344 
PROFESSOR A. R. FORSYTH ON THE DIFFERENTIAL INVARIANTS 
I + 
4- R -4- F -I- ‘-"F 
■*" '"'0E„i "*3E„ ■'■ " "" aE(,,, 
+ aK, + all + 3f7„ + all + all 
01 
SF,o 
¥ 
11 
0 ? 
sf 
+ 2F.,,if +(G,„+-2F,„) +2F,, Y +(G,,„+2F„)4^' +(2F,,+2 Cx„),-;1: 
OVt,,, Ovjqi FOtoq oOtip 
'll 
'20 
-L J. _L _1_ 9^ J- ^ J- 9^ J_ 
■F ^ “F -F ^9]] 4T ' + 930 Y; + -921 ';nX' + ^ 
dcpo] *^9 o2 ^921 ^912 ^9o3 
, , 3/’ r , 9F , , 3/ , , 3/- , ,, , a/’ , , a/' _ .. X 
+ ^10 ;xA- 1 - '^20 K , - 1 - -'/'li oA- 1 “ 'Aso a; -F -^^21 oi-F '^^12 '^ ',- — 0 . . (I3), 
di//|„ di//ii di//|,x dv//.x| d9i. o9o3 
Ie + I' + It' + N I + 3Q % + 2 -RI + s 1 ; 
+ (Foi+’^Ft,j)^^ +-2Foi^^- +(^F|i + 2Foo)^^- +(Eoo+2Fii)^|f- +2Fy^,^-|f 
10 
aE 
01 
aE, 
20 
aE 
n 
3E||2 
i/l 
2A + (2F„ + G,„) + (F,,, + G„) //- + G,Jf 
20 
aF 
11 
+ (Foi + F^io)^^+ ^^^aF- 
I r< 3 / I 3 y I p 3 / 
"T '-^01 “r *■''-^11 ^/~^ \ 
CljrjQ OLto() ^'^11 
I / 3 /‘ , , a/' . , 9 /’ 1 o / 3 /' , a/ , a/’ 
~F 9oi oA- + -9i 1 + 9oi YY' + '^921 + -9 i2 + 9o 3 ;^4r 
d(pio ^920 *^9ii ^930 ^9:i *^9ii 
I / 3/' I , a/‘ I , 3/‘ I .3, a/-* I , a/-’ , , a/ _ 
~F ^01 sA—F y;—F V^o 2 —F ^^-21 —F ^1-2 oA—F '/'03 ^ 7 - — ^ 
3910 3i//.o d9n dxjj.^Q ov/zoi dv//i2 
F, 
02 
(I.)> 
which come from the coefficients of respectively ; 
9]i’ _3/_ I 2;p'' 3/ . _a/^ 
aE,„ ^ aE.,„ ^ aE 
no 
9/ 
aF 
+ F ^4I, + 3 Fi,j —[- F„i 
10 
20 
i/ 
aF 
+ G 
20 
9/‘ 
a’G, 
11 
¥ 
aF 
11 
20 
o- ^ iF j_ -A 3/ , , a/ , , df ,0, a/‘ , a/' 
■F aT' “F '^'320 + ^10 o‘, + 34,0 — -h 
3920 ^ 9 so <^921 ^920 31//3U 
= 0 . . (II,), 
