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into ('x)D. This, in fact, reproduces the known rule for 
the change of the independent variable. 
From (14) we conclude that the change of 
D into oD, 
and 
z into (¢'D)'7, 
is a legitimate one. The validity of this change has not, we 
believe, been noticed before. It is unnecessary to adduce any 
more particular instances of the general law of interchange of 
symbols which may be established, viz.: If from (1) we can 
deduce any equation of the form 
PIT=1IP +1; 
when P and II canbe expressed in terms of p and 7, then, in 
any symbolical equation derived from (1), we are at liberty to 
change p into P, and z into II. 
Some very important deductions may be made from the 
equation (1). As a particular case of formula (5), we have 
pe’ = eo + evar, 
therefore, 
ptpr= eY™eV" 5 
whence we conclude, that 
S(p + ¥n)=eMfper. (15) 
That is to say, the symbol, 
CA ens 
operating on any function of p will change it into the corre- 
sponding function of p + wz. 
Changing 7 into p, and p into — 7, we should find 
F (n+ ¥p)=erefi ev, (16) 
which shows that the symbol, 
eve ( ) ev, 
