﻿(>2(> Prof. 0. W. Richardson : Some Applications 



is completely specified by 0<f>v and its two components 

 polarized in two mutually perpendicular planes, the amount 

 incident as above but polarized either in the plane of incidence 

 or the perpendicular plane is 



^- sin cos 0d0dd> 1 E>(v)dv. .... (66) 

 The amount absorbed in unit time is 



~ sin cos dO dd> (ej [v6) or e 2 (v0)) E(v)dv, 



u7T 



where efoff) is the emissivity for radiation polarized in the 

 plane of incidence, and e 2 (i'0) the corresponding quantity for 

 the perpendicular plane of! polarization. €^0) and e 2 (y0) 

 are functions of v and 6 and also of the temperature 

 T = (2^R)" 1 . Let ¥ x {y$) and ¥ 2 (v0) be the numbers of 

 electrons emitted when unit quantity of sethereal energv 

 specified by v0 and the respective planes of polarization is 

 absorbed, the temperature of the material being (2ffi) _1 , 

 Let the respective proportions of these which have velocity 

 components between u and u + du be f\\v.9.u.v.w.k)du and 

 f 2 (v.0.u.v.w.k)du, the corresponding quantities for the per- 

 pendicular components being; denoted by <?,( )dv, g 2 { )<h\ 

 h l ( )dw f and h 2 { )dw. The number of electrons having 

 velocity components between u and u-\- da which are emitted 

 from unit area per second under the influence of the com- 

 plete sethereal (black body) radiation may therefore be 

 written 



f*7Tl2 [*2TT p™ 



du\ I ( sin 6 cos Ev{e 1 (v0)F 1 (v0)/ 1 (v.0.w.t\Ma) 



«.'o Jo Jo 



+ e 2 (v0)F 2 {v0)f 2 (i>.0.u.v.ic.k)}d0 d<j> dv. . (67) 



The expressions for the numbers emitted with velocity 

 components between v and v + dv and to and xo + dw respec- 

 tively are obtained by replacing fidu and f 2 du by g±dv and 

 g 2 dv in the first cuse and h l div and h 2 dw in the second. But 

 as the distribution of velocity among all the electrons emitted 

 under the influence of the complete radiation is to be in 

 accordance with Maxwell's law, we have as an alternative 

 expression for the number emitted with velocity components 



