AND GENERA OF TERNARY QUADRATIC FORMS. 
291 
Substituting for pp- and for V their values, given by the equations (45) and (46), we 
find 
Hm p=f 4 x£x yax n(i-J) xn(i-i) x n (i-t) 
xnj(i-i)xni(i-^)xni[i+(^)i] 
T 
which is the second determination of the limit of the quotient j-j. 
. . . (47) 
1 ..’J 
Finally, equating the two values of this limit, and denoting the coefficient jp X j by 
we obtain the following determination of the weight of the proposed genus, 
w=^ x ?xn}(i-i)xni[i+(^)i]xni[i+(=^)i], . . (48) 
the values of £ (which are computed from those of o’, yj, 0) being as follows : — 
(A). — (f) and (F) properly primitive. 
0=1, mod 2. 
0=2, mod 4. 
0 = 4, mod 8. 
0=0, mod 8. 
A=l, mod 2. 
4[2+¥] 
* 
r AT+n 
iL3+(-i)“j 
A =2, mod 4. 
i 
i 
4 
i 
A=4, mod 8. 
r oF+i i 
iL3+(-i)“J 
i 
4 
1 
4 
i 
8 
A=0, mod 8. 
1 1 
+L 
c* 
7 
+ 
CO 
1 1 
1 
8 
1 
8 
1 
16 
(B). — (f) improperly, (F) properly primitive. 
0=1, mod 2 ; 0F=3, mod 4. 
A =2, mod 4. 
i 
A=0, mod 4. 
^L2+(-l)— J 
(C). — (f) properly, (F) improperly primitive. 
A=l, mod 2 ; A/=3, mod 4. 
0=2, mod 4. 
0=0, mod 4. 
r a 2 / 2 -i~i 
*L2+(-irrj 
