620 
PHYSICS: E. H. HALL 
Proc. N. a. S. 
Comments. — There is a curious tenacity in the value of (^o ^loo) for 
any metal, as found by the method of this paper. Thus in jio case ex- 
cept that of Co, where a great range of {kf k) was tried, did the value 
of (^o ^loo) change from >1 to <1 with any variations of 5 and X'o- 
Out of seventeen cases, including those of constantin and manganin, the 
value of (^o ^100), as found by experiment or calculated by the use of the 
Wiedemann-Franz ratio, is in nine greater than 1 and in eight less than 1 . 
In only two of these cases, those of aluminium and gold, does the method 
of this paper fail to give a value of (^o ^ ^100) on the right side of 1. 
In nine of these seventeen cases, Bi, Co, Fe, Ni, Pd, Pt, Sn, Tl, Zn, 
it has been found practicable to get a combination of q, s and X'o that will 
account for Bridgman's cr and give the desired values of both 60 and 0ioo 
to any reasonable degree of accuracy. In all of these nine cases, except 
that of Bi, the value of Ki in the equation a = Ki T K2 tT is positive. 
In six of the other eight cases the value of (^o ^100) here found is larger 
than the one found by experiment or indicated by the W-F rule. In 
four cases, Ag, Al, Au, Cu, the discrepancy is about 6-10%; in one, that 
of Mo, it may be considerably greater, but this is a W -F case ; in only one, 
that of Cd, is the disagreement hopelessly great. In constantin and in 
manganin the calculated (^o ^100) is less than the observed. 
The value of y, the percentage of ionized atoms within a metal, has been 
estimated by means of the formula^ 
, n c I e- 
When T is taken as 273, we have, approximately, 
= 1.91 X 10-^0 = 1.91 X lO-'^'yvl, 
or 
7 = 5.24 X 10-^^ {kf ^ vl), 
where v is the number of atoms of the metal per cu. cm. and / is the length 
of the "mean free path" of the electrons among the atoms. 
Concerning the value of /, I have been and am still much in doubt. 
Adams and Chapman, in a study of the Corbino effect,* estimated it to 
be in copper not far from 3 X 10"'^ cm., which is about 13 times the dis- 
tance from centre to centre of adjacent atoms, if a cubical arrangement 
of the atoms is assumed. Compton, K. T., and Ross^ concluded that a 
photo-electrically excited electron may move about 2.67 X 10"'^ cm. in 
platinum, about 11 times the centre to centre distance of the atoms, and 
approximately 5 X 10 cm. in gold, nearly 20 times the atomic distance. 
I have taken / as 10 times the atomic distance, thus putting / = (10 v\) 
and making 
y = 0.52 X 10^^ X kf vl 
A much smaller estimate of / than the one I have used would be disas- 
trous for my speculations, as it would give large values of 7 and thus in- 
