JVIE.  A.  CAYLEY’S  EIFTH  MEMOIE  UPON  QUANTICS. 
431 
S (6) 
{oh'—a'b,  ad—a'c,  hd—Vc 
fey)'. 
(7) 
{\ci,  X5  -{-]W<5 , \c-\-yjd 
fe.  y)'. 
(8) 
{ac —If  , ad —2hV -\-C(f , a’d 
(9) 
(1)  and  (2)  are  the  quadrics,  (3)  and  (5)  are  the  discriminants,  and  (4)  is  the  lineo-linear 
mvariant,  or  connective  of  the  discriminants;  (6)  is  the  resultant  of  the  two  quadrics, 
(7)  is  the  Jacobian,  (8)  is  an  intermediate,  and  (9)  is  the  discriminant  of  the  interme- 
diate. And  where  it  is  convenient  to  do  so,  I write 
(1)  = U, 
(2)  = U', 
(3)  = □, 
(4)  = Q, 
(5) = 
(6)  = E, 
(7)  = H, 
(8)  = W, 
(9)  = 0. 
97.  The  Jacobian  (7)  may  also  be  written  in  the  form 
y\—yx,  x'  , 
a , 5 , c 
a!,  V , d 
The  Resultant  (6)  may  be  written  in  the  form 
«,  25 , 
a,  25,  c, 
a',  25', 
a',  25',  c', 
3 M 
MDCCCLVIII. 
