48 Messrs. Paterson and Dudding on Estimation of 



this limited range in direct proportion to the amount radiated, 

 but weights it according to its own peculiar sensitivity to 

 energy of that wave-length. This appreciation of power by 

 the eye is expressed in lumens which may be denned as the 

 measure of the appreciation of the eye for radiant power. 



An expression must, therefore, be found connecting lumens 

 and the temperature of the radiating body both in terms of 

 the power distribution throughout the visible spectrum and 

 of tbe sensitivity characteristics of the eye. 



The theoretical investigation of the problem thus subdivides 

 itself naturally into three distinct parts : — 



(a) The rate of energy dissipation of the radiator at any 

 temperature. 



(6) The quantitative distribution of this radiant power 

 throughout the spectrum at any temperature, with special 

 reference to that range of the spectrum over which the 

 energy stimulates the sense of vision. 



(c) The relative capacity of equal amounts of radiant power 

 in different wave-lengths for stimulating vision, this being 

 necessarily referred to the average or normal human eye. 



(a) Relation between Watts and Temperature. — Attention 

 has been already drawn to curves showing the relation 

 between the rate of dissipation of energy by a lamp and its 

 temperature as measured by the colour-identity method. 

 Many lamps of ordinary dimensions have been examined, 

 and in all cases the results can be expressed by an equation 

 of the form 



watts oc T m or (log W = log D + m log T), . . (1) 



m being 4* 5 to 4* 6 for carbon lamps and 5'0 5 to 5* 2 for tungsten 

 lamps. 



In no case has any appreciable deviation been observed 

 from this logarithmic relationship for temperatures ranging 

 from 1700 deg. to 2300 deg. abs. 



This relationship is at once recognized as being identical in 

 form with that ascribed to Stefan and Boltzmann connecting 

 the temperature and radiant watts of the ideal black body, 

 m in the latter case being 4* . 



(6) Distribution of Radiant Poiuer throughout the Visible 

 Spectrum. — In the case of the ideal black body, the radiant 

 power in any wave-length of the visible spectrum at any 

 temperature below 3000° C. can be expressed according to 

 the well-known law of Wien 



c 2 



E K =0 1 X--.e A1 \ (2) 



