476 nutting: gray radiation 



PHYSICS. — Criteria for gray radiation. P. G. Nutting, Roches- 

 ter, New York. (Communicated by N. E. Dorsey.) 



If the logarithm of the energy radiated from a body within 

 a short range of wave lengths be plotted against the reciprocal 

 of the absolute temperature, the result is known to be a sensibly 

 straight line over a wide range of temperatures. These logarith- 

 mic isochromatic lines pass through a common point in some 

 cases, not in others. Benedict 1 concludes that this stigmatic 

 condition is characteristic of gray radiation, while the lack of 

 it means that the radiation is selective. Hyde 2 from his own 

 data on lamp filaments concludes that the stigmatic condition 

 is insufficient as a criterion for grayness. Foote and Fairchild 3 

 have shown further that the stigmatic condition may hold even 

 for a body known to be strongly selective. 



The mathematical side of the problem appears to have been 

 neglected, although capable of rather simple treatment. Let 

 the equilibrium radiation from a "black body" be represented by 



J = Bi X- 5 e-xr (1) 



in which B x and B 2 are independent of wave length and tem- 

 perature. Also let 



E = d X-»e-X? • (2) 



represent radiation from some body, but not in equilibrium 

 with it. 



log J = logCBiX- 5 ) - — (3) 



hence for any fixed wave length, log J" is a linear function of 1/T. 

 Writing (3) ' 



y = a — bx (4) 



it is seen to represent a family of straight lines whose Y inter- 

 cept is a and whose direction tangent is b. 



But the general representation of a stigmatic pencil of lines 

 passing through the point (x 0) y 0) ) is 



V - 2/o = -b (x - Xo), (5) 



1 E. Benedict. Ann. d. Physik, (4) 47: 641. 1915. 



2 E. P. Hyde. Ann. d. Physik, (4) 49: 144. 1916. 



* Foote and Fairchild. This Journal, 6: 193. 1916. 



