A New Determination of Molecular Dimensions
-I NVESTIGATIONS O N
THE THEORY .OF ,THE
BROWNIAN MOVEMENT
BY
ALBERT EINSTEIN, PH.D. e This new Dover edition, first published i 1956, is an unabridged n .and unaltered republication of the translation first:published in 1926.
It is published through special arrangément with Methuen and Co.,
L d , and the estate of
t.
Albert Einstein.
Manufactured i the United'States n of America.
EDITED WITH NOTES BY
R. F ü R T H
TRANSLATED BY
A. D. COWPER
WITH
3
DIAGRAMS
DOVER PUBLICATIONS, INC.
l.
MOLECULAR DIMENSIONS
III
A NEW DETERMINATION OF MOLECULAR
DIMENSIONS
(From the Annalen der Physik (4), 19, 1906, pp. 289-306. Corrections, ibid., 34, 1911, pp.
591-5922.](23)
T
HE kinetic theory of gases made possible the earliest determinations of the actual dimensions of the molecules, whilst physical phenomena observable in liquids have not, up to the present, served for the calculation of molecular dimensions. The explanation of this doubtless lies in the difficulties, hitherto unsurpassable, which discourage the development of a molecular kinetic theory of liquids that will extend t b details.
It will be shown now in this paper that the size of the molecules of the solute in an undissociated dilute solution can be found from the viscosity of the solution and of the pure solvent, and from the rate of diffusion of the solute into the solvent, if the volume of a molecule of the solute is large
36
'
37
compared with the volume of a molecule of the solvent. For such a sofute molecule will behave approximately, with respect to its mobility in the solvent, and in respect to its influence on the viscosity of the latter, as a solid body suspended in the solvent, and it will be allowable to apply to the motion of the solvent in the immediate neighbourhood of a molecule the hydrodynamic equations, in which the liquid is considered homogeneous, and, accordingly, its molecular structure
is
THE THEORY .OF ,THE
BROWNIAN MOVEMENT
BY
ALBERT EINSTEIN, PH.D. e This new Dover edition, first published i 1956, is an unabridged n .and unaltered republication of the translation first:published in 1926.
It is published through special arrangément with Methuen and Co.,
L d , and the estate of
t.
Albert Einstein.
Manufactured i the United'States n of America.
EDITED WITH NOTES BY
R. F ü R T H
TRANSLATED BY
A. D. COWPER
WITH
3
DIAGRAMS
DOVER PUBLICATIONS, INC.
l.
MOLECULAR DIMENSIONS
III
A NEW DETERMINATION OF MOLECULAR
DIMENSIONS
(From the Annalen der Physik (4), 19, 1906, pp. 289-306. Corrections, ibid., 34, 1911, pp.
591-5922.](23)
T
HE kinetic theory of gases made possible the earliest determinations of the actual dimensions of the molecules, whilst physical phenomena observable in liquids have not, up to the present, served for the calculation of molecular dimensions. The explanation of this doubtless lies in the difficulties, hitherto unsurpassable, which discourage the development of a molecular kinetic theory of liquids that will extend t b details.
It will be shown now in this paper that the size of the molecules of the solute in an undissociated dilute solution can be found from the viscosity of the solution and of the pure solvent, and from the rate of diffusion of the solute into the solvent, if the volume of a molecule of the solute is large
36
'
37
compared with the volume of a molecule of the solvent. For such a sofute molecule will behave approximately, with respect to its mobility in the solvent, and in respect to its influence on the viscosity of the latter, as a solid body suspended in the solvent, and it will be allowable to apply to the motion of the solvent in the immediate neighbourhood of a molecule the hydrodynamic equations, in which the liquid is considered homogeneous, and, accordingly, its molecular structure
is