498 UADIATION lUOLOGY 



intensity / impiiijics upon the skin surface is /f, and /„, is the intensity at 

 the bottom of the malpighian hiyer. The difTerence between Ic and /„, 

 must represent the amount of ladiation absorbed phis the amount 

 scattered per unit time in the nial|)i^liian layer, and of this A is some 

 dehnitc fraction. We may tiierefore write 



A = (/c - 1^0 (13-7) 



where (3 is a proportionaHty factor which may be different for different 

 wave lengths. The light absorber is assumed to be present in such large 

 amount that its concentration is virtually' unchanged during exposure. 

 If Ic is the thickness of the corneum and Uc the attenuation coefficient 

 (see footnote 14) of that layer, we may write 



/^ = /e-«ci., (13.8) 



Similarly, 



Ln = 7,e-«"''- (13-9) 



where a„, is the attenuation coefficient and /„, the thickness of the mal- 

 pighian layer. Combining E(is. (13-8) and (13-9), 



/„, = le--dc^-<^.j..., (13-10) 



and substituting from Eqs. (13-8) and (13-10) in Ecj. (13-7), we obtain 



A = I[c-'-''{l - c-"-''")/i]. (13-11) 



Combining Eq. (13-11) with Eqs. (13-3) and (13-6), 



<3x = [g-a.^.(i _ e-'^-'-'-)0]y\' (13-12) 



Then for polychromatic radiation, 



^_, I ^1 , _ D2 



V '^c \. „, /, a...u.\o^ .. \ ' r„— a 



"^ ■ ■ ■ "^ [e-«''<l - e-«'"''")iS],7,X,r (^^"^^^ 



We note in this expression that the intensity terms for the various lines 

 have dropped out.'^ Hence there is nothing to indicate why the dis- 

 crepancies in Table 13-1 should appear when the relative intensities of the 

 lines are changed by interposing filters, as indicated in Fig. 13-3. Differ- 

 ences in absorption in the corneum and malpighian layer, represented by 

 the terms within the brackets [see Eq. (13-11)] would be the same for a 

 given individual and hence would not account for such discrepancies. 

 Variation in the coefficient 7 with wave length would alter the shape of the 



'* It will be seen that reciprocity, wliich is implicit in these equations, is obeyed for 

 monochromatic radiation. 



