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itself as an element of measure。 The motion of the earth on its axis
from noon to noon of a mean solar day； has been divided from time
immemorial； and by very general consent； into 86；400 portions of time
called seconds。 The length of a pendulum vibrating in one of these
portions； is determined by the laws of nature； is invariable under
the same parallel； and accessible independently to all men。 Like a
degree of the meridian； indeed； it varies in its length from the
equator to the pole； and like it； too； requires to be reduced to a
mean。 In seeking a mean in the first case； the 45th degree occurs
with unrivalled preferences。 It is the mid…way of the celestial ark
from the equator to the pole。 It is a mean between the two extreme
degrees of the terrestrial ark； or between any two equi…distant from
it； and it is also a mean value of all its degrees。 In like manner；
when seeking a mean for the pendulum； the same 45th degree offers
itself on the same grounds； its increments being governed by the same
laws which determine those of the different degrees of the meridian。
In a pendulum loaded with a Bob； some difficulty occurs in
finding the centre of oscillation； and consequently the distance
between that and the point of suspension。 To lessen this； it has
been proposed to substitute for the pendulum； a cylindrical rod of
small diameter； in which the displacement of the centre of
oscillation would be lessened。 It has also been proposed to prolong
the suspending wire of the pendulum below the Bob； until their
centres of oscillation shall coincide。 But these propositions not
appearing to have received general approbation； we recur to the
pendulum； suspended and charged as has been usual。 And the rather as
the the laws which determine the centre of oscillation leave no room
for error in finding it； other than that minimum in practice to which
all operations are subject in their execution。 The other sources of
inaccuracy in the length of the pendulum need not be mentioned；
because easily guarded against。 But the great and decisive
superiority of the pendulum； as a standard of measure； is in its
accessibility to all men； at all times and in all places。 To obtain
the second pendulum for 45 degrees it is not necessary to go actually
to that latitude。 Having ascertained its length in our own parallel；
both theory and observation give us a law for ascertaining the
difference between that and the pendulum of any other。 To make a new
measure therefore； or verify an old one； nothing is necessary in any
place but a well…regulated time…piece； or a good meridian； and such a
knowledge of the subject as is common in all civilized nations。
Those indeed who have preferred the other element； do justice
to the certainty； as well as superior facilities of the pendulum； by
proposing to recur to one of the length of their standard； and to
ascertain its number of vibrations in a day。 These being once known；
if any accident impair their standard it is to be recoved by means of
a pendulum which shall make the requisite number of vibrations in a
day。 And among the several commissions established by the Academy of
Sciences for the execution of the several branches of their work on
measures and weights； that respecting the pendulum was assigned to
Messrs。 Borda； Coulomb & Cassini； the result of whose labors；
however； I have not learned。
Let our unit of measures then be a pendulum of such length as
in the latitude of 45 degrees； in the level of the ocean； and in a
given temperature； shall perform its vibrations； in small and equal
arcs； in one second of mean time。
What ratio shall we adopt for the parts and multiples of this
unit？ The decimal without a doubt。 Our arithmatic being founded in
a decimal numeration； the same numeration in a system of measures；
weights and coins； tallies at once with that。 On this question； I
believe； there has been no difference of opinion。
In measures of length； then； the pendulum is our unit。 It is a
little more than our yard and less than the ell。 Its tenth or dime；
will not be quite 。4 inches。 Its hundredth； or cent； not quite 。4 of
an inch； its thousandth； or mill； not quite 。04 of an inch； and so
on。 The traveller will count his road by a longer measure。 1；000
units； or a kiliad； will not be quite two…thirds of our present mile；
and more nearly a thousand paces than that。
For measures of surface； the square unit； equal to about ten
square feet； or one…ninth more than a square yard； will be generally
convenient。 But for those of lands a larger measure will be wanted。
A kiliad would be not quite a rood； or quarter of an acre； a myriad
not quite 2 1/2 acres。
For measures of capacity； wet and dry；
The cubic Unit = 。1 would be about 。35 cubic feet； 。28 bushels
dry； or 7/8 of a ton liquid。
Dime = 。1 would be about 3。5 cubic feet； 2。8 bushels； or about
7/8 of a barrel liquid。
Cent = 。01 about 50 cubic inches； or 7/8 of a quart。
Mill = 。001 = 。5 of a cubic inch； or 2/3 of a gill。
To incorporate into the same system our weights and coins； we
must recur to some natural substance； to be found everywhere； and of
a composition sufficiently uniform。 Water has been considered as the
most eligible substance； and rain…water more nearly uniform than any
other kind found in nature。 That circumstance renders it preferable
to distilled water； and its variations in weight may be called
insensible。
The cubic unit of this = 。1 would weigh about 2；165 lbs。 or a
ton between the long and short。
The Dime = 。1 a little more than 2。 kentals。
Cent = 。01 a little more than 20 lb。
Mill = 。001 a little more than 2 lb。
Decimmil = 。0001 about 3 1/2 oz。 avoirdupoise。
Centimmil = 。00001 a little more than 6 dwt。
Millionth = 。000001 about 15 grains。
Decimmillionth = 。0000001 about 1 1/2 grains。
Centimmillionth = 。00000001 about 。14 of a grain。
Billionth = 。000000001 about 。014 of a grain。
With respect to our coins； the pure silver in a dollar being
fixed by law at 347 1/4 grains； and all debts and contracts being
bottomed on that value； we can only state the pure silver in the
dollar； which would be very nearly 23 millionths。
I have used loose and round numbers （the exact unit being yet
undetermined） merely to give a general idea of the measures and
weights proposed； when compared with those we now use。 And in the
names of the subdivisions I have followed the metrology of the
ordinance of Congress of 1786； which for their series below unit
adopted the Roman numerals。 For that above unit the Grecian is
convenient； and has been adopted in the new French system。
We come now