The electron, its isolation and measurement and the determination of some of its properties — John Stuart Mill — John Shaqi
The electron, its isolation and measurement and the determination of some of its properties
John Stuart Mill · en
This work was concluded in August, 1916, and occupied the better part
of two years of time. The final table of results and the corresponding
graph are given in Table XI and in Fig. 10. The final value of
computed on the basis is seen to
be now instead of 61.085, or .07 per cent
higher than the value found in 1913. But Dr. Harrington’s new value
of , namely, .00018226, is more reliable than the old
value and is lower than it by .07 per cent. Since appears in
the first power in , it will be seen that the new
value[54] of , determined with new apparatus and with a completely
new determination of all the factors involved, comes out to the fourth
place exactly the same as the value published in 1913, namely,
The corresponding values of and are now .000617 and .863,
respectively.
Since the value of the Faraday constant has now been fixed virtually by
international agreement[55] at 9,649.4 absolute electromagnetic units,
and since this is the number of molecules in a gram molecule
times the elementary electrical charge, we have
Although the probable error in this number computed by the method
of least squares from Table XI is but one part in 4,000, it would be
erroneous to infer that and are now known with that degree
of precision, for there are four constant factors entering into all
[Pg 121]
of the results in Table X and introducing uncertainties as follows:
The coefficient of viscosity which appears in the ³⁄₂ power
introduces into and a maximum possible uncertainty of
less than 0.1 per cent, say 0.07 per cent. The cross-hair distance
which is uniformly duplicatable to one part in two thousand appears
in the ³⁄₂ power and introduces an uncertainty of no more than 0.07
per cent. All the other factors, such as the volts and the distance
between the condenser plates, introduce errors which are negligible
in comparison. The uncertainty in and is then that due to
two factors, each of which introduces a maximum possible uncertainty
of about 0.07 per cent. Following the usual procedure, we may estimate
the uncertainty in and as the square root of the sum of the
squares of these two uncertainties, that is, as about one part in 1000.
We have then:
Perhaps these numbers have little significance to the general reader
who is familiar with no electrical units save those in which his
monthly light bills are rendered. If these latter seem excessive, it
may be cheering to reflect that the number of electrons contained
in the quantity of electricity which courses every second through a
common sixteen-candle-power electric-lamp filament, and for which we
pay ¹⁄₁₀₀₀₀₀ of 1 cent, is so large that if all the two and one-half
million inhabitants of Chicago were to begin to count out these
electrons and were to keep on counting them out each at the rate of two
a second, and if no one of them were ever to stop to eat, sleep, or
die, it would take them just twenty thousand years to finish the task.
[Pg 122]
TABLE XI