167 
1921-22.] Concomitants o£ Quadratic Differential Forms. 
second derivatives. After the transformations have been eftected, the 
forty equations run as follows : — 
(i) From the coefficients of , 7;^^ , Cn , , 
da^ oh-^ dg^ c\ 
+ (^-2?0^ + («i-2-/3)|^ + ('i.-2gg 
+ (/l “ ■^*3 + 6'2)g^ + (”*1 ~ ^'4 + ’ 
2h^ + b^ + M + ,n^ 
ca-^ oh-^ cg^ cl-^ 
- + (”2 -fi - »» 3 )|| = 0 , 
„ Bd> ,.d<l> BS 8d> 
2^5r^+/5rr + «7^ + »P,; 
ca-^ on-^^ cg^ cl^ 
+ (^3-2/2)g-%|^ + ('i3-2»/^ 
-4t+K-/4-»4^-<^4||“0, 
2l^ + m^f- + npt + lf 
ca^ oh^ cg-^ cl^ 
+(/4-«%-«2)f-<^2|^-^sg=o. 
(ii) From the coefficients of ^^2 > '^12 ’ ^12 ’ ^12 > 
2|^+"-f ) + A 
uCt(2^ ^'^'1 
+ 2^) + ?' 
.a/^2 dh^ ' 
dcf) 
^ 9-2 ' 
\ -i_ 
+ . + .<3-^ + «4—+ (</., + /i-3 /i)^^ 
+ (h, + 1^- V,/4 - - 2/4^ + (<74 + - gf ) = 0 . 
dp 
^dfX 
♦ t (*.*/, -«i+(*.+«,-'.)| 4 ».g 
+ - 2/3^ - 2,„,^ - (/4 + ,n3)( ^ - 1^) = 0 , 
‘0p '“0/4 
'0^ 
^O) 
