151 
with 7 and p, in conformity with the law expressed by the 
equations, 
d d 
pee 
gis 1 
dato dpe e 
The formule (6) and (8) may now be expressed in the sym- 
bolical form, 
ae 
op Wr=e* Fhe gp, (18) 
dd 
Ur gp=e "pp dr. (19) 
But it must be observed that they are no longer as gene- 
ral as they were in their original form. The equations (6) 
and (8) would hold good, whatever expression involving 7 
and p was written to the right of each of their terms. Whilst 
the operation of the exponentials in (18) and (19) must be re- 
stricted to the terms Yz gp and gp yz, which immediately fol- 
low them, and not allowed to affect the subject operated on 
by these terms. 
Gis é : ae 
As ap is commutative with 7, and ae with p, we may 
write the formule (18) and (19) in the form, 
d 
ge Yr=y i ae $ps 
tn yp=9(p-< dm, 
and, for the same reason, are at liberty to develope 
seed 
; : : d aie 
according to ascending powers of either 7 or az A similar 
P 
observation applies to the development of 
