164 
PHYSICS: E. H. HALL 
applied from without, may well determine what course the electron in 
question will take. 
The experiments and arguments of Professor Bridgman now make it 
seem probable that I have greatly underestimated the range, of tem- 
perature through which the normal atoms may, in spite of the heat 
vibrations, be regarded as remaining in conductive contact with each 
other, and that, accordingly, the important function which my theory 
has given to the ions may not belong to them, except perhaps at rela- 
tively high temperatures or in the liquid state of the metals. 
Nevertheless, the potentiality of the ions for conduction is so great, 
under certain conditions which do not appear impossible, that it seems 
worth while to make some exposition of it. 
Fig. 1 (A) 
1(B) 
1(C) 
0 0 
Fig. 2 (A) (^^^ (^^7^ 
0 o 
2(B) 
FIG. 1. TRANSMISSION COL- FIG. 2. TRANSMISSION COL- 
LISION BETWEEN TWO ATOMS. LISION BETWEEN AN ATOM 
IMPROBABLE. AND AN ION. NOT IMPROB- 
ABLE. 
Three questions will be considered: 
1. How numerous must the ions be in order to maintain currents of 
great density? 
2. Would the conductive action of the ions conform to Ohm's law? 
3. What should be the temperature relations of conductivity, if it is 
due to ions? 
1. Requisite Number of Ions per Unit Volume, — The number of ions 
required for maintenance of electric currents, even currents of great 
intensity, may be small compared with the number of atoms — that is, 
the degree of ionization may be low. To show this let us consider, for 
example, copper at 300°C. absolute. 
German investigators have shown that the specific heats of metals 
at low temperatures can be satisfactorily accounted for on the h3^oth- 
esis that the frequency of to and fro vibration of the atoms is nearly 
independent of the temperature. Griineisen takes from Nernst and 
Lindemann 320 as the value of for copper, where v is the frequency 
in question and /5 = 4.8 X 10~i^ Accordingly we have 
I. = 320 ^ 4.8 X 10-11 = 6.7 X lO^^. 
