Cambridge Philosophical Society. 311 



it becomes of course necessary to employ the equation TjV= — -inp. 

 The solution having been obtained, the electricity may now be sup- 

 posed to be condensed into a point, and one of the summations may 

 be effected. The potential is thus expressed in a double series, 

 which appears to be the simplest form that it admits of. 



May 8, 1848. — Supplement to a paper "On the Intensity of Light 

 in the neighbourhood of a Caustic." By G. B. Airy, Esq., Astro- 

 nomer Royal. 



The author, after referring to the paper printed in a former volume 

 of the Society's Memoirs, in which he has shown that the expression 



for the intensity depends on the integral / cos (w 3 —mtv) between 



the limits w=0, w = infinity, where m is proportional to the distance 

 of the point at which the intensity is required, from the geometrical 

 caustic, and in which he has calculated by quadratures the value of 

 the definite integral for different values of m as far as m=+4 , 0, 

 states that he was induced to have recourse to the method of qua- 

 dratures only because every expansion which he attempted made it 

 necessary to rely (for some of the terms) upon definite integrals 



equivalent to the integral / cps 9 from 9 = to 9 = infinity, and that 



he was not satisfied with the reasoning upon which some mathema- 

 ticians had given a determinate value to that integral. Professor De 

 Morgan, however, who felt no doubts upon it, had furnished him 

 with a series proceeding by ascending powers of m, and had also 

 explained in detail (in a letter embodied in this paper) his views on 

 the evidence for the value of the series, and on the method of de- 

 termining it. From this series, the values of the definite integral are 

 computed for all the values of m for which the computation had been 

 made by quadratures, and the result is that the two sets of computed 

 numbers are entirely accordant. The computations are also extended 

 to the limit m= + 5*6, which is the greatest value to which it is 

 possible to extend the calculations by the use of 10-figure logarithms. 



June 5. — On some new Fossil Fish of the Carboniferous Period. 

 By Frederic M'Coy, M.G.S., N.H.S.D. 



The author having premised that the species of fish of the carbo- 

 niferous limestone enumerated in the third volume of the Poissons 

 Fossiles of M. Agassiz are for the most part still unpublished, being 

 without definitions or figures, states that through the kindness of 

 Capt. Jones, R.N., M.P., &c. he was enabled to study the original 

 specimens of twenty-eight out of the thirty unpublished species 

 from Armagh in M. Agassiz's list, and is therefore certain of the 

 species described by him being so far distinct from those alluded 

 to. The greater number of the examples here described are in 

 the cabinets of the University of Cambridge (principally collected 

 by the Rev. W. Stokes, of Caius College), and of Captain Jones ; 

 a few from the lower carboniferous shales of Ireland are only 

 known in that of Mr. Griffith of Dublin. The descriptions are 

 accompanied by drawings of all the species of the natural size, and 



