DISTRIBUTION OF ENERGY IN FLUORESCENCE; SPECTRA. 



185 



Fig. 179. 



For purposes of graphical computation we may conveniently express the 

 approximate value of r" in terms of the distance DC, Fig. 179. If this dis- 

 tance be called br it may be readily shown that 

 r" = 28/a\ 



_di 2 T _25r_iArA/~| 



d*? L 3 r 6 r f J 



In computing these correction terms the lumi- 

 nosity curve given by Tufts was used. 1 The 

 values of Ar and br were taken from the curve 

 showing the relation between X and the approxi- 

 mate value of r. 



The correction depending upon br is important 

 only when the curvature of the r curve is con- 

 siderable. In the present instance this correction 

 is large for regions near the crest of the curve, 

 but insignificant elsewhere. The importance of the correction is well shown 

 in the curves for resorufin (Fig. 176), where the points marked with crosses 

 show the curve after the slit correction has been applied. In the case of 

 eosin and fluorescein the region near the crest was uncertain for the reasons 

 already mentioned (p), so that the slit correction has not been applied in 

 this region. 



The second correction term, depending upon the product ArAf, is negli- 

 gible near the crest of the luminosity curve of the source, where A/ is small. 

 The term is thus of no significance in the case of eosin and fluorescein. 

 Even with resorufin, where the whole luminescence spectrum lies well t? ths 

 infra side of the crest of the luminosity curve, this correction is important 

 only on the steep side of the curve. The result of applying the correction 

 is shown by the points in Figs. 176 and 177 that are marked with crosses. 



THE CORRECTION FOR ABSORPTION. 2 



The fluorescent light which enters the slit of the spectrophotometer in the 

 foregoing experiments comes from a layer of liquid in the fluorescence cell 

 having a thickness determined by the opening de, Fig. 175, through which 

 the exciting light enters the cell. This layer, which is to be considered as 

 uniformly fluorescent, extends from x = X\ to x = X2, where x is the distance 

 from any point from which fluorescent light emanates to the wall of the 

 cell in the direction toward the slit of the spectrophotometer. 



Let the intensity of light, of any wave-length X, sent toward the slit 

 from the unit layer be i, and from a layer of thickness dx, be idx. If the 

 coefficient of absorption of the liquid be a the light reaching the slit from 

 the layer dx is idxe~ ax and the total intensity of light reaching the slit from 

 the whole of the excited layer is 



<c 



/= *v 



K dx = -[e- axl -e- ax *] 

 a 



Tufts's curve (see Physical Review, xxiv, p. 453) was obtained for an incandescent light. But the dif- 

 ference between the color of the acetylene flame and that of the glow lamp in the region considered is so small 

 that the error introduced is quite inappreciable. 



-For a full description of the methods employed in determining the absorption of such solutions see 

 Chapter XIII. 



