551 



pier form. If r+t differ indefinitely little from 1, a and /3 will 

 be indefinitely small. Making a and ft indefinitely small in (13) 

 and (14), and putting 1 r for t, we find 



mr lr l + (w l)r 



In this case it is evident that each of the 2m reflecting surfaces 

 might be regarded as a separate plate reflecting light in the proportion 

 of p to 1, and therefore we ought also to have, writing 2m for m and 

 p for r in the denominators of the equations (19), 



2^,0 1 p l + (2ml)p 



It is easy to verify that when ^=1 (4) reduces (19) to (20). 



The following Table gives the intensity of the light reflected from 

 or transmitted through a pile of m plates for the values 1, 2, 4, 8, 

 16, 32, and oo of m, for three degrees of transparency, and for certain 

 selected angles of incidence. The assumed refractive index p is 

 1*52. S=l e~? T is the loss by absorption in a single transit of a 

 plate at a perpendicular incidence, so that ? = corresponds to per- 

 fect transparency. The most interesting angles of incidence to select 

 appeared to be zero and the polarizing angle OT=tan -1 /n ; but in the 

 case of perfect transparency the result has also been calculated for an 

 angle of incidence a little (2) greater than the polarizing angle. 

 denotes the intensity of the reflected and \ft that of the transmitted 

 light, the intensity of the incident light being taken at 1000. For 

 oblique incidences it was necessary to distinguish between light po- 

 larized in and light polarized perpendicularly to the plane of in 

 dence ; the suffixes 1, 2 refer to these two kinds respectively. For 

 oblique incidences a column is added giving the ratio of ^ to ^ 2 , 

 which may be taken as a measure of the defect of polarization of the 

 transmitted light. No such column was required for 3=0 and z=cr, 

 because in this case \// 2 =1000. 



* From a paper by M. Wild in Poggendorff's 'Annalen ' [vol. ix. (1856) p. 240], 

 I find that the formulae for the particular case of perfect transparency have 

 already been given by M. Neumann. His demonstration does not appear to have 

 been published. 





