76 Cambridge Philosophical Society. 



light polarized in planes at right angles to each other, of which it 

 has suppressed one, and transmitted the other to the eye. The cal- 

 culation founded on this, represents correctly the phaenomena. But 

 it is plain that, allowing the truth of this general explanation, dif- 

 ferent kinds of analysis may be conceived : — of these, that which 

 comes next in simplicity to the ordinary kind is, the resolution of 

 the emerging light into two streams ; one, circularly-polarized and 

 right-handed; the other, also circularly-polarized, but left-handed ; 

 and the suppression of one of these streams. The effect of this 

 analysis is not immediately obvious when the light incident on 

 the crystal is plane-polarized ; but when it is circularly-polarized, 

 one remarkable result presents itself. As the only incident light 

 has no relation to sides, and the only light allowed to emerge has 

 no relation to sides, the coloured rings can have nothing which 

 bears any trace of sides except in the crystal itself. Consequently 

 there can be no black cross or black curve as with the usual ap- 

 paratus (for the positions of these are determined by the planes 

 of polarization), and therefore Iceland spar will produce circular 

 rings ; and nitre, &c. will give uninterrupted lemniscates. And as a 

 general rule, the amount of light of any ray which comes to the eye 

 will depend upon nothing but the difference of paths of the cor- 

 responding ordinary and extraordinary ray in the crystal. An 

 analysis of this kind might throw considerable light on the me- 

 chanical state of unannealed glass, &:c. The author then showed 

 that such an analyser would be produced by combining the ordinary- 

 analysing plate with Fresnel's rhomb, or with a plate of mica of 

 the proper thickness. The experiments (which were exhibited to 

 the members of the Society present) corresponded completely with 

 the anticipation. Allusion was also made to a more general kind 

 of resolution ; namely, into two streams of elliptically-polarized 

 light; but this subject was not pursued by the author into the same 

 details as the other. 



.\ memoir by Mr. Murphy, of Caius College, was read. The 



- author's object in this memoir is to furnish a general method, 



t; by which an unknown function, entering under the sign of defi- 

 nite integration, may be found from the known integral. Adopt- 

 ing the limits and 1, he shows that in the equationyy(f) .t* — 

 ^ (k), if we assign to x a series of values, from the greatest root of 

 .the equation (p (x) = c»^ to }i=co^; ^(x) converges to zero as 



. its limit, •wheny{t) is any of the functions commonly received i~* 

 in analysis; and proves, that if we multiply, in this case, ip (x) by 

 and divide by t the coefficient of — on the product, we shall obtain 

 f{t). To remove the difficulty presented by discontinuous func- 



•'• tions, he considers the character of least, which distinguishes the 

 root of an equation solved by the method which the author com- 

 municated in a former paper ; and he finds in this circumstance the 

 means of representing explicitly such functions under continuous 

 forms. In applying the above principles to the distribution of elec- 

 tricity on the surfaces of bodies, the author has been led to new 

 and remarkable results, on the nature of the accumulation, neces- 



