‘ 
ANNALS 
OF 
PHILOSOPHY. 
JANUARY, 1816. 
Bee 
- ARTICLE I. 
Account of the Improvements in Physical Science during the Year 
1815. By Thomas Thomson, M.D. F.R.S, 
THE following account will be much less complete than I could 
have wished; but Iwas prevented by illness from commencing it 
till within three weeks of the period at which it was to,be sent to 
the press, I was unable, in consequence, to peruse the vast number 
of papers and books which it was requisite to read (above 200 in 
number) with that attention which would have been necessary in 
order to give a complete account of their contents. I have, how- 
ever, endeavoured to do as much justice to the subject as the short- 
ness of the time would allow. 
I. MATHEMATICS, 
The observations of Professor Christison on the nature of fluxions 
(Annals of Philosophy, vol. v. p. 328, vol. vi. p. 178, 420,) will be 
read with interest by all those who wish to understand the meta- 
physics of this branch of mathematics, and to be satisfied of the 
accuracy of the calculus. 
Only one mathematical paper has been published in the Philoso- 
phical Transactions for 1815, namely, an Essay towards the Cal- 
culus of Functions, by C. Babbage, Esq. The term function has 
long been used in analysis for the purpose of denoting the result of 
every operation that cau be performed on quantity. ‘The author of 
this curious and important paper first explains the notation which he 
makes use of, and the various orders of functions which may occur. 
He then solves 20 different problems, and shows their application 
to the solution of various interesting questions, 
Vox, VII. N° I. A 
