Proceedings of the Cambridge Philosophical Society. 391 
galvanoscope, was the same as if the larger had been composed 
of a more oxidizable metal. The effect of two brass-rods was the 
same, under the same circumstances. A similar effect was pro- 
duced by equal rods, provided that one of them, by being placed 
obliquely in the acid, presented a greater surface to its action. 
Mr Spilsbury then noticed the effects produced by interposing 
water, or different acids in the galvanic circuit The paper was 
concluded with a theory, by which Mr Spilsbury proposed to ac- 
count for these effects, and a description of a mode of increasing 
the sensibility of the galvanoscope, by suspending the needle from 
a fine silk fibre, and inclosing the instrument in a glass-case. 
Nov. 25. — 44 On the Construction of Achromatic Reflecting 
Telescopes , with silvered Lenses in the place of Metallic Mirrors ,” 
by G. B. Airy, Esq. Trinity. The advantages of this construc- 
tion were described, and it was shewn, by an investigation of the 
requisite formulae, that the aberrations, both spherical and chro- 
matic, of the two mirrors in Gregory’s or Cassegrain’s telescopes, 
might be made to correct each other ; rules were given for the 
determination of the radii of the surfaces, and a formula investi- 
gated for making the eye-piece achromatic. It was mentioned, 
that an experiment had been tried, which had not entirely suc- 
ceeded, though the principle appeared to hold good, and that 
the trial, on the whole, gave hopes of more complete success. 
Dec. 9. — A paper was read, by the Rev. G. Peacock, M. A., 
Tutor of Trinity, 64 On the Principles commonly employed in 
the Demonstration of the Binomial Theorem .” After defining 
the meaning of the term Equal or Equivalent, as applied to two 
algebraical expressions, Mr Peacock proceeded to consider to 
what extent most writers on this theorem have assumed the 
existence of a general form of the series, and whether such an 
assumption can be considered as perfectly legitimate, consistently 
with other assumptions in algebra. This paper concluded with 
some remarks on the steps of the process which appear to have 
led Newton to the discovery of this theorem, as described by 
himself in the second of his celebrated letters to Oldenburg. 
A paper was read by the Reverend W. Cecil, M. A., Fellow 
of Magdalene, describing a machine for grinding and polishing 
spherical telescopic mirrors, very accurately, and without manual 
labour. 
