50 Messrs. Paterson and Dudding on Estimation of 



Nutting* shows that the above expression for the photo- 

 metric value of radiant power reduces to 



L = a(i+?-) _ \ (6) 



where the photometric value of the total radiant power in 

 lumens at a given temperature, T, is represented by L. 



A = ~PV m \ a m e a (a\ m )- p .r P , 



p=n-\-a — 1 . 



It follows from what has been said above that the lumens 

 radiated by carbon or tungsten filaments should be capable 

 of being represented by an expression of the form of equation 

 (6). Combining with this expression that for the watt- 

 temperature relationship for the filament under consideration 

 (equation 1), we get for the equation connecting lumens per 

 watt and temperature 



^=A 1 ^l + rj ,j T" TO , 



or expressed for convenience in the logarithmic form 



log^ = 0-mlogT-plog(l+?). • • (7> 



From the measured values of lumens/watt and temperature, 

 which are plotted in fig. 3, the following values of the constants 

 in the foregoing equation are found. 



For carbon filaments 



log 10 ^ = 21-51-4-581og 10 T-1851og I0 (l+^ (8> 



and for tungsten filaments 



log 10 ^ = 23-31 2 -5-llog 10 T-185]og 10 (l+ ^). (9) 



Tne curves drawn in fig. 3 are those derived from these 

 equations, and it will be seen at once how nearly the obser- 

 vations fall on the curves; in fact, it would hardly be possible 

 to find a form of curve which would fit the observations 

 better. The error in temperature rarely exceeds 2 per cent. 



* Loc. cit. 



