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