the calculus of functions* 
4^3 
^cc-=f{oc, x (x,'!'#, •• 4'"- 1 x),x[x,^cc, . . 4/«-i#)&c.} 
from which equation of the n — i th degree must be found. 
When we apply these considerations to functional equations 
of many variables, other and even greater difficulties present 
themselves ; the first step in that direction must be an improve- 
ment in the notation. 
Since the above was written, I have bestowed some atten- 
tion on functional equations involving two or more variables, 
and I have met with considerable success: I am in possession 
of methods which give the general solution of equations of all 
orders, and even of those which contain symmetrical func- 
tions. I have also discovered a new and direct method of 
treating functional eq> ations of the first order, and of any 
number of variables, and this new method I have applied to 
the solution of differential and even of partial differential func- 
tional equations. 
