A standard measure of length at first sight appears to be very
simple--merely a bar of metal of any length, according to the unit of any
country; and comparisons of different standards do not seem to present
any difficulty. But on looking further into the thing, we find that
standards are referred to some natural invariable length, and we are at
once confronted with a mass of scientific reductions giving different
values to the same thing, according to successively improved means of
observation. We find, also, that comparisons of one standard with another
differ, as given by reductions carried to great apparent exactness.
Every author appears to assume the right of using his own judgment as to
what reduction is to be considered the most exact, and the result is a
very confusing difference in apparently exact figures, with nothing to
show how these differences arise.
I have endeavored to indicate what may be the cause of this confusion by
giving the figures of actually observed comparisons and reductions; in a
manner, the roots of the figures used as statements of length.
Sir Joseph Whitworth gives 1/40000 of an inch as the smallest length that
can be measured with certainty, with an ultimate possibility of 1/1000000
of an inch; but imperceptible variations of temperature affect these
infinitesimal lengths to such an extent that he believes the limit can
only be reached at a standard temperature of 85° F., to avoid the effect
of heat of the body.
It appears to me that comparisons should be made of double yards and
mètres with the old French toise, as the limit of exactness would be
thereby doubled.
Another great defect in statements of relative values is the omission
of necessary facts--the material of which the bars or standards are
made, the temperature at which comparison was made, and the standard
temperatures used as to the final reduction, with the coefficient of
expansion adopted.
Again, bars of different metals appear in time to sensibly change their
relative length.