70 Mr. S. B. McLaren on tlie Emission and 



The average square of the total deviation in a given time t 

 is the sum of such terms as x P 2 . If we denote it by 6 2 , 

 then 



¥=(-^) 2 \ f°° — (2-2cosa-2i i sin W + w 2 )(e aw -l)- 1 , . (6) 

 \mirJ c d J u K A ; 



u = pt and a = A(2ttR0O ~ x . 



In metals, it would seem *, the length of the free path 

 varies inversely as the square root of the temperature, 

 while the average velocity with which it is described varies 

 directly in the same ratio, t is therefore inversely pro- 

 portional to 0, and 6t is a constant. 



The following numerical data are available : — 

 For = 300 the free path = 10~~ 6 . Large as this seems, 

 if we suppose the collisions to be with single atoms, it is 

 the result obtained from the measurements of conduction in 

 metals. Since the average velocity of the electron is 10 7 , it 

 follows that t is 10~ 13 . Put R = 10~ 16 , h = 7 x 10~ 27 (Planck), 

 and a appears to be of order unity. 



Also -= 6xl0 17 , c = 3xl0 10 . 

 m 



Hence (6) reduces to 



P = 10" 23 I —(2-2 cos u-2u sin M + M «)(g«»-l)-i. 

 Jo u 



S' 2 is of the order 10~ 23 , and the mean deviation is of 

 order 10 ~ n at most, for the time of a free path. 



§ 3. Significance of Wien's Law. 



If the time required to describe a free path is really 

 inversely proportional to the absolute temperature, an obvious 

 explanation of Wien's law suggests itself. Wien ; s formula 

 for complete radiation in spite of minor differences agrees 

 with Planck's in making E\, the ratio of the emission and 



_ ch 



absorption, contain a factor e R ^0 when \0 is small. We 

 cannot without further evidence decide if this factor is 



ch, 



to be assigned to the emission or the factor e~& KQ to the 

 absorption. Actual experiment leaves no doubt on the 

 matter. 



For by Planck's formula, the ratio of emission to absorp- 

 tion begins to differ from its long-wave value so soon 

 * See Kiecke, Physikalische Zeitschrift, 1909, p. 512. 



