ME. A. CAYLEY ON TSCHIENHAUSEN’S TEANSEOEMATION. 
565 
3cC— 36®, — «B— 45C— 6cD, — aC— 45D, —oD Xl, ar)=0, 
eJ), y- ^B-3(?C+ dD, - «B-4JC , - aQ 
gC , 4(^C-j- 6*D, 5B-l-3cC-}~ 6?!), — 66® 
eB , 46ZB+ eC , 6 cB+ 46ZC+ eD, ?/+3 JB+3cC+6?D 
and the transformed equation is therefore found by equating to zero the determinant 
formed out of the matrix contained in this equation. 
The developed result, which was obtained by a different process in the ‘ Deuxieme 
Note’ above referred to, is 
(1, 0 , c, 13, exy, iy=o, 
where 
BC 
BD= 
CD 
D” 
ac 
+ 3 
ad 
+ 6 
ae 
+ 2 
+ 1 
he 
+ 6 
ce 
+ 3 
V- 
—3 
be 
-6 
hd 
-2 
+ 8 
cd 
-6 
— 3 
• 
-9 
+ 3 
+ 6 
+ 2 
±9 
+ 6 
+ 3 
B^ 
B^C 
B^D 
BC^ 
BCD 
C' 
BD= 
C=D 
CD* 
D^ 
a*? 
+ 1 
a^e 
+ 1 
abe 
+ 1 
+ 4 
ad"^ 
-6 
-4 
ade 
— 1 
— 4 
ad 
— 1 
be^ 
-1 
ahe 
-3 
ahd 
+ 2 
acd 
— 3 
— 12 
de 
+6 
+ 4 
bed 
+ 3 
+ 12 
bde 
—2 
ede 
+ 3 
+ 2 
ad 
-9 
hH 
+ 2 
+ 8 
bed 
bd^^ 
—2 
— 8* 
de 
+ 9 
d^ 
-2 
dc 
+ 6 
hd 
d 
dd 
cd'^ 
-6 
±3 
±9 
±3 
0^ 
+1 
1 - 
±6 
±4 
±3 
±12 
±9 
±3 
and 
B‘ 
B^C 
B'D 
BT^ 
B^CD 
BC" 
B^D" 
BC=D 
C^ 
de 
+ 1 
dbe 
+ 8 
dee 
+ 12' 
- 6 
dde 
— 4 
d^d 
+ 2 
— 4 
+ 1 
a^bd 
— 4 
ded 
-12 
aW^ 
-12 
abce 
+ 60 
- 12 
abde 
-16 
+ 20 
- 16 
a^ 
add 
— 20 
ade 
- 8 
+ 30 
abd^ 
— 72 
+ 16 
ac^e 
+ 36 
+ 36 
— 18 
ade 
+ 6 
abc^ 
+ 36 
abed 
+ 12 
-48 
add 
+ 36 
+ 36 
acd^ 
-18 
W 
+ 48 
d 
—3 
dc 
-12 
ad 
+ 54 
de 
-36 
+ 48 
dee 
— 18 
+ 48 
dd 
— 4 
-48 
ded 
+ 12 
-192 
dd‘^ 
+ 14 
-160 
dd 
. 
+ 18 
bd 
+ 108 
bcH 
+ 108 
— 144 
• 
• 
+ 81 
±7 
±44 
±24 
±102 
±108 
±208 
±52 
±164 
±178 
BCD^ 
C"D 
BD" 
C^D" 
CD" 
D' 
abd 
— 4 
acd 
+ 12 
- 6 
add 
+ 8 
ae" 
+ 1 
aede 
+ 60 
— 12 
ad^e 
— 8 
+ 30 
bed 
-12 
bdd 
-4 
ad^ 
-36 
+ 48 
dd 
-12 
bd^e 
—20 
dd 
dde 
-72 
+ 16 
bede 
+ 12 
-48 
dde 
+ 36 
cd~e 
+ 6 
bc^e 
+ 36 
+ 36 
bd^ 
— 4 
-48 
cd^ 
-12 
d^ 
— 3 
bed^ 
+ 12 
-192 
de 
+ 54 
dd 
• 
+ 108 
cH'^ 
• 
+ 18 
±108 
±208 
±24 
±102 
±44 
±7 
