40 PROFESSOR KELLAND ON A PROCESS 
or, which is the same thing, 
fm m 
Ee 
o ——l r 
= ye a’ e "“ da; from which it follows, by equation (1.), that 
m™ 
in ( 2 aN OE oa Sh aera 
|r (ea a) . a a (-—a@r) e Bd da 






MT we 
=i 
=(-Nom fe g e dé 
|m+r p 
=e ul r 
gr tre 
1 d\el pee 1 
—I\u 
Consequently, = Tae el = = PREP (2.) 
[r 
Let ~ be a function, supposed to be capable of being represented under the 
form of a series of functions, such as e-* ; then we shall have 








[7 
: 1 d du rdu 
2. Since v- ae Fda dx 
OR BN eh ay CRY 
it follows that = =) ee (ga) ; 
. d\e. ef oe 
ogee) op ee yaaa 
3. If we write d, u for _—_ eS u; then from the last Art. it will be evident, 
a 
without demonstration, that 
a = ay 
d, (wu) =ovdu + ud,vd, u + LBD #, od u+ &e. 
4. Let  (d,) be any function of d, capable of expansion in the form 
¢ (d,)=2ad_; then, by the last Article 
$ (d,) (wr)=3afodurpd, vd w+ae.} 
=P (Zad") utd v(Sapd')u+&e. 
