foote: pyrometer color screens 527 



which has a real physical basis. They haA^e defined the effective 

 wave length of the glass used between these two temperatures 

 as that wave length for which the ratio of the two radiation 

 intensities corresponding to the tw^o temperatures exactly equals 

 the ratio of the integral luminosities through the screen for the 

 same two temperatures. 



In the following discussion the difference between the "center 

 of gravity" and the true effective wave length is discussed and 

 a simple and accurate method is derived for obtaining the true 

 effective wave length. 



Let J^ = Ci X~' e~>^ = Wien's law. 



T =/(X) = transmission of color screen. 



V = (p (X) = visibility. 



T and V are functions of X only but the analytical forms of the 

 functions are unknown. Consider two temperatures di and 62. 



c.. 



for du /i = Ci X "e xe, 



(1) -i 1^ 



[ for 02, J 2 = Ci \~'e ^e 



(2) Jx'J, = eVe. eJ 



Since X may have any arbitrary value from to »= the ratio 

 /i //o may have any chosen value by properly choosing X. Let 

 Li = luminosity at temperature di and Lo = luminosity at 

 temperature do. 



/■• CO /^ an 



Li = JVTd\ = J (X^i) T (\) V (X) dK 

 Jo Jo 



Lo = r JiX^2) ^(X) V {\)d\ 

 Jo 



(3) LJL. = /o? ^^^^) ^^^^^ ' 



' - JU (Xd.) TVd\ 



Li and Lo, and hence the ratio Li/Lo, can be determined by graph- 

 ical integration. Let the ratio be any definite number. It 



