180 BUCKINGHAM! WIEN's DISPLACEMENT LAW 



The boiling point of sulfur. The evidence based on all the data 

 at present available is that the best value for the temperature of 

 the boiling point of sulfur at normal pressure, is 444? 6 to the near- 

 est 0?1 on the thermodynamic scale. 



PHYSICS. — On the deduction of Wien's displacement law. Edgar 

 Buckingham, Bureau of Standards. 



The least satisfactory step in deductions of this law is usually 

 the treatment of the change of wave-length of perfectly diffuse 

 radiation upon reflexion from a moving surface. This step maybe 

 taken in the following manner: 



Let a closed evacuated shell, with walls which are perfectly 

 but somewhat irregularly reflecting, be filled with perfectly diffuse, 

 approximately monochromatic radiation of wave-lengths between 

 X and X + d\. Let R\d\.ds.dw be the amount of radiant energy 

 which passes in unit time from the negative to the positive side of 

 a small plane surface element of area ds, inside the shell, in direc- 

 tions comprised within a cone of the infinitesimal solid angle dw 

 described about the normal to ds. For diffuse radiation, the 

 " radiant vector" R\ is the same at all points and in all directions. 



Let M be a small plane piece of the shell wall of area s, and let 

 it have a normal velocity @C outward, C being the velocity of 

 light and /? an infinitesimal. The rest of the shell wall remains 

 at rest. If T = X / C is the period of the waves at a point fixed 

 in space, their period of arrival at a point fixed on M, from an 

 angle of incidence tp, is T' = T/(l — /3 cos <p) and the effect of 

 arrival at this angle is to increase the period in the ratio 



r a = 1 + 13 cos <p (1) 



terms of higher orders in /3 being negligible. Similarly, a disturb- 

 ance starting from a point on M with a period T' and propagated 

 at an angle of reflexion \p, suffers a further increase of its period, 

 measured at a point fixed in space, in the ratio 



r d = 1 + jS cos yp (2) 



Our problem is to find the effect on the original period T, of 

 all the arrivals and departures at all possible angles <p and \p 



