T 
597 
2 
“separation of the variables” for the quantization of the motions of 
more degrees of liberty. Therefore the question may be put: In 
how far are the additional parts, with which P. Epstrim and also 
P. Desie [Gött. Nachr. 1916] form the action integral adiabatic in va- 
riants ? In SOMMERFELD's case they are still invariant, as shown in $ 7. 
Physics. — “On the electric resistance of thin films of metal’. By 
S. Weser and E. OosrerHuis. (Communicated by H. KaMERLINGH 
ONNEs). 
hi 
(Communicated in the meeting of Sept. 30, 1916). 
1. Introduction. 
Various investigations have shown that the specific resistance of 
thin films of metal differs from the normal value, which is found 
for thicker layers of the metal. This fact is of importance in con- 
nection with the theory of electric conduction in metais. 
The first investigations of the subject were made by A. C. LONGDEN!) 
and by J. Parrrrson ®); they obtained the following results which 
have been on the whole confirmed by later investigators : 
1. The specific resistance of thin metallic films may become many 
times larger than the normal value; the specific resistance, when 
measured for films of diminishing thickness, is found to increase 
gradually ; beyond a definite thickness (for platinum about 7 uu) 
this increase becomes pretty suddenly much stronger. 
2. The temperature-coefficient of the electric resistance is negative 
for very thin films; as for thick layers the temperature-coefficient 
has a positive value, there must be a definite thickness for which 
the metallic film has a temperature coefficient equal to zero. 
3. The resistance of thin metallic films changes with time and 
ultimately reaches a constant value. This final value may be reached 
in a shorter time by heating the substance, , 
The question at what thickness a perceptible conduction begins 
to show itself in a metallic tilm was investigated by A. Rigepe *) and 
B. Pogany *) amongst others; for most metals the beginning of con- 
duction was observed in films of from 1 to 3 uu thickness, only 
1) A. G. LONGDEN. Phys. Rev. 11. p. 40. 1900. 
2) J. PATTERSON. Phil. Mag. Vol. 4. Ser. 6. p. 652. 1902. 
5) A. Rrzpe. Ann. der Phys. Bd. 45. p. 881. 19'4. 
4) B. Pogany. Ann. der Phys. Bd. 49. p. 53). 1916 and Phys. 4.5 17. p. 251. 1916, 
