Elementary arithmetic, with brief notices of its history... by Robert Potts.

WEIGHTS AND MEASURES.

17

and thus tend, in no small degree, to facilitate the commercial intercourse, and by so doing to consolidate a lasting friendship between
the two great nations of the world, most assimilated by their language,
their laws, religion, customs, and manners."
In the course of this year, 1821, Mr. John Quincy Adams, Secretary to the United States, by order of the Senate, made and published
an important report on weights and measures, from which the following brief abstracts are taken. He observes that "When Mechain and
Delambre were employed by the National Assembly of France to
make an admeasurement of the arc of the meridian to an extent which
had never before been attempted, and to weigh distilled water with an
accuracy which had never before been effected, Nature, as if grateful
to those exalted spirits, who were devoting the labour of their lives to
the knowledge of her laws, not only yielded to them the object which
they sought, but disclosed to each of them another of her secrets.
"She had already communicated, by her own inspiration, to the
mind of Newton that the earth was not a perfect sphere, but an oblate
spheroid, flattened at the poles; and she had authenticated this discovery by the results of previous admeasurements of degrees of the
meridian in different parts of the two hemispheres. But the proportions of this flattening, or, in other words, the difference between the
circles of the meridian and equator, and between their respective
diameters, had been variously conjectured from facts previously
known. To ascertain it with greater accuracy was one of the tasks
assigned to Delambre and Mechain, for, as it affected the definite
extension of the meridian circle, the length of the m~tre, or aliquot
part of that circle, which was to be the standard unit of weights and
measures, was also proportionably affected by it. The result of the
new admeasurement was to show that the flattening was of X~; or
that the axis of the earth was to the diameter of the equator as 333 to
334. Is this proportion to the decimal number of 1000 accidental?
It is confirmed as matter of fact by the existing theories of nutation
and precession, as well as by experimental results of the length of the
pendulum in various latitudes. Is it also an index to another combination of extension, specific gravity, and numbers hitherto undiscovered? However this may be, the fact of the proportion was, on
this occasion, the only object sought. The fact was attested by the
diminution of each degree of latitude in the movement from the north
to the equator; but the same testimony revealed the new and unexpected fact that the diminution was not regular and gradual, but very
considerably different at different stages of the progress in the same direction, from which the inference seems conclusive that the earth is no more
in its breadth than in its length, perfectly spherical, and that the northern and southern hemispheres are not of dimensions precisely equal."
After this slight digression,. Mr. Adams proceeds to observe that.
"Considered as a whole, the established weights and measures o~
England are but the ruins of a system, the decays of which have been
often repaired with materials adapted neither to the proportion nor to
the principles of the original construction. The metrology of France
is a new and complicated machine, formed upon principles of mathematical precision, the adaptation of which to the uses for which it was
devised is yet problematical, and abiding, with questionable success,
the test of experiment.
"To the English system belong two different units of weight,