PHILOSOPHICAL 
TRANSACTIONS. 
XI. An essay towards the calculus of functions. Part II. By 
C. Babbage, Esq. Communicated by W. H. Wollaston, M. D. 
Sec. R. S. 
Read March 14, 1816. 
In a former Paper which the Royal Society honoured with a 
place in the last Volume of their Transactions, I endeavoured 
to explain the nature of the calculus of functions, and I pro- 
posed means of solving a variety of functional equations con- 
taining only one variable quantity. My subsequent enquiries 
have produced several new methods of solving these, and 
much more complicated functional equations, and have con- 
vinced me of the importance of the calculus, particularly as an 
instrument of discovery in the more difficult branches of ana- 
lysis ; nor is it only in the recesses of this abstract science, 
that its advantages will be felt : it is peculiarly adapted to the 
discovery of those laws of action by which one particle of 
matter attracts or repels another of the same or of a different 
species ; consequently, it may be applied to every branch 
of natural philosophy, where the object is to discover by 
calculation from the results of experiment, the laws which 
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