318 foote: temperature and emissivity 



C2J> q_ 



(1) A=A'e*eT 



By proper choice of A', p, and q, the above equation can be 

 adjusted to fit almost any curve of emissivity which is likely 

 to be found experimentally. A type of dispersion of emissivity 

 which it can not represent is that in which the emissivity pos- 

 sesses a very decided maximum in the middle of the visible 

 spectrum. There is no experimental evidence of such a form 

 of emissivity as a function of the wave length for metals, possibly 

 excepting gold and copper. Over the small range of wave lengths 

 comprised by the visible spectrum the emissivity of most metals 

 is, within experimental observations, either increasing or de- 

 creasing linearly or exponentially with the wave length. All 

 such variations are accounted for by adjusting the constant p. 

 If the emissivity is constant with wave length, as in the case. of 

 a gray body, p = 0. Similarly, all probable variations in the 

 emissivity with temperature over a reasonable temperature range 

 are accounted for by adjusting the constant q. The only serious 

 restriction to equation (1) is that it assumes all wave lengths 

 of the visible spectrum have the same temperature coefficient 

 of emissivity. This assumption is probably practically correct — 

 there is no satisfactory experimental evidence bearing directly 

 upon this point. 



If a material having an emissivity coefficient given by equation 

 (1) is compared spectrophotometrically with a black body at 

 various temperatures, and the logarithmic isochromatics are 

 plotted for various wave lengths (viz., logarithm of the ratio, 

 ait a definite wave length, of the intensity of radiation of the 

 non-black body at true absolute temperature T to that of a 

 black body at absolute temperature 6, versus 1/0) these isochro- 

 matics will show the following form. (Natural logarithms 

 throughout.) 



(2) l0i g_(^ + i). ? g_(i. p )} 



where 



