400] GIVEN PENCIL OF SIX LINES. 109 
As regards the discriminant Q 1() , this as already remarked, has been calculated for 
the general form, but for the present purpose it is easier, by dealing directly with the 
form [(a, h, k, b^x, y) 3 ] 2 + 32and then interpreting □, V, ©, R and restoring the 
coefficient c as above, to obtain the discriminant Q w of the function 
[c(a, h, k, b\x, y) 3 ] 3 4-4[(j, l, f\x, y) 2 ] 3 
in the required form, as a function of c 2 D, V, c©, cR. 
I find after some laborious calculations 
Q 2 = 
10 No. 31 
= c* 
9 □ 
+ 0 j 
40 R 
1 
,+ 
288 V© 
+ 
256 V 3 
q 4 = 
10000 No. 34 
= c 4 
99 D 2 
+ C 3 
400 RD 
j 
+ 
2304 V ©□ 
1 
+ 
8640 © 3 
+ c 2 j 
12800 AV© 
-1 
+ 
82944 V 2 © 2 
u 
4608 V 3 D 
+ c 
20480 AV 3 
1+ 
147456 V 4 © 
+ 
65536 V 6 
Qg = 
1000000 No. 35 
= c 6 
{+ 
7992 D 3 
+ c 5 
'+ 
72000 RD- 
+ 
145152 V © 2 D 
^ — 
622080 © 3 D 
+ c 4 
r 
160000 R-D 
+ 
691200 AV©□ 
+ 
3456000 A© 3 
+ 
3815424 V 2 © 2 D 
+ 
36080640 V© 4 
L 
635904 V 3 D 2 
+ c 3 
'+ 
33177600 AV 2 © 2 
+ 
4669440 AV 3 D 
j + 217645056 V 3 © 3 
[+ 23003136 V 4 @D