646 Prof. 0. W. Richardson on the Distribution of tl\ 



le 



by the universal constants e, m, It, and h, whereas thermo- 

 dynamics alone is nnable to determine anything about A 2 

 except that it is independent of T. 



We are furnished then with what apears to be a crucial 

 test of the theory outlined in § 1, or at least of its capability 

 of application to the electron theory of metallic conduction. 

 According to these theories A 2 should, for any conductor for 

 which Vx is fairly small, i. e. for any good conductor, be 

 given by 



A2 = 2^^M| €X . 4724 = l . 47xl0l0>(36) 



Unfortunately the issue is not so clean cut as it might at 

 first sight appear to be, on account of the extreme difficulty 

 of obtaining even the order of magnitude of A 2 with certainty 

 from the experiments. For example, H. A. Wilson * found 

 that surrounding a platinum wire by an atmosphere of 

 hydrogen could reduce the value of the quantity corre- 

 sponding to A 2 by a factor of nearly 10 6 , and Langmuir f 

 has shown that with tungsten filaments still larger changes 

 in this quantity are produced by the presence of various 

 gases. At the first glance it might be thought that these 

 facts alone would be sufficient to discredit the present theory, 

 but I do not think that that is a valid inference. There is 

 no reason, according to the theory,, for expecting that A 2 will 

 have the value given by (36) unless the quantity corresponding 

 to w 2 — w 1 is independent of T. Not only A 2 but also the 

 energy difference w 2 — w^ is very susceptible to the presence 

 of certain gases. The value of the latter quantity will thus 

 be determined by the conditions of equilibrium between the 

 gas and the metal, and will clearly vary quite appreciably 

 with the temperature when these gases are present. It is 

 only in the absence of gases that w 2 — w 1 would be expected 

 to be almost independent of T and that A 2 would be ex- 

 pected to be given by (36). Of the measurements so far 

 published, those which are most satisfactory from the point 

 of view of the elimination of noxious gases have been made 

 by Langmuir f with tungsten. 



All the available experimental data are expressed by the 

 equation 



i = A 3 Tv- B 3/ T (37) 



Both (37) and (35) are approximations and are equally 



* Of. ' Electrical Properties of Flames, etc' p. 18. London. 1912. 

 t Phys. Rev. vol. ii. p. 464 (1913). 



