Re: consistent, overdetermined facts

[Hugh Logan <hlogan1@BELLSOUTH.NET>]

John Denker wrote:

> Occasionally there are corners of science that are underdetermined, like
> the unadorned Hoberman sphere.  For instance, before Millikan came along,
> people knew the charge-to-mass ratio of the electron, but they didn't know
> the charge or the mass.

The last sentence above is typical of  the sequencing of scientific knowledge --
leading
one to believe that only one path to the charge of the electron need be
considered --
selecting the Millikan method.

It seems to me that the charge of the electron ( and its mass if e/m is known)
is another example of a quantity that is overdetermined by the facts, even at
the time Millikan performed his experiments on the charge of the electron. From
electrolysis, it was known that the product of Avogadro's number and the
electronic charge was the Faraday (the charge per mole of electrons). The
Faraday was measurable. To the extent that Avogadro's number was known, the
charge of the electron could be determined -- assuming that one accepted the
explanation of electrolysis in terms of electrovalence and the transfer of
electrons.

When I was an undergraduate student at The Johns Hopkins University, the
spectroscopist Gerhard Dieke, then Chairman of the Physics Department,
substituted for a professor who had to be away for the day. His lecture was on
the various methods of
determining Avogadro's number. I do not remember all the details, but I do
recall that he mentioned estimating Avogadro's number from the color of the sky
(undoubtedly based on Lord Rayleigh's scattering formula of 1871) , and I heard
of Perrin's work for the first time -- presumably on the sedimentation of
suspensions, the equation for which involves Avogadro's number. (These examples
of fluctuation phenomena are briefly reviewed in the first chapter and Appendix
I of Max Born's _Atomic Physics, Sixth Ed._. Estimates of Avogadro's number, or
the closely related Loschmidt's number have been available since 1865. Referring
to Born, the kinetic theory of gases yields the result that the mean free path
is inversely proportional to the product of Avogadro's number and the square of
the molecular diameter. The mean free path can be determined experimentally by
various methods including heat conduction, viscosity, and diffusion. (The
relevant measurable constants can be expressed in terms of the mean free path
and measurable quantities.) Born also mentions determining the mean free path
from the attenuation of molecular beams. And he  refers to the determination of
Avogadro's number from radioactive decay experiments and from  the later (after
Millikan) X-ray diffraction experiments of Siegbahn and Compton in 1925. I
recall that one of the physics encyclopedias credited one of my professors, J.
A. Bearden, with contributing to the determination of Avogadro's number by this
method.

Admittedly, determining the electronic charge from experimental and estimated
values of Avogadro's number and the Faraday  is not as precise and accurate as
Millikan's method, but such determinations are nonetheless further evidence of
the overdetermination and consistency of scientific knowledge.

(Quite a few years ago there was an article by Jones and Childers in TPT
involving
experimental evidence for the atomicity of matter. Perrin's work leading to the
determination of Avogadro's number from sedimentation experiments was described
in some detail -- along with the connection of Avogadro's number to the
electronic charge
and the Faraday. Since moving, most of my references are packed away, so I don't
know which issue of TPT.)

Hugh Logan
Retired physics teacher