PHYSICS: E. H. HALL 
165 
The distance from center to center of copper atoms at 0° absolute 
and zero external pressure must be about 2 X 10-^ cm., and we may 
take this as the normal value of the atomic diameter. At ordinary 
room temperatures the distance from center to center is probably only 
about 0.5 of 1% greater. 
Let us now, taking for simplicity conditions which must be modified 
later, imagine a row of atoms and ions arranged along a straight line in 
the direction of the potential gradient, maintained from without, in 
the metal, the mean distance from center to center being 2 X 10"^ 
cm., and let us suppose each particle to vibrate in its heat motion exactly 
in the straight line of the row in question, from colHsion at the left to 
collision at the right and back again, 6. 7 X lO^^ times per second. Let 
us suppose every ion in the row to capture an electron at every left- 
hand collision, thus transferring the ion condition to its left-hand 
neighbor. 
All these assumptions lead to the conclusion that from every ion in 
the row the ion condition would travel along the row at the rate of 2 X 
10-8 X 13.4 X 1012, or 268,000, cm. per second. This is equivalent to 
one electron traveling with the same velocity. Acting thus one ion 
per linear centimeter would enable a conductor to maintain a current 
of 268,000 X 15 X lO-^i, about 4 X lO-i^ electromagnetic units; and 
10^^ such ions per linear centimeter would carry a current of 40 
amperes. 
In a copper rod of unit cross-section there are about 88 X lO^i atoms 
per linear centimeter — that is, 3.5 X 10^ times the number of ions re- 
quired to carry a current of 1000 amperes, if these ions were all as 
effective as they are in this preliminary calculation supposed to be. 
We must now let fall some of the favoring assumptions of this calcu- 
lation, in order to approach more nearly to actual or possible conditions. 
Instead of assuming every vibration to be in the line of the potential 
gradient, we must imagine the progress of the ion condition to follow a 
zig-zag course, the mean distance of travel in the direction of the poten- 
tial gradient being not 2 X 10"^ cm., but, let us say, 10"^ cm. The great 
departure, however, from numerical truth was made in assuming that 
every ion gains an electron at its left-hand collision — that is, at the 
negative-potential end of its heat path. This is equivalent to assuming 
that all the existing ions are moving in one direction, from -|- toward — , 
through the metal. In fact, the gradient of potential, even if very 
steep, would probably determine or inhibit the passage of an electron 
in only a very small proportion of all the collisions between atoms and 
ions. Let us suppose that a gradient of potential sufficient to main- 
