PROFESSOR CAYLEY’S TENTH MEMOIR ON QUANTICS. 
653 
viz., the terms other than those divisible by d 2 all disappear : we may either abbreviate 
the calculation by omitting them ab initio, or retain them for the sake of the 
verification afforded by their disappearance. The factor a 2 divides out, and the final 
result is 
ch2=±aj - W+¥ubh - $cg, 
which is the proper segregate expression of the derivative ch2 : of course, we have 
deg-order CH2 = 8.16, deg-order ch2 = G.6, and the difference is 2.10, the double of 1.5, 
so that the factor d 2 is as it ought to be. 
Table 100 (The Derivatives up to the Sixth Order). 
Degree 2. 
2.2 
6 1 2.6 
0 
aa 4 
+ 1 
aa2 
+1 
Degree 3. 
3.1 
3.3 
d 
3.5 
e 
3.7 
ab 
3.9 
/ 
ac5 
0 
at 2 
-3 
a61 
+ i 
ae 2 
+ 1 
ac 1 
+ 1 
- ac4 
+ ¥ 
etc 3 
+ do 
Degree 4. 
4.0 
9 
4.2 
ae5 
— 2 
ad3 
0 
562 
1 
4 
ae 4 
0 
cc 6 
l 
4 0 
4.8 
ad 
be 
4.10 
ae 1 
6 
5 
—2 
of 2 
a/3 
+i§ 
5 
cc 2 
+ 4 
1 
2 0 
4.4 
5 3 
h 
4.6 
i 
acZ2 
1 
3 
+i 
aril 
+i 
ae3 
4 
5 
6 
5 
ae 2 
+1 
a/ 5 
+H 
8 3 
■B"3 
af 4 
i 1 3 
5c 2 
+i 
1 
2 
6c 1 
+ 2 
cc 4 
+A 
1 
1 O 
ae 
4.12 
v a 2 6 
c 2 
+i 
of 1 
‘ 9 
-2 
