152 Prof. A. Schuster on the Number of Electrons 
the addition of the total energy of the moving electrons dis- 
regarding their mutual influences. If the apparent mass of 
the electron is m, so that its energy is }mu?, then if N be the 
total number of electrons per unit volume, and ¢ the current 
density, which is Nue, the required energy per unit volume 
is $02”, where 
Nomw’=a? 
—o N07? 
m 
SOS segs) 1 (1) 
Let us consider what data we have for the calculation of ¢. 
Let N, be the number of atoms per unit volume, and put 
N=pN,. Let further h be the weight of a hydrogen atom, 
a the atomic weight of an element, and d its density. Then 
N,ah=d, or writing for the atomic volume a/d, we have 
ca) ee 
Caen 
Of the quantities involved h/e is known with considerable 
accuracy from electrolysis, and e/m is known with fair ac- 
curacy from recent experiments on the deflexion of cathode 
rays. Hence everything is known except p. Simon’s value 
for e/m, which is 1°86 x 107 in electromagnetic units, is now 
generally considered the most accurate, though giving some- 
what higher results than that of other observers. Adopting 
this value we find 
1°04 % TOF yi tee ary: ss 
Tia balON melee 6 x LO 2 (3) 
The atomic volumes of the metals range from 6°6 (iron) to 
56°3 (rubidium), but of the metals for which the optical 
constants are known the highest atomic volume is 21 (bis- 
muth), so that if p=1 the values of o vary from 3°7 x 10~™ 
to 11°8 x 10-1, which fixes the order of magnitude. Let us 
now turn to the optical portion of the argument. For the 
conduction current w! we must write, if R be the electric 
force 
Oo 
du! 
ay aw 
wi = ORs Coy) se 
where C is the conductivity. To this we must add the 
current N,ef formed by electrons on molecules which are 
capable of vibration, but not of leaving these molecules. 
Their number x must be at least equal to N, the number of 
molecules present. is the displacement, or if it is desired 
to consider the vibration of a doublet, we may consider ¢ to . 

