1884.] Energy and Radiation in Incandescence Lamps. 157 



XIV. " The Relation between Electric Energy and Radiation 

 in the Spectrum of Incandescence Lamps." By Captain 

 ABNEY, R.E., F.R.S., and Lieut.-Colonel FESTING, R.E. 

 Received June 6, 1884. 



In the " Philosophical Magazine " for September, 1883, we showed 

 that certain relations existed between potential, current, watts (volt- 

 amperes), and radiation in incandescence lamps, and that if j?=the 

 potential, c= current, w;=watts, B=radiation, and a and b were con- 

 stants, then 



(i) c= 



(ii) w=p\a 



further we showed that after the carbon filaments attained a certain 

 heat, the radiation varied directly as the energy. 



(iii) RO; (w m) where m is a constant. 



We may incidentally mention that this relationship appears to hold 

 good in a properly exhausted lamp, be the filament of carbon or of 

 platinum, or presumably of other metals. In this case the sign in 

 the left hand members of equations (i) and (ii) is changed. 



On laying down graphically the curve obtained by using the watts 

 as the abscissas and the radiation as ordinates, it was at once evident 

 that the straight part is an asymptote to a curve having its origin 

 at 0. It might, therefore, be presumed that each individual ray 

 should increase in intensity in somewhat the same manner when the 

 energy in the filament was increased, i.e., in some simple curve which 

 would have an asymptote. 



The result of our researches which we now communicate to the 

 Royal Society is that the curves for rays of refrangibility lower than 

 about A8500 are hyperbolas, and that when near the limit of visibility 

 the hyperbolas approach tbe parabolic form, the origin of the curves 



loving away from the zero of energy as the rays are more refrangible. 



?his may be put in the form of an equation 



When the rays are of very low refrangibility we have the sign 

 the equation, " I " gradually diminishes as the refrangibility of the 

 lys increases till it becomes 0, with a still further increase it takes the 

 sign; " k " gradually diminishes from the greatest wave-length till 

 it approaches 0, after which the curves practically become parabolas. 

 reference to fig:. 2 will show the forms of the curves for different 



