144 THEORY OF COLLINEATIONS. 
Their resultant 7T,, is also of the same form : 
| © Yy z 0 an WY] z 0 
; _ |Ae Bo Ce Az |, __|A2 Bo Co Bo |. 
T. 0 (HD Ve = | Ad B! Cos keAy |? P2 Ys — As! Bo! Co! keBo! |? 
| Ag! Bs" Co! Kee! Ag!” | Ad!’ B,! C,!! kp! Bo! 
la y z 0 | 
As By C2 C2 
A,! B,! Cl ke C,! 
Ao!’ Bo! Co! Keo! Co! 
wes (15”’) 
Eliminating ,, y,, and z, from the equations of T and T,, we 
get T, as follows: 
Az Ay Az 0 | Au Ay Az 0 
y = A, By Cy Aj | ex A, B, Ci B, 
PP1 2 ad Aj! By Gil ky, Aj! ’ PP1 Y2= By Cy! k, By 
A," B,!’ (On kA," 
Au Ay Az 0 
A,!! By! Cy!’ ky'B," 
Sl eBincr Se 
PP1%2 ar” Bae By iG) WeiGil (16) 
| Ay” By" Cc," ky'C," 
~ 
\ 
where Ax is the determinant value of pw,, ete. 
The resultant may be expressed in the form of determinants 
of the seventh order, as follows : 
Ee wf Brg 0 0 0 
Ale Ba, A B C 
Al BUG) KAY KB kG! 
0 Ve — Al B’ (Od ki A” k/B’ k/iCv 
te 
O @ © A, B, CQ A; 
O Oh @ A; By Gy kyAy! 
0 0 0 Ai’ By! Gy” kA," 
CY) Nz 0 0 0 0 
Als Bua, A B Cc 0 
A! B! OC KA! kB kC’ 0 
(0, Yo = All B!’ (Gi? kiA" k/B"” k’'C" 0 
O MD @ Ay ih CG By 
0 ® @ i B/ Cy kB 
0 0 0 / By!’ Ci!’ ky By" 
ey ial ee, 0 0 0 0 
ZN de Gh LE 0 
A! B! @’ kA! kB’ kC’ 0 
‘00; Zp =| A” BY Cl WA" WB! kC! @ |. (17) 
Aj! By Cy’ ky, Cy’ 
y/ By!’ C,!" ky Cy" 
