Mechanics of Luminosity. 161 



yet immeasurable. F . Stenger has published another expla- 

 nation *. 



B. Let us now turn to the second case. Let the luminous 

 energy be brought by any cause to a constant height, and 

 then at a time £ = let the radiating body be left to itself, 

 after the exciting cause has been removed. We will further 

 assume that the loss of energy takes place by radiation and 

 not by absorption. Further, the luminous energy contained 

 in a particle shall not receive any further increase during the 

 radiation, in consequence of processes going on within the 

 molecule itself, or by the impact of two molecules. 



If, then, i is the intensity measured in any units, i. e. the 

 energy emitted in the unit time at the time t, and b the con- 

 stant introduced above, then during the time dt the radiating 

 body suffers a loss of luminous energy 



di = — hidt. 



If we integrate this expression from to co we obtain the 

 total store of energy of the vibrating particles, for in an 

 infinitely long time all the energy will be radiated; hence 

 the total luminous energy present is 



= J idt = I i ( 



Jo Jo 



■ u dt=\. 



o 



If, then, we know the intensity i at the time 0, and the 

 constant Z>, we can find the total luminous energy contained 

 in the luminous body under the above assumptions. The store 

 of luminous energy is equal to i , the initial intensity, divided 

 by b, the constant of loss of energy. 



Total and True Coefficient of Emission. 



14. We may express the energy emitted by the unit weight 

 of a body in the unit time contained in the rays lying within 

 an infinitely small breadth of the spectrum between wave-length 

 X and X + d\ by s^dX ; s x would then denote the energy con- 

 tained in the region between X and X + 1 if at all points 

 within the same the same energy is yielded as at the point X ; 

 we may appropriately call s K the true coefficient of emission 

 at the point A, referring, of course, to the unit weight. The 

 radiating layer is supposed to be so thin that the absorption 

 of the emitted rays within it may be neglected. The energy 

 is to be measured in calorimetric units. If the region of the 

 spectrum that we are considering extends from X x to X 2 , the 



* Wied. Ann. xxxiii. p. 577 (1688). 



