Fluorescence of Dyes on Wave-Length of Exciting Light. 311 



interval of waves is xc, where c is concentration. Following 

 (1), the intensity of fluorescence in the named point of vessel 

 will be 



fc x .I K . xc . e~ xcd . 



Let further a light-filter be placed between the source of 

 light and the vessel transmitting the part of light /(X). In 

 this case the integral intensity of fluorescence will be ex- 

 pressed by 



P a 2 



= A 



KK .\.f{\).xc.e~™ d .d\, . . (6) 



where Xi, X 2 are the practical limits of the disappearance of 

 the function 



I x ./(X) . xc . e~ xcd 



(these limits depend evidently upon the applied light-filter) 

 and k\ is the specific fluorescence (2). 



In the experiments of Nichols and Merritt and in the 

 theory of Einstein, k\ is an increasing function of X. In both 

 cases we can apply to (6) the theorem of the middle value 

 of a definite integral — i.,e., we have 



(?) 



i? 



I A ./(X) .xc.e- xcd .d\ 



where k is the middle value of k k corresponding to X', 

 lying between X t and A 2 . When k\ is a linear function (as 

 follows from the theory of Einstein and also from Nichols 

 and Merritt's experimental results for Eosin and also in a 

 long interval for Resorufin), and when the subintegral 

 function in (7) is symmetrical relatively to 



. X 2 -Xx 



then it is easy to prove that k! corresponds to X, through 

 which passes "the ordinate halving the area 



^=y\.f(X).xc.e- xcd .dX. ... (8) 



In cases when the subintegral function is only approxi- 

 mately symmetrical (with which we are chiefly concerned), 

 * ' corresponds only approximately to the halving ordinate 

 of area cj>. The formula (7) can be applied evidently also in 



