PARTICULARLY THOSE OF TWO VARIABLES. 799 
By (xxiii), (xxvi), and two others, 
C la 2 '^li. 2 H" C 9 2, ^8 3 = C 4 S ^5'" “l” C 6 2, ^7 3 .... (38) 
By (xxv), (xxvi), and two others, 
C 15 3 ^ll 2 C 9 2 ^13 2=: — C 12 2 ^'8 2 "i~ C 8 2 ^'12 2:= —H“ C 3 2, ^7 2 .... (39) 
The first members of (34), (36), (37) are given by Bosenhain, in the paper already 
cited, in his formula (94), and of (38), (39) in his formula (99) ; but the second 
members are not noticed. The equivalents of (xxvii), (xxviii), (xxix) are given in 
his formulae (98) and (102) ; and of the following equations (40), and (a)-(ie), in (89) 
and (90). 
11. By making both the variables zero in (31), (32), (33) there at once follow the 
equations 
4 — C l > ~\~ C '6 h — G 2^~\~ C 
4_^ 4 
A — 4 —r* 
=c 6 4 +c 8 4 =c 4 4 +c 
c 0 4 —c 15 4 —c 2 4 +c 
4_^ 4 
°l+ C * J 
and the following are obtained from (23), 
(40) 
'Co V=c*V+CsV . . . 
.(“) 
si 2 s> 2 r% 2 st 2 | st 2 si 2 
°3 °12 — c 6 °9 0 C 15 ... 
. 08) 
s> 2 st 2 — st 2 st 2 [ st 2 st 2 
.°0 °3 —°1 °2 ’T°12 c 15 * * 
.(y) 
c 2 r 2 — 0 2 0 2 is. 2s, 2 
°0 °4 — (/ 2 °6 °12 ... 
. (8) 
OjV =CaV+e/c la a • ■ ■ 
.(«) 
,c 0 V =c 2 V+c 8 V • • • 
.(*) 
2^ 2 _ ^ 2 xi 2 1 xi 2xi 2 
^0 °8 —°1 °9 l °J2 ... 
.«) 
2^» 2 — x» 2x, 2 | fi 2 0 2 
°2 °8 —°3 °9 °12 ... 
. 0?) 
p 2 r 2 —/} 2x* 2 Lxi 2xi 2 
C/Q 0 2 —Oi 0 3 C 6 • * - • 
.(*) 
'c/c/ =CoV+o 9 2 c 16 ® • ■ • 
. (0 
ri 2 r 2 . — x* 2xi 2 j 2^-» 2 
°3 — G 1 °6 °15 ... 
.(«*) 
✓» 2xi 2 _ p 2 si 2 | s% 22 
°2 °12 —°6 °8 °15 
.(<0 
2p 2 — /v 2xi 2 I s^ 2^ 2 
°1 °8 —°0 °9 1 °6 °15 * - . 
. M 
2xi 2 - x» 2 xi 2 [ si 2 s% 2 
°3 °8 — °2 °9 °4 °15 ... 
.(.8) 
2xi 2 — x» 2xi 2 | si 2st 2 
°1 °12 —°4 °9 C.16 ... 
.(“) 
5 K 
MDCCOLXXXII. 
