^lE. A. CAYLEY’S SEVENTH MEMOIE ON QHANTICS. 
283 
as may be verified without difficulty. That between & and p is 
A. 
as appears by the identical equation 
(12A, 8T, -6A^ -6TA, _T^_iA^Xi(i>+^), 1)^ 
=^4(3A, 8T, -12A^ -72TA, -46A^-64P, -72TA^ -12Ah 8TA^ SA'^J^, 1/ 
1)^(3A, 8T, 6A^ 0, 
where the second factor of the product on the right-hand side is 
-^(1, 0, -6A’ -8T, -SA‘1p 1)‘. 
The relation between p and ^ is then at once found to be 
9.= 
A 
^+-+ A 
A 2T 
P 
or (since p^ and A, B may be simultaneously interchanged) 
2A^ 
B 
p-. 
B 2T 
5 H h 
^ q B 
242. Let the equations in p, q be represented by (pj9 = 0, \pq=0 respectively; then we 
have 
(pp =p* — 6Ap^ —8p — 3 Ah 
and therefore 
whence 
and therefore 
<p'p=p^—8Ap — 2T, 
^pp'p =p* — 3A^^ — 2T^ 
= 3A/+6Tp+3Ah 
_ 2Bho _24B2 
Ap<^'p~ ^'p ’ 
with a hke formula for p, that is we have 
which with the equation 
24B2 24A2 
9 i^'p 1 P ’ 
are the system of equations connecting 6, p, q. 
243. As already remarked, we have to consider the two derived covariants, 
CU = -T.U+24S .HU, 
DU= 8S^U- 3T.HU, 
2 Q 2 
