may be written 
Pi 
2i3 
5i3 
*12*23 
1 
Pi 
^23 
= Pi23 j 
"l3 
1 
Ps 
this is a quadratic equation for the evaluation of ais/aigacsj '^'"hich may be written 
f _ i.'\ _ Q 
\«12«23 ^13/ \'^13‘’‘23 ^31/ 
Thus two of the three quantities a^o, a^g, aog remain undetermined, and the co¬ 
efficients of Vg are not subject to any condition. 
The matricular relation is either 
or the one involving’ the matrix similar to the above with Cg^ written for Cjg. 
“i 2 j “23 ^1’® undetermined quantities, and c^g”^, Cg;^"^ are the roots of the above- 
