160 Prof. E.Wiedemann on the 



tion (1) and consequently equation (2) will take a different 

 form : but since with increasing intensity the quantity 

 radiated must also increase, we shall have an equation analo- 

 gous to (2). The further conclusions will therefore not be 

 essentially affected. 



Strictly speaking a separate equation of the form of (1) is 

 required for rays of each wave-length. For the value of b 

 may be very different for the rays of different wave-length 

 emitted, as the experiments described above with eosin and 

 fluorescein show ; and, again, the value of A is very differ- 

 ent for exciting light of different colours, as we learn from 

 numerous experiments with fluorescent substances. 



The intensity if of the fluorescent light, i. e. the intensity of 

 the light observed upon continuous illumination, is determined 

 by the value of i for t = co . It is so great that the loss is 

 equal to the gain ; hence dijdt = 0. Hence it follows that 



fr-£ (3) 



From this expression we see that the brightness of the 

 fluorescent light depends upon two quantities — first, on the 

 fraction of the incident energy converted into light- vibra- 

 tions ; and, secondly, on the loss of energy determined by b. 

 The first quantity is dependent upon absorption &c. ; but the 

 second upon the strength of the emission and the loss of 

 energy either in the impact of two molecules or in conse- 

 quence of mutual attractions of the constituent atoms of a 

 molecule. 



The great increase in intensity of the fluorescent light, 

 which occurs when solutions of fluorescent substances are 

 thickened by addition of glycerine, gelatine, &c, may be 

 referred to the decrease in that portion of b which corre- 

 sponds to the loss of energy by mutual impacts, since, in 

 consequence of the greater friction and consequent less 

 mobility, the molecules of the same kind impinge much 

 less frequently. 



In other cases we may find in solutions of the same sub- 

 stance in different media hardly any difference in the 

 intensity of the absorption, but a displacement of the absorp- 

 tion-bands, as with saffranine and magdala-red, and at the 

 same time a complete disappearance of fluorescence. The 

 explanation in my opinion is to be sought in the forma- 

 tion of hydrates &c, and a consequent alteration of ab- 

 sorption-relationship within each molecule in a way as 



