Flint/Einstein/Newton on Velocity vs Size.  S.H. Shakman  

Insofar as velocity of ions in aqueous solution varies directly with ionic conductivity (*1), Flint's use of Graham's law of diffusion in the case of solutes (*2) treated conductivity values as relative (inverse-sq.) measures of ionic weight (*5). Graham's law had preceeded and described a relationship required by the kinetic theory (*3).

Einstein had characterized velocity as varying w/the inverse-sq.-root of mass for particles in colloidal platinum solutions but not for H+ & K+ (*4). For these he calculated displacement as varying w/the sq.-root of conductivity (or velocity); Einstein had also characterized displacement as varying inversely with the square root of diameter as he illustrated in the case of the sugar molecule (*4). Thus velocity might be indirectly characterized as varying inversely with diameter.

Note that both perspectives may be derived from Newton's characterization of resistances as varying (a) "... as the squares of the velocities and the squares of the diameters ..." and (b) "... directly as the squares of the velocities and the quantities of matter ...".(*6)

But as Newton affirmed, "more is in vain when less will serve".(*6)
*1 KOHLRAUSCH, Gottingen Nachrichten, 1876, p. 213. 
*2 FLINT, L.H., J. Wash. Acad. Sci., 22, (1932), 99,234. 
*3 PAULING, L., Chemical Bond 1967, p. 174. 
*4 EINSTEIN, A., Brownian Movement (Dover, 1956), 64,82-85. 
*5 SHAKMAN, S.H., 1987 AAAS Abstract #111. 
*6 NEWTON, I., Principia (1687), III, Rule 1; II, Prop. 33.  

(c) 1987 SHShakman Txu271794/ (c) 1990 as amended.

Enstein, Brownian ..., p. 12: "The coefficient of diffusion of
the suspended substance therefore depends (except for
universal constants and absolute temperature) only on the
coefficient of viscosity of the liquid and on the size of
the suspended particles."

p. 26: "formula for density of radiation corresponding to
the frequency v - pv = dd(R/N)(8 pi v-sq./L-cube)T where L is
the velocity of light, ... the fact that we obtain in the
manner indicated not the true law of radiation but only a
limiting law, appears to me to have an explanation in the
fundamental incompleteness in our physical conceptions."

On Mistakes/Corrections:
Einstein corrected a 1906 paper in 1911: "Correction of My
Paper 'A New Determination of Molecular Dimensions'". And
Newton, in Priincipia, asked "... that my labors ... may be
examined, not so much with the view to censure, as to remedy
their defects."

Einstein, Brownian ... p. 114, Principia, Preface.



Copyright 1987 S H Shakman Txu271794. All rights reserved.
Proposed for 1988 AAAS Meeting, AAAS # 0925.14; withdrawn 25 Sept. 1987. counter [HOME]