312 Prof. J. Larmor on the Mange of 



leaks in each case at a particular temperature can be 

 calculated. 



In this way the following numbers were obtained for the 

 temperature 1600° C. 



Leak in air 5 x 10~~ ampere. 



Air with lime 5 x 10~ 2 „ 



Hydrogen 10 _1 ,, 



Hydrogen with lime ... 10 +3 ,-, 



Thus the leak with hydrogen, as with lime, is about 

 10 5 times greater than with air alone, while that with both 

 hydrogen and lime is 10 10 times greater. These ratios do 

 not vary much with the temperature. 



In conclusion I have to thank Prof. H. A. Wilsou, at 

 whose suggestion these experiments were undertaken, and 

 who was ever ready with kind advice and assistance. 



XXVI. On the Ranqe of Freedom of Electrons in Metals. 

 By Prof. J. Lakmok, FM.8* 



IT has been ascertained that complete metallic conduction 

 is established in a small fraction of the period of low 

 ultra -red radiation. This is proved by the experimental 

 result of Ha gen and Rubens that radiation of about ten or 

 more times the period of light is reflected from all metals in 



* Communicated by the Author. 



This brief discussion was drawn up in forgetfulness of Prof. Schuster's 

 estimate of the number of free elections in metals (Phil. Mag. vii. 1904). 

 His method was, I find, criticised and enlarged on in an interesting way 

 later in the same year by Drude (Ann. der Phys. xiv. p. 936), with a view 

 to greater precision ; but the widely uncertain assumption that the optical 

 frictional term is represeuted for visible radiation by the full ohmic 

 resistance seems to enter fundamentally. The values there obtained are 

 about 10 times larger than the admittedly very rough estimate in the 

 text. Later in the same paper (p. 956) Drude estimates the length of 

 free path of the electrons, obtaining results ranging in order of magnitude 

 from 10~ 6 cm. for the nobler metals to 10 — 8 cm. for bismuth ; these 

 were intended to replace estimates (of almost the same order for the 

 nobler metals) deduced by J.J. Thomson and J. Patterson from magnetic 

 influence on the resistance of thin sheets. The lower estimate, about 

 10 — 8 cm. for most metals, deduced in the text directly from the time 

 necessary for establishment of complete conduction, is the main point of 

 this paper; the result might possibly be stretched toward 10 — 7 , 

 but hardly further, if the velocities of the free electrons are really 

 determined by the gas-law. If velocities so small as these are retained, 

 the negative conclusion that hardly any poitions of the paths by which 

 the electrons travel are free, and that therefore estimates of number 

 made in this way are uncertain, seems not unnatural. 



