348 
PROFESSOR A. R. FORSYTH OX THE DIFFERENTIAL INVARIANTS 
2 F-|f +gJ^- + 4 . 
dRio SJ'io 
d(j). 
5/ I , df dr 
'01 i + V'oi - - 
20 
dip 
20 
dd 
~ 4Fio)-'--] + ~£-[2V=^(^o 2 — Go]/’ — 2Foi^j] 
-F -£^[6Y-rp,, - iG,,p - (Eo, + 4Fio)<^] “ Go,p - 2 F 01 O-] = 0 
(n,)'. 
•)E 4 -E--^ + F-2/1_l .>;^^ -F,/, 4 - 
BE,,, ■ "aFi,, 
— F r I 3/ 
‘-'JO' ^ 
Of'., du^ 
in 
aG 
].U 
10 4 / 
^9n 
¥ 
' dxb. 
''111 
de 
■'#'iN — — 3E|,,s] + gj' [4V-^jj — (Gk, + 2F(„) r — 4fl,,s] 
+ (G,„-2F„,)s®-^ 
dll, 
Sl\ 3)1~ “^F.IIP — 3E|ocrJ + [4V-i;<„ — (Gjo + 2F(„)p — 4 E(,j<t] 
+ (G|„-2F,„)<Ty = (i . (n.r, 
c/’, ^ ~ ' 
gF’ Af _J_ F I r; ¥ I or ¥' \ A \ I I on S/’ 
aE, + aF; + aG^, + a^; + a^ 
10 
- 01 
*■10 
'll 
+ (E„, - 2F.„)). |i + |£ [4V^,^,„ - 4G,„r - (E,, + 2F.,) „•] 
+ H - 3G„,,- - 4F,„s] - G„,. 4 
+ (E,), ^Fo)Pg£ + ■” (Eol + 2F,(,) O'] 
3l 
dv 
+ H - 3Go,/> - 4F„,cr] - G„,o-= (I . (II,)', 
aF,. ^^^acx, 
01 GGTqj d(p„o 
— E 
ai/zij, 
+ II +-‘Fi) »• - 
on — 3F,„p — Ei(,(r] + |£ [6V*,^„ — (G,,, + 4Fo,) p — 
4Eois] 
' ^^01^] = ^ • (II 3 ) > 
^ 3F„, + afn aL 
+ ~ 2Gi( 3?’ —- Eg^s] + [6 V'(^g3 — 
3 ^4- 
-1- |£ [2VV„ - 2G.„p - E„,o-] + |£ [eV^fc - 
a^ 
5Goir + ( 2 G 10 
^Gqip + (2G^o 
6Foi)5] 
6 F 01 ) cr] = 0 . (IIJ. 
