546 FOOTE, MOHLER, AND FAIRCHILD : PYROMETER GLASS 



of the present note is to describe an absorption glass for which 

 the quantity A would be independent of the temperature of 

 the black-body source. 



When the light is not monochromatic, the simple equation 

 above can not be employed. With heterochromatic conditions, 

 the setting of the pyrometer is correct when the luminosity of 

 the black-body source as viewed through the lens and absorp- 

 tion-glass system exactly equals the luminosity of the standard 

 lamp as viewed through its lens and absorption-glass system. 

 The condition for a match is as follows: 



C TT'VJ (\,0)d\= f" TVJ(\,S)d\ (1) 



Jo Jo 



where T =f (X) is the transmission of the red glass screen usual- 

 ly employed, V =f (X) = visibility, J (X, 0) the intensity rela- 

 tion as given by Wien's law for the black-body source, J (X, S) 

 the similar relation for the lamp, and X, S, and T' have the 

 significance noted above. This assumes that the lamp radiates 

 as a black body and that the absorption due to the various 

 lens surfaces is negligible, but the method for deriving the 

 proper form of T' = /(X) is the same when these factors are 

 considered. 



Let T' have the form T' = e x where a is a negative constant. 

 Equation (1) may be rewritten thus: 



TVC 1 \- 5 e~^ { e- a) d\= TVC\\- 5 e~^d\ (2) 



o Jo 



In order that (2) be true it is necessary that: 



(3) 



Whence, if the transmission of the absorption glass has the form 



st£* 1 1 



T' = e x , we have = A = a = a constant independent of 



6 S 



the temperature. 



Thus, using an absorption glass of this type, it is possible 

 to calibrate the glass at temperatures less than 1500°C, i.e., 



/ 



