645 



on the tangent line of the section. Hence from (5) or (6) 



cos t'fy _ cr* t mm' t m' 3 ^m' 1 _ nfri* 

 cosi'ty' p 4 n van w 2 p 4 ~~ p 4 



since i mm l =.mn. This agrees with Mr, Stewart's result(p. 197), since 

 the R e and |R of Mr. Stewart are the same as the R' and R of equa- 

 tion (3). 



IV. " On the Intensity of the Light reflected from or transmitted 

 through a Pile of Plates." By GEORGE G. STOKES, 

 M.A., Sec. R.S., Lucasian Professor of Mathematics in 

 the University of Cambridge. Received January 1, 1862. 



The frequent employment of a pile of plates in experiments relating 

 to polarization suggests, as a mathematical problem of some interest, 

 the determination of the mode in which the intensity of the reflected 

 light, and the intensity and degree of polarization of the transmitted 

 light, are related to the number of the plates, and, in case they be 

 not perfectly transparent, to their defect of transparency. 



The plates are supposed to be bounded by parallel surfaces, and 

 to be placed parallel to one another. They will also be supposed to 

 be formed of the same material, and to be of equal thickness, except 

 in the case of perfect transparency, in which case the thickness does 

 not come into account. The plates themselves and the interposed 

 plates of air will be supposed, as is usually the case, to be sufficiently 

 thick to prevent the occurrence of the colours of thin plates, so that 

 we shall have to deal with intensities only. 



On account of the different proportions in which light is reflected 

 at a single surface according as the light is polarized in or perpendi- 

 cularly to the plane of incidence, we must take account separately of 

 light polarized in these two ways. Also, since the rate at which 

 light is absorbed varies with its refrangibility, we must take account 

 separately of the different constituents of white light. If, however, 

 the plates be perfectly transparent, we may treat white light as a 

 whole, neglecting as insignificant the chromatic variations of reflecting 

 power. Let p be the fraction of the incident light reflected at the 

 first surface of a plate. Then ip may be taken as the intensity of 



TOL. xi. 2 R 



