FOOTE AND FAIRCHILD : GRAY BODY RADIATION 195 



Suppose that A can be represented, within observational er- 

 rors, by a function of the following form, where p and A' are 

 constants 



{C2P 

 ,log e 4=log e A' + ^ 



A 



Substituting in (3) 



(5) log.^-log.A'-S^i + p-I 



Since by the method in question T is maintained constant, the 

 only variables being J 2 /Ji, A and 6, the above equation is of the 

 form 



(6) (y — a) = m (b — x) 



i.e. a family of straight lines with the variable parameter c 2 /X. 



The common point of intersection has the coordinates log e A' 



i 1 

 and - + p. 



We have accordingly shown that the intersection may occur 

 when the material is not gray and that the temperature corre- 

 sponding to the point of intersection T' is not the true tempera- 

 ture T but related to it by the reciprocal expression — - = — \- p, 



where p is a constant which requires an entirely different mode 

 of experimentation for its determination. It is of course recog- 

 nized that only a- few functions of the type represented by equa- 

 tion (4) will satisfy the condition that intersections of the iso- 

 chromatics occur, and that there is probably no physical reason 

 why the true emissivity relation should take this one peculiar 

 form, which invalidates the conclusion that the emissivity must be 

 independent of the wave length. But it may be remarked that 

 the intersections are never perfect, that the straight lines at best 

 are only a smoothed mean of the observed points, that there are 

 only a few radiating materials which do show intersections, and 

 finally that within the observational errors involved in work 

 upon radiation the proper choice of A' and p of equation (4) will 

 satisfactorily determine almost any function desired. 



