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into (yz)1D. 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 
zx into (¢'D)'z; 
js 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 
PHP +t; 
when P and II can‘be 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). Asa particular case of formula (5), we have 
pelt = el" + ety, 
therefore, 
p tpn =evrper" 5 
whence we conclude, that 
Sle + ¥n)=e "foe. (15) 
That is to say, the symbol, 
evr( jew; 
operating on any function of p will change it into the corre- 
sponding function of p + Wr. 
Changing 7 into p, and p into — 7, we should find 
Sf (w+ Yip) = evefr es (16) 
which shows that the symbol, 
evr ( ) ev, 
