314 Prof. J. Larmor on the Range of 



In a simple wave-train o£ period 2irjp, 



wliicb yields on substitution 



c z m c~ 



thus giving for the square of the quasi-index fi ( = c/c y ) the 

 value 



m }r 



For radiation (D line) of wave-length 6.10~ 5 cm., lir/p is 

 2.10-1-5, so that 



2= __ N * 10-20(9 jo 20 )(4.10- 30 ) + 1 

 it m v /v ' 



e 9 

 = — N' — . x . 10 -29 approximately. 



If the ions are all free electrons, ?/m is 17.10 6 , thus 

 /x^-^.2.10- 22 . 



For the nobler metals, in red and yellow light, the real 

 (and five times preponderant for gold, silver, magnesium) 

 part of yu, 2 is of the order -10 ; this would give N'=s±. 10 23 *, 

 so that the number of free electrons taking part would be of 

 somewhere about the same order as that of the molecules of 

 the metal. 



A view of metallic electric conduction, which fits in with 

 its parallelism to thermal conduction, is that it takes place by 

 free electrons whose velocities are prescribed by collisions 

 with the molecules, and so are taken as determined by the 

 law of equality of mean energies in gas-theory. For 

 hydrogen under standard conditions., the average velocity in 

 the free path is 2.10" cm./sec; as the electrons are a thousand 

 times less massive, their average velocity would thus be about 

 b\10 6 . And we know that metallic conduction is fully 

 established in a small fraction of the time 2.10 -14 sec, which 

 is the period of ultra-red radiation of ten times the wave- 

 length of light. If then, as theories involving free electrons 

 require, the establishment of conduction is intimately con- 



* If undamped resonance of adjacent free molecular periods contributes 

 sensibly to the real part of — fx 2 , otherwise than by shaking out more 

 electrons into freedom, this would be an over-estimate. 



