Vol.. 8, 1922 
PHYSICS: E. H. HALL 
311 
ion, cc the line of centres, and 5 a little three dimensional space within 
which the point p must be in order to capture an electron from the atom. 
It is to be noted that the pit in i allows the point p to pass through s during 
a very close approach of the ion and the atom.^ 
16. Let us for convenience suppose the atom to remain at rest, all 
the relative motion of the two particles being, for the present discussion, 
attributed to the ion. Ignoring any small long-period rotary oscillations 
the ion may have, we see that its vibrations may be resolved along three 
axes, one the line cc, and the other two at right angles with cc and with 
each other. The little vital space s, within which the point p of the ion 
must be in order to take up an electron from the atom, lies at the middle of 
the second and third of these component vibrations but nearer one end than 
the other of the vibration parallel to cc. 
17. The probability that p will gain an electron during any single pas- 
sage through 5 is proportional to the length of time spent in this passage. 
It is, then, so far as the second and third axes are concerned, inversely 
proportional to the product of the amplitudes of vibration parallel to these 
axes, each of which amplitudes is proportional to T^- ^. As to the vibra- 
tions parallel to cc, the space s lies relatively nearer the end in a short vi- 
bration than in a long one. Accordingly it may be assumed, provisionally, 
that, so far as motion along cc is concerned, the time spent by p in passing 
through 5 will be inversely proportional to some power of T higher than T^-^. 
The result, all three component vibrations being considered, is a proba- 
bility, that p will gain an electron in a single passage through s, propor- 
tional to r~*, where % is some quantity a little greater than 1.5. 
18. The conductivity under discussion should, other things being equal, 
be proportional to the amount of orientation suffered by the ions, which 
according to (5) varies as T"^ and to the frequency of transmission con- 
tacts between ions and atoms, which according to (17) varies as 
Hence if n, the number of ions per cu. cm., remained constant, we should 
have this conductivity proportional to where (^+^) is somewhat 
greater than 2.5. 
19. In the series of papers on thermo-electric action, thermal conduc- 
tion, etc., which I have published in these ProcKE^dings^ during the past 
few years, I have been led to the conclusion that the value of n can be 
usefully represented by the formula n = zT^, where z and q are constants, 
the value of the latter varying in the many metals considered, from 1.2 
in bismuth and in iron to 1.6 in nickel, palladium and platinum, the mean 
being 1.48. This general rate of increase of n with rise of temperature, 
taken with the propositions of (18), suggests that the conductivity ka, 
now under discussion, should vary, approximately, inversely as the abso- 
lute temperature, though individual metals might depart rather widely 
from this relation. The relation in question is: 
