402 
PROFESSOR CAYLEY ON THE TRANSFORMATION 
k'° 
k 9 
k s 
k 7 
h 6 
¥ 
¥ 
¥ 
k 2 
¥ 
¥ 
SI 12 
+ 1 
m 
£i n 
-1024 
+ 1408 
- 396 
ii 10 
-5632 
+ 4400 
+ 1298 
£2 9 
-16192 
+ 16368 
- 396 
H 8 
-18656 
+ 19151 
Q? 
-16016 
— 1144 
+ 16368 
£1 6 
+ 4400 
- 7876 
+ 4400 
J 
£2 5 
+ 16368 
- 1144 
-16016 
£2 4 
+ 19151 
-18656 
a 3 
- 396 
+ 16386 

-16192 
Q? 
+ 1298 
| + 4400 
—5632 
- 396 
+ 1408 
-1024 
n° 
+ 1 

— 32208 
+ 1408 
— 18656 
+ 8800 
- 1936 
+ 32736 
- 7876 
+ 40900 
- 1936 
+ 32736 
-18656 
+ 8800 
-32208 
+ 1408 
-1024 
—5632 
—30800 
— 9856 
+ 30800 
+ 33024 
+ 30800 
- 9856 
— 30800 
— 5632 
-1024 
— 12 
+ 66 
-220 
+ 495 
-792 
+ 924 
-792 
+ 495 
— 220 
+ 66 
- 12 
+ J 
Equation-systems for the cases n= 3, 5, 7, 9, 11. — Article Nos. 8 to 10. 
8. n= 3, cubic transformation. Jc=u i , Q=^ (here and in the other cases). 
P=ee, Q=f3. The condition here is 
7cW+ (2aj3 + j3 2 ) = Q£{ (a 2 + 2aj3) + £V}, 
and the system of equations thus is 
£« 2 = 0 / 3 2 , 
2«j3+/3 2 =M(a 2 -f 2«j3), 
and similarly in the other cases ; for these it will be enough to write down the equation- 
systems. 
n— 5, quintic transformation. 
¥=a-\-yx l i Q=/3. 
ft 2 a 2 =Qy 2 , 
2c C y + 2c i f3+p 2 =Q(2ay + 2Py+n 
y 2 + 2/3y=0£ 2 (« 2 + 2 a /3). 
