166 Profs. Hagen and Rubens on some Relations 
hada good spherical shape, they were neither quite free from 
oxidation nor were they thick enough, so that they necessarily 
gave too small a reflecting-power. But the want of exactness 
of the values obtained for bismuth is not the only reason why 
we excluded them from our calculations. Bismuth follows 
the law given above in no respect, as will be proven by our 
further experiments. 
Comparison with the Theory. 
Maxwell’s original theory, which (as has been mentioned ) 
does not consider the molecules and their vibration, leads 
to this simple expression for the reflecting-power * 
200 
R=100— a 

* Cf. P. Drude, ‘ Physik des Aethers,’ p. 574, Formula (66), 1894; 
and E. Cohn, ‘Das electromagnetische Feld,’ p. 444 (1900); also M. Planck, 
Sitzungsber. d. k. Akad. d. Wissensch. zu Berlin, p. 278 (1903). Prof. 
Planck arrives at the equation (2) in this way :— 
If a plane linear polarized light-wave propagates in a metal which 
does not possess any dielectric qualities and absorbs the vibrations only by 
ordinary galvanic conduction, this process is represented by the Maxwell- 
Hertz equations 
oH _ oH 

si ri oe 
ait _ ae 
of Or. 
Herein E and H mean the intensity of the electric and magnetic field, 
ec the velocity of light in the vacuum, and A the galvanic conductivity of 
the metal in absolute electrostatic measure. From these equations we 
obtain 
OE en ee OE 
deg? eee oe 
Of a ape ae 
This equation is satisfied by the expression 

Gt 
n(it a, 
iA we 
if the further condition is fulfilled 
nu(1+p*)+4rA=0; 
wherein » means the number of vibrations in 27 seconds and 
P=J9 +u, 
y is the ratio between the wave-length in vacuum and that in the metal ; 
g means the coefficient of extinction, defined by the law, that the intensity 
of a ray proceeding in the metal is reduced to e—479 of its initial intensity 
after having passed over a distance as long as one wave-length in vacuum. 
By substituting the value of p, and by separating the real and 
imaginary terms, we obtain 
—2qyn+4rA=0 
and 1+¢°—v?=0. 

