[C] Flint/Einstein/Newton on Velocity vs Size. S.H. ShakmanInsofar 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 ...as 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.
Copyright 1987 S H Shakman Txu271794. All rights reserved.
Proposed for 1988 AAAS Meeting, AAAS # 0925.14; withdrawn 25 Sept. 1987. [HOME]