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XV. On the Number of Electrons conveying the Conduction 
Currents in Metals. By Arntaur Scuvuster, F.R.S.* 
(WHE number of free electrons in a metal is equal to the 
number of metallic atoms in the same volume, or eaceeds 
that number not more than three times. 
This law may be deduced with considerable confidence 
from optical considerations. Drude has supplied us both 
with the equations regulating the transmission of light 
through metals, and with the necessary observations. He 
has also shown that the number of ions conveying this charge 
may be calculated, and has given an example in the case of 
nickel without noticing, however, apparently the coincidence 
of that number with the one indicating the number of atoms 
per unit volume. I think the matter may be put somewhat 
more convincingly than was done by Drude, inasmuch as the 
uncertainty arising from want of knowledge as regards one 
important factor may be to some extent dealt with by 
assigning an upper limit to the number obtained. 
As there are several. matters of principle involved, and it 
is desirable to be clear as to the data and assumptions on 
which the above conclusion depends, we may shortly sum- 
marize the whole line of argument. In the ordinary electro- 
magnetic theory the inertia is calculated from the known 
magnetic field external to the conductor, and from an asswmed 
magnetic field inside the conductor. The latter is calculated 
on the hypothesis that the current flows like an incompressible 
fluid which continuously fills the whole space. But if we 
take the now, I believe, universally adopted view, that the 
current is conveyed by definite charges each concentrated 
within a small volume on the electron, the actual magnetic 
field in the immediate neighbourhood of the electron is con- 
siderable in comparison with that determined by the former 
assumption. I have discussed this question in a previous 
papert, and calculated the additional terms which have to be 
added to the coefficients of self-induction. If the distance 
between the electrons is great compared with their size the 
additional energy is practically the whole energy ot motion 
of the electron. That part of the field which overlaps the 
field of other electrons is effective in increasing the energy 
of self-induction calculated in the usual way, and I this, though 
large, 1s already provided for. As regards our present pur- 
pose, we may conclude that the whole electr omagnetic energy 
is equal to that taken account of in the usual formule with 
* Communicated by the Author. 
+ Phil. Mag. Feb. 1901. 
