392 
A TENTH MEMOIR ON QUANTICS. 
[693 
= column next written down; but this column contains congregate terms which have 
to be replaced by their segregate values (see Table No. 96, deg-order 8.16); and we 
thus obtain 
a 3 j a 2 b 3 d 2 bh a 2 cg abed b 2 c 2 c 2 h 
i a 2 bh 
+ 1 
+ 
+ i 
— 2abcd 
- 2 
~\bef 
1 
2 
+ 3 +2 
— 2 c 2 h 
- 2 
+fl 
1 _ 1 2 _ 1 
3 3^3 3 
- 1 - 2 +2 
viz. the terms other than those divisible by a 2 all disappear : we may either abbreviate 
the calculation by omitting them ah 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 
c/i2 = %aj - ±b 3 + ^¡bh - \cg, 
which is the proper segregate expression of the derivative ch2 : of course, we have 
deg-order CH2 = 8.16, deg-order cA2 = 6.6, and the difference is 2.10, the double of 
1.5, so that the factor a 2 is as it ought to be. 
Table No. 100 (The Derivatives up to the Sixth Order). 
Degree 2. 
2 . 2 
b 
2.6 
c 
<m4 
+ 1 
aa2 
+ 1 
Degree 3. 
3 . 1 
CO 
CO 
d 
3.5 
e 
3 . 7 
ab 
3.9 
ae 5 
0 
ab 2 
- 3 
ab 1 
+ 2 
ac 2 
+ 1 
ac 1 
+ 1 
ac 4 
+ ¥ 
ac 3 
+ VO 
Degree 4. 
4.0 
9 
4.2 
ae 5 
- 2 
ad 3 
0 
bb2 
l 
4 
ae 4 
0 
cc 6 
1 
~ 4 0 
4.4 
b 2 
h 
4.6 
i 
ad 2 
i 
3 
+ * 
ad 1 
+ ¥ 
ae 3 
4 
5 
_ 6^ 
ae 2 
+ 1 
<*/5 
,02 
8 3 
— ¥¥ 
afi 
+ F¥ 
be 2 
+ i 
~ h 
be 1 
+ V 
cc 4 
+ 2 3 5 
1 
- TIT