2 Improvements in Physical Science [Jan, 
little room, and as we have no British publication appropriated to 
the subject, I conceive it better to notice them. 
1. In the Annals of Philosophy for 1816 some mathematical 
papers of considerable importance have appeared. I consider the 
anonymous paper on the Present State of the Mathematical Sciences 
in Great Britain (Annals, vii. 89) as a very just and fair picture, 
and hope it will have the effect of rousing the latent energies of our 
countrymen, and of producing another mathematical era in this 
island not inferior in brilliancy to that in which Wallis, Barrow, 
Newton, Cotes, Maclaurin, and many other illustrious mathema- 
ticians, made their appearance. As mathematics require encourage- 
ment more than any of the other sciences, there can be no doubt 
that its cultivation would be greatly promoted if a society could be 
formed to facilitate the publication of mathematical papers by de- 
fraying the requisite expense. I believe that such a society might 
be established without difficulty, if any person of sufficient in- 
fluence could be found to patronize it. 
2. The paper on the Quadrature of the-Circle (Annals, viii. 13) 
is likewise curious and interesting. 
3. The other mathematical papers in the Annals are—A Demon- 
stration that the Ellipse in certain Positions appears circular (Annals, 
vii. 205): A general Demonstration of the Binomial Theorem 
(Ibid. vii. 346): A Demonstration of a curious Relation between 
the various Orders of Differences, by Mr. Harvey (Ibid. vii. 475) : 
Theorems for determining the Amount of Annuities increasing in 
the constant Ratio of the natural Numbers 1.2 .3....2, by Mr. 
Benwell (Ibid. vii, 119): On Annuities, Imaginary Cube Roots, 
and Roots of Binomials, by Mr. Horner (Ibid. viii. 279): and the 
Solution of a curious Mathematical Problem, by Mr. Ivory (Ibid. 
viii. 272). 
4. In the first number of the Journal of the Royal Institution 
(p. 6) there is a demonstration of a considerable number of Dr. 
Stewart’s Problems, by Mr. Babbage. 
5. On the Developement of Exponential Functions, together 
with several new Theorems relating to Finite Differences, by J. F. 
W. Herschel, Esq. F.R.S. (Phil. Trans. 1816, p. 25.) 
G. An Essay towards the Calculus of Functions, Part II., by C. 
Babbage, Esq. F.R.S. (Phil. Trans. 1816, p. 179.) 
7- A new Demonstration of the Binomial Theorem, by T. 
Knight, Esq. (Phil. Trans. 1816, p. 331.) ; 
_ 8. On the Fluents of Irrational Functions, by E, F. Bromhead, 
Esq. (Phil. Trans, 1816, p. 335.) 
II], ACOUSTICS. 
1. Influence of the Wind on the Propagation of Sound.—In the 
Ann. de Chim, et Phys. i. 176, there is a curious set of experi- 
ments on this subject by M. Delaroche. His method was to have 
two drums or bells giving exactly the same sound. The experi- 
