528 foote: pyrometer color screens 



is possible to choose X in (2) such that Ji //o = Li/L^. Call 

 this value of X = X^,. Substituting in (2) : 



Ji-i) 



\ a D I 



(4) mean X^, = — ? (natural logarithms) 



log Li — log Lo 



This is the definition, expressed analytically, of the mean effec- 

 tive wave length over a given temperature range, proposed bj^ 

 Hyde. Cady, and Forsythe. Instead of referring the effective 

 wave length to a given temperature range it may be referred 

 to a definite temperature by letting the two temperatures ap- 

 proach one another. Let Qi and 0o approach d as a limit. The 

 right term of (4) is indeterminate but can be evaluated by 

 the ordinary rule of L'Hospital, observing in the differentiation 



TVJdX where only J is a func- 

 tion of 6. Then for the limit di = 02 = 6, the following value 

 of \l is obtained. 



(S) j_./:rFja 



J 



■ d\ 



X 



This is the true effective wave length of the glass for a tem- 

 perature e. Define the wave length corresponding to the line 



which bisects the area of I TVJdX as X^, that is, the axis of 



the center of gravity of the luminositv curve, so chosen that 



I TVJdX = 2 j TVJdX. Then by definition of the center 



of gravity: 



... . _ f;Tvj\dx 



^ ^ ' i; TVJdX 



Having drawn the luminosity curve on any arbitrary scale 

 whatever, paying no attention to actual values of the scale 

 of ordinates (L) , only relative values of L needing consideration, 

 Xg can be determined with a planimeter having two indicating 

 dials, one of area and the other of moments, such as the Amsler 



