480 Royal Society : — 



and therefore if i\> v, denote the principal radii of curvature, 



Hence 



and 



rt—tf 



cos ??</> 



cos i 1 ^(j> 1 



==C0S V.VjV# (5) 



cosz'fy cosity ^osijifa cos 4 v.v x v 2 /g\ 



cos i'^0 1 cosi 1 ccp 1 cos i'hy'~~ cosV. v^v.J 



which proves the proposition enunciated. 



In the particular case of an ellipsoid of revolution of which n is 

 the axial and m the equatorial semi-axis, compared with a sphere of 

 radius unity, hoth having their centres at 0', one of the principal radii 

 of curvature is the normal of the elliptic section, which hy the pro- 



perties of the ellipse is equal to — m 1 , m 1 denoting the semi-conjugate 



it 



diameter ; and the other is the radius of curvature of the elliptic 



7)1 



section, or — . Also mr is the perpendicular let fall from the centre 

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



cosz'(k> or 4 mm 1 m' 3 crW 4 m 4 ?i 2 



cos i'ty' p 4 n mn n 2 ^ ' p 4 



since mn!=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). 



ce On the Intensity of the Light reflected from or transmitted through 

 a Pile of Plates." By George G. Stokes, M.A., Sec.R.S. 



The frequent employment of a pile of plates in experiments relating 

 to polarization suggests, as a mathematical problem of seme 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 onlv. 



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, 



