1 84 STUDIES IN LUMINESCENCE. 



The two integrals therefore become 



C C ' a \f(\+x)+f(\-x)\dx= ( a [2f(\) + x'f"(\)}dx 

 Jo ~ ; o 



x ,, (c-a) 3 ,, 



= 2(c-fl)/+- -./ 



and 



J c -a L 2 a 2d J 2 a L 3 J 



_-r {(c+a) 3_ (c - a)I}/+ (^>'-^>> ] 



2a\_ 4 - 1 



where /and/" are written for /(A) and /"(X) respectively. 



Upon adding the two integrals and introducing the factor am/di 2 

 we have 



c(a 2 +c 2 ) 



"* di 2 L - ' 3 J J di z ' ' "' 

 where 



3 

 The form of the expression may be shown to be the same when a<c. 

 Similarly for that portion of the field which is illuminated by 5 2 



*-?[*+*&) VI 



When the two fields are set to equality we have therefore 



2ma r / . t ///i 2mb r /-la c 2 ( y /) i 



|_ 2c/4 -^J = ^[ 2 cr/+^-^J 



Expanding <r 2 0/)/cX 2 and remembering that the second term in the bracket 

 is in each case small we have: 



di 2 b\_ 2c/J L 2crj J 



dfbL 2cf erf 2cr J 



An approximate value of r, usually a close approximation, is obtained by 

 neglecting all terms after the first. This approximate value having been 

 plotted as a function of X, r' and r" may be determined; and since/' and/" 

 may be obtained from the luminosity curve of the source A , the correction 

 terms in the above expression can readily be computed. 



In the experiments described in this paper the conditions were so chosen 

 as to make a = b = c. In this case the expression for r becomes 



_aVr _a 2 r" 2aVf l 

 ~<VL 3 ' r" zrf A 



If Ar is the increase in r which results from changing the wave-length 

 from X to X+2a, and if A/ is the corresponding increase in/, we have approxi- 

 mately : 



r' = Ar/2a, f' = Af/2a 



