ate i 
¥ 
151 
with + and p, in conformity with the law expressed by the 
equations, 
d 
d 
Bi gods 
d d 1 
dae dps e 
The formule (6) and (8) may now be expressed in the sym- 
bolical form, 
ae 
op Yr=E™ be op, (18) 
dd 
Yr go=e ™ gp Yr. (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 Yr gp and ¢p pz, which immediately fol- 
low them, and not allowed to affect the subject operated on 
by these terms. 
a. : : pas 
As di is commutative with 7, and ra with p, we may 
write the formule (18) and (19) in the form, 
go dead (w+7) op 
tx 9p=9(p-< \um, 
and, for the same reason, are at liberty to develope 
urea) 
; . es d shire 
according to ascending powers of either 7 or a A similar 
. p 
observation applies to the development of 
