Mechanics of Luminosity. 257 



Let us take, as a first approximation, the law of cosines* 

 as holding good for the radiation, then we replace the semi- 

 cylindric surface of the wire radiating to each point of the 

 siit by the rectangle y$=f. 



Let the quantity of energy radiated by each square centi- 

 metre be E, then the surface / gives, on the whole, the 

 quantity of energy E/. 



If the width of the slit is s, then the unit of length of the 

 slit receives a portion which is to the total radiation as the 

 surface of the slit corresponding to the unit of length s. 1 is 

 to the half surface of a sphere of radius 77. (In the quantity 

 E determined by experiment we have only the quantity of 

 energy radiated outwards, and not that radiated towards the 

 interior of the wire.) This fraction is sftirrf. 



Hence upon the unit length of the slit there is radiated 

 from the surface /of the glowing platinum wire a quantity of 

 energy 



— 27T7j 2 " ~" e 2tt7) 2 \e / 2ttt} 



In our experiments 



h/e = 0-063, 8 = 0-026 cm., 77 = 4-4 cm.; 



consequently 0-09rt 



A=0-063 ~-^r- A *E = 0-0 4 6*E. 

 2-77x4-4 4 



(b) We will now calculate the similar expression for the 

 energy sent to the slit by a flat-shaped source of light of con- 

 siderable extent, like that of the amyl-acetate lamp, or the 

 Bunsen flame co'oured with sodium, which is so near to the 

 slit that the cone passing through the diaphragm of the colli- 

 mator and a point of the slit in its prolongation towards the 

 flame is completely filled with luminous particles. 



The cone from the diaphragm through a point of the slit 

 cuts the flame in a circle ; if the flame is at a distance 7/ from 

 the slit, and if 8' is the diameter of this circle, then the 



* The validity of the law of cosines may, upon theoretical grounds, "be 

 open to doubt. As is well known, it is established by regarding as the 

 radiating quantity that contained in a parallelopiped whose base is the 

 radiating surface, and of which the edge forms a portion of the prolonga- 

 tion of the rays under investigation, equal to the depth from which, in 

 general, rays still issue. But it is certainly not the particles contained in 

 this parallelopiped which give the rays issuing in the direction in question, 

 since in their introduction the refraction from metal into air is neglected, 

 of the existence of which (even before the direct proof given by Herr A. 

 Kundt) evidence was offered by the strong polarization of the emergent 

 light. Further experimental investigations are required to explain the 

 contradiction between theory and the observations of Herr Moller ( Wied. 

 Ann. xxvi. p. 266), which tend to confirm the law of the cosine. 



