152 
: d 
p (6 dz < 
The very general theorems already stated may be ex- 
tended to any number of systems of variables connected by 
equations, such as define the mutual action of + and p. 
Thus, if 
pr=7pt1 
and 
Pim = 7101+ 1, 
the symbols being otherwise mutually commutative, we shall 
have 
aa 
pl a 
I (p» pr) ) (7, 71) = fm dt dm dy ? (7, 7) S(p, P1)s 
and so on for any number of pairs of symbols. 
Again, as a generalization of the formula (15), we shall. 
find, if y denotes a function of 7 and 7, 
d d 
And, analogous to (16), 
t(= +e m+3) = eVf (n,m) e; 
y denoting in this case a function of p and pi. Writing 2 
and y for 7 and 7, and = and for p and p, in these latter 
formule, we obtain results of considerable importance, the 
statement and discussion of which is reserved for the conclud- 
ing part of this Paper. 
The Secretary read a paper by W. H. Harvey, M.D., on 
the Marine Botany of Western Australia. 
Robert Ball, LL.D., drew the attention of the Academy 
to the fact, that in the celebrated statue, known as the Dying 
