m A. CATLET ON TSCHIENHAUSEN’S TEANSEOEIVIATION. 
571 
And since upon writing a—h~c—dj—e—f—\ the transformed equation becomes 
it is clear that in the coefficient of any monomial product of B, C, D, E, the sum 
of the numerical coefficients of the several monomial products of «, c, d, e^f must be 
= 0, which is the property above referred to as affording a verification of the calculated 
expression of the transformed equation. 
The final result is that the equations 
(«, 5, c, d, 1)==0, 
y= {ax h)B 
-]-{ax^-{-5ix + 4c)C 
-{-{ax^-\-5hx^-{-10cx + 6fZ)D 
-\-{ax*-{- bhx ^ + 1 0da’+ 4(?)E 
give for the transformed equation in y 
(1, 0, c, m, c, fly, iy=o, 
where 
B- 
BC 
1 
BD 
c- 
BE 
CD 
CE 
D‘ 
DE 
E^ 
ac 
+ 2 
— 2 
ad 
be 
+ 1 1 
ae 
bd 
+ 4 
— 4 
+ 2 
+ 10 
-12 
of 
be 
cd 
+ 1 
— 1 
+ 1 
+ 15 
-16 
¥ 
ce 
dr 
+ 4 
— 4 
+ 2 
+ 10 
— 12 
¥ 
de 
+ 1 
df 
e‘ 
+ 1 
±2 
±6 
±4 
+ 12 
±1 
±16 
±4 
+ 12 
±6 
±2 
B® 
B'C 
B^D 
BC 
B'^E 
BCD 
C^ 
BCE 
BD' 
CD 
d'd 
+ 2 
ede 
+ 4 
of 
+ 1 
+ 1 
abf 
+ 1 
+ 10 
+ 3 
acf 
tjcn 
+ 6 
+ 4 
abc 
-6 
aUd 
+ 2 
abe 
+ 3 
+ 19 
ace 
— 4 
— 8 
— 4 
ade 
-12 
-22 
- 46 
¥ 
+ 4 
a(r 
-24 
acd 
-52 
ad- 
ten 
-48 
— 20 
bf 
+ 8 
+ 4 
+ 20 
b^c 
+ 18 
b^d 
— 4 
+ 20 
We 
+ 3 
+ 30 
+ 25 
bee 
+ 4 
+ 20 
+ 70 
bc^ 
• 
+ 12 
bed 
• 
+ 16 
— 20 
bd" 
— 8 
— 80 
• 
• 
+ 16 
c^d 
+ 32 
±6 
+ 24 
+ 4 
+ 52 
±4 
+ 56 
+ 44 
±12 
±30 
±126 
BDE 
iCE 
CD' 
BE' 
CDE 
D* 
CE' 
D'E 
DE' 
F/ 
adf 
aW 
hef 
bde 
e"e 
ed^ 
un 
— 8 
+ 12 
— 4 
- 6 
— 4 
+ 22 
— 20 
+ 8 
— 4 
- 20 
+ 46 
- 70 
+ 80 
— 32 
aef 
bdf 
be- 
ef 
ede 
-1 
+ 4 
-3 
— 10 
+ 8 
-30 
+ 48 
-16 
— 3 
+ 4 
-25 
+ 20 
+ 20 
-16 
of 
bef 
edf 
ce' 
dre 
— 1 
-3 
+ 4 
— 1 
-19 
+ 52 
—20 
— 12| 
bf- 
eef 
df 
dW 
— 4 
— 2 
+ 24 
-18 
def 
e^ 
— 2 
+ 6 
— 4 
±12 
±30 
±126 
±4 
±56 
+ 44 
±4 
±52 
±24 
±6 
