JOURNAL 



OF THE 



WASHINGTON ACADEMY OF SCIENCES 



Vol. VII JUNE 4, 1917 No. 11 



PHYSICS. — A visibility equation derived from the Ives and 

 Kingsbury new luminosity equation. Paul D. Foote, Uni- 

 versity of Minnesota. 



In a recent paper Ives and Kingsbury' have found that the 

 simple expression L = 24000 exp. - 1/(0.00250 4- 0.00003795 0) 

 quite closely represents the relation between the luminosity 

 L of a black body and its absolute temperature §. It is inter- 

 esting to enquire what function of the wave length X the visi- 

 bility must be to satisfy this equation of luminosity. We have: 



L= \VJd\= Cv (\)c x \- h e~~^d\ = ie"«"+^ (1) 



Jo Jo 



where V (X) represents the visibility, J = intensity as given by 

 Wien's law, and the expression on the right is the new luminosity 

 relation. 



Equation (1) is a simple integral equation which may be 

 readily solved for V(\). If one makes successively the sub- 

 stitutions x = \/§, ax 4- b = at, p = b/a, p' = p/a, and 



g(s) = 2 7T i e l/a A~ l c x cf 4 V (X) s 3 e ps , one obtains: 



h (t) = e pVt = J_. r g (s) e~ ts d s (2) 



2 it i Jo 



^hys. Rev., 8: 325. 1916. 



317 



