no Roi/al Society\ 



nate, both the reflected and the transmitted light would ex- 

 hibit that prevailing colour : but if their surfaces are undu- 

 lated as in mother-of-pearl, from the form of the shell and 

 other causes, — if the iridescent films vary in thickness, and 

 consequently in colour, — if they are wanting in some parts of 

 the shell, and abound in others, — and if films of equal thick- 

 nesses occur in several laminpe in succession, and films of 

 other thicknesses in other laminae, which must necessarily 

 take place from the varying and remitting action of the animal 

 agent, then we shall have the very structure which is necessary 

 for the production of the incommunicable colours of mother- 

 of-pearl. 



I have no doubt that this is the true cause of the phaeno- 

 mena which had so long perplexed me; and the results which 

 I formerly obtained, though I could then attach no meaning 

 to them, are in perfect unison with the preceding views. In 

 order, however, to obtain something like an experimental 

 confirmation of this opinion, I have examined \k\e.fracture of 

 a mother-of-pearl shell where the laminae have been all de- 

 posited with considerable regularity, and where their over- 

 lying edges are exhibited, and I find distinct and positive 

 proofs of the existence of iridescent films, sometimes green, 

 and sometimes red in several successive strata. 

 I am, my dear Sir, 



Ever most truly yours, 



J3. Brewster* 

 To Leonard Horner^ Esq. 



XLVI. Proceedings of Learned Societies, 



ROYAL SOCIETY. 



Nov. 17, *' r> ESEARCHES in the Integral Calculus." Part II 

 1836. ~" JlV By Henry Fox Talbot, Esq., F.R.S. 

 Having explained, in the first part of his paper, a general method 

 of finding the sums of integrals, the author proposes, in the second 

 place, to apply this method to discover the properties of different 

 transcendents, beginning with those of the simplest nature. With 

 this view, he first shows its application to the arcs of the circle and 

 the conic sections j and demonstrates the possibility of finding three 

 arcs, such that, neglecting their signs, the sum of two of them shall 

 be equal to the third, though not superposable in any part : an 

 equality which has been hitherto deemed impossible in the ellipse 

 and hyperbola, without the addition of some algebraic quantity. 



November 24, 1836. — " Investigation of New Series for the Rec- 

 tification of the Circle." By James Thomson, LL.D., Professor of 

 Mathematics in the University of Glasgow. Communicated by 

 Francis Baily, Esq., V.P. and Treasurer R.S. 



