foote: temperature and emissivity 319 



<*• 

 «/i = Ci X -5 e~ a7 for black body 



Ji = Ci A X -5 e~ >^ for non-black body 



Equation (2) represents a family of straight lines of variable 



parameter — intersecting at log A' + — and — — p. At 



A J- J- 



the point of intersection the ratio of the intensity of the non- 

 black body to the intensity of the black body is the same for 

 every color. This by definition is a "color match" and the tem- 

 perature of the black body when the condition of color match 

 exists is the "color temperature"of the non-black body. Denote 

 the color temperature by T', then 



(o) rp, = rp — P 



If S denotes the apparent temperature of the non-black material 

 for a wave length X, equation (4) follows immediately from Wien's 

 law, 



(A) 1 X log A _ 1 



S c 2 T 



and from equations (1), (3) and (4) 



,5) 1 1 _ Xg/logA' 1\ 



(5) ST' e,\ q +V+ r) 



which is a straight line of slope — ^r when ( -^ — — j is plotted 



against — ;. The apparent temperature S and the color tem- 

 perature T', easily measured quantities, may therefore be used 

 to determine the constant q, and thus give the temperature 

 coefficient of monochromatic emissivity. 



Color temperature of carbon. From the work of Elisabeth 

 Benedict 2 and also from some unpublished work of the writer 

 it appears that the logarithmic isochromatics for a carbon lamp 



2 Ann. d. Physik, 47: 641. 1915. 



