746 ENERGY AND VISION 



limits, arbitrarily chosen, that is to say, the integral of the curve 

 between these limits, will express the total energy radiated. As the 

 source yields in the same time invisible and visible rays, and as 

 the methods used for measuring the radiation give us figures corre- 

 sponding to the total radiation, R (visible + in\'isible), a segment 

 extending between the limits of the visible spectrum must also be 

 integrated. This latter integration gives the quantity of energy 

 spread in the visible part of the spectrum; let it be L. Then the ratio 

 of these two areas will be the luminous efficiency of the source, and 



will be expressed by - = E. The percentage of the visible to the 



invisible is now known. Let us call / the intensities in function 

 of the wave lengths, Xi the loM'^er limit of integration, X2 the upper 

 limit of integration for the visible, then: 



. = ^ 



P 





)r 



The quantity of energy spread by the slit over the visible 

 spectrum being thus known, a suitable screening of each monochro- 

 matic light decreases its intensity until the threshold of sensitivity 

 is reached. Knowing exactly the amount of energy absorbed by 

 the screens, the amount which is allowed to pass may be calcu- 

 lated easily: it is the minimum energy necessary to produce visual 

 sensation. 



Technique. 



Limits of Integration. — Limits of Total Radiation. — Lower limit: 

 For most light sources, the energy in the ultra-violet is so small 

 that the lower limit, 0.4 /x, may be taken as zero without any ap- 

 preciable error. Gage (10) takes it as the limit in his study of the 

 electric arc, which is one of the richest sources in ultra-violet. The 

 Nernst lamp, on the contrary, yields very little ultra-violet radiation, 

 and it was assumed that this limit could safely be taken. Upper 

 limit: The plotting of energy distribution curves showed that above 

 7fx in the infra-red, the amount of energy radiated by the Nernst 



