384 Prof. E. Wiedemann on the 



two parts: — (1) measurement of the energy received, and (2) 

 measurement of the energy radiated. 



(1) The brightness of the incident light was obtained by 

 measuring the fraction of it, which, after reflexion from a 

 plane glass plate G at an angle of 45°, reached the photometer, 

 after having been sufficiently weakened by passing through 

 interposed smoked glasses. 



The fraction x reflected from the glass plate (which is so 

 thick that only the reflexion at the front surface has to be 

 taken into account) can be calculated from Fresnel's formula : 



_ 1 sin 2 ( i — r) 1 tan 2 (7 — r) 

 X ~* sin*(i + r) + * tan 2 (i + r) ' 



where i denotes the angle of incidence, and r the angle of 

 refraction. 



We take the index of refraction of the glass plate at 1*5, the 

 angle of incidence 45°, then ^ = ^ , so that of the total inci- 

 dent light 2?q reaches the observing-telescope. The weaken- 

 ing by the smoked glasses amounts to xsooo* Consequently 

 only 3 oq-qoq of the total energy incident upon the glass plate 

 reaches the observing-telescope. 



Further, the physiological sensitiveness for the region of 

 the spectrum occupied by the phosphorescent light is about 

 four times as great as that for the exciting light which lies 

 nearer the violet*. The brightness of the latter is therefore 

 in absolute energy four times as great as that of the phos- 

 phorescent light for the same impression of brightness. 



The reading on the photometer gave for the exciting light 

 a = 6°'12 ; the brightness is proportional to sin 2 6°"12 = 0*011. 



The brightness, and consequently also the energy of the 

 exciting rays referred to the comparison lamp in the proper 

 colour is therefore proportional to 



0-011x300000x4 = 13200, 



The factor 4 is used to take account of the physiological 

 sensitiveness for the two impressions of colour. 



(2) After a tablet placed accurately in the same place as the 

 surface of the glass plate had been illuminated for one second, 

 the following readings for ex! were obtained at the times t, 

 from which are calculated the brightnesses proportional to 

 10 3 sin 2 a'. 



t ... 6". 20". 46". l'lO". 2'. 3'. 4'. 7'. 9'. 11'. 

 «' ... 4-6 2-4 1-7 1-4 11 0-8 06 0-6 0-5 04 

 10 3 sin 2 «' ... 6-43 1-75 0-88 0*60 0-37 0-19 0-11 011 0"08 005 



* Cf. H. Ebert, Wied. Ann. xxxiii. p. 154 (1888). 



