159 
1921-22.] Concomitants of Quadratic Differential Forms. 
^rs “ ^rs — ^\r^s ^is^r ”1“ ^i^rs + ^9s^zr + 
"1“ ^frsVz ^2 tVs ^2sVr + ^2Vrs "I” ^fsVsr + ^fr'Oss + ^JVsrs 
+ Cgg^y + Cg + 2Cg^gy + 2Cf ^gg + 2c ^grs 
+ 2?iyg0g + C^y^g + Cgg^y + C^^yg + ^rigd^r + ’^^r^3S + 27l0g^s] ; 
dr' -dr = €[2/^^^ + d^$r + 
■+■ 2my774 + d^rjr + 
+ 2Wy^^ + <^3^r “f" 
+ 2idrd^ + (^4^7* + 2d9r^^ , 
^rs ’ ^rs — ^[2^rs^4 "I" ^\r^s + ^\s^r ^\^rs “f" 2^r^4s + 
+ 2m^g7^4 + c?2r'>7s + «^^2s'>?r + ^2'^rs + + 2^^7745 + 2m'J74„ 
+ '2nrs^^ + d^r^g + d^g^r + ^z^ts "1“ + 2?Z^^^g 
+ 2drs0^ + d^r^s + d^gdr + d^drs + 2dgd^r + ^^rO^g + 2d9^rs\ • 
fr ~ fr — ”*" 9r^2 "I" 9^2^ 
+ KVs +frV2 +/2^r +/V2T + 
+/r^3 + +/3^r + +f^zr 
+ ?nr9^ + Ur9^ + ft^r + ^^^2r + > 
./rs ./rs — ^\_9rs^2 +/ir^s ^”./is^r '^/il’rs + 9r^2s ^s$sr 9s^2r ^r^ss 9^2rs + 
+ /rs'^2 ^tsVb f2rVs f2sVr f2Vrs + frV2s ^s'Osr “1“ fs92r ^rVss fV2rs + ^'^srs 
+ Crs^2 frs^B + fsr^s + fss^r + fz^rs + ^r^2« fs^zr ^s^2»* fr^zs ^^2’’s f^zrs 
+ nr$92 + '^rs^z f^r^s f 4S^r f ^^rs "1“ ‘^r^2S '^^s^zr ^s^2»* "f" '^^2‘i's ^^^3ra] j 
9r' - 9r = ^[9r^i + 3 + r + 9^ir + «^3r 
+/r^l + ^h'nz + 92Vt +fVir + hrj^r 
+ ^rSl + 9 rlz + 9 z^r + + 9 ^zr 
+ Ur9j^ + lr9^ + g^9r + n9j^r + ^^zr\ 9 
9rs ~~ 9rs — ^[^rs ^3 *^" Ors^i 9ir^s 9is^r "1" 9i^rs ^“ ^s^zr ^r^zs 9s^ir 9r^is 9^irs ^$zrs 
+ KsVs +^3^1 + 92tVs + 92sVr + ^2^rs + KVzr + KVzs +fsVir +frVls +fVirs + ^Tj^rs 
+ 9rs^s + ^rs^i + 9zr^s + 9zs^r + 9z^rs 9s^zr "I" 9r^zs ^s^ir + ^r^is + ^^irs + d^z'i's 
"f" ^rs^s .^4r^s "t“ 9is^r 9 ifirs ^s^3r "I" ^r^zs '^s^\r ^r^\s '^^\rs ^^srs] ] 
hr — hr — €\a,r^2 ^^2r ^^ir 
+ hrr }2 + Wr)^ + h^r^r + hr^^r + brj^r 
+ 9ri>2 +/ r^l + ^Z^r + 9^2r +/^ir 
+ Zr^2 ftlr^i h^9r + ”1“ ^^ir] > 
^^rs ~ ^^'rs ~ ^[^rs^i ^rs^2 ^ir^s ^i^rs "t" ^s$2t ^r^2s ^h^ir ^^2‘rs “1" ^^\rs 
+ ^ra'^i + K3r}2 + Kr'ns + ^2s'^r + K^nrs + K'92r + ^r^2S + ^s^ir + ^r'^is + h^q^rs + ^irs 
+ frs^l + 9rX>2 ^zr^s + ^3s^r + ^3^rs + 9s^2r 9r^2s “^" fs^ir + fr^is + 9^2TS + f^irs 
+ 7)1 r s^ \ ^rs^2 ^^4,r^s ^4s^r “^” 2f ^'T^2S "^s^xr "I” “^r^\s ^^2fs ^^irs] ; 
/; -lr = e[/rfi + 4 + k^r + ^^ir + 
+ TllrT]^ + Ar'>?4 + kVr + '^Vir + 
+ “f" S^r^4 + ^3^r + y^4r “ 
+ dr9^ + lr9^ + l^9r + d9^r + ^^4r] 9 
