The rival propositions

• I. The National assembly proposes actual mensuration of a considerable portion of a meridian (e.g. 9 degrees) bisected by the 45th. degree of lat. and terminated at each end by the sea. To1 these 9 degrees found by mensuration they will add the other 81.° to be found by calculation on the hypothesis that the earth is spheridical in it’s figure, and having thus the quarter of the circumference of the globe, they take it for their Unit, and dividing it decimally, the ten millionth part yeilds them a measure for common use very near 6. feet, their present toise.

  Objections.	1.	The inaccuracies of admeasurements over hills, vallies, rivers, and, in this instance, over high mountains, the Pyrenees.
  	2.	This gives them but 9.° or 1/10 of the quadrant. The other 9/10 they are to obtain by calculation, founded on hypothesis.
  	3.	The length of time, the apparatus, the number of Mathematicians to be employed (to wit 6. committees of 3. in each).
  	4.	That there is but one portion of a meridian to be found on all the globe involving all the conditions they require, which is exactly the one passing through France and a small portion of Spain from Dunkirk to Barcelona.
  	5.	If other nations adopt this unit, they must take the word of the French mathematicians for it’s length, or they must send their mathematicians into that country to make the admeasurement, whenever they wish either to establish or verify their standard.
  	6.	Spain has refused to permit the admeasurement to be made on her part of the meridian. So there is an end of it.

  • II. The Pendulum, and III. the Rod, vibrating seconds under the 45th. degree of latitude. The 45th. degree is assumed 1. because it’s pendulum is a mean between those vibrating in equal times under the equator and pole. 2. because it is a mean between any two taken under parallels equally distant on both sides. 3. it is a mean of the pendulums for every degree added together and divided by their number. 4. it is within a convenient distance and temperature for the inhabitants of both hemispheres. 5. because a very great portion of it lies in, or bordering on, the U.S.
    • The Disadvantages common to both the Pendulum and Rod.
      • 1. The variations in their length under different parallels of latitude.
      • Ans. This difference between 31.° and 45.° (our extremes) is but 1/679 of the whole pendulum. This difference, for any parallel, can be found by a calculation, on pretty certain principles, so as to reduce it to a very minute part of a very minute difference, consequently it is insensible and may be called nothing.
      • 2. Variations of length according to the degree of heat or cold.
      • Ans. This is got over by placing it in a cellar deep enough to be of the mean temperature of the earth. 20. feet deep suffices.

    • Advantages common to both Pendulum and Rod vibrating seconds.

      • 1. In every country their lengths are already well known in the measures of that country, and consequently, taken as our Unit, it is already2 the common measure of every country.
      • 2. If an actual verification of them be required, it can be had by the aid of a common house clock, by actual experiment under any parallel whatever, only supplying by calculation the small difference resulting from the difference of parallel.

Advantages peculiar to the Pendulum.
Not a single one.

Advantages peculiar to the Rod.

• 1. It avoids the impracticability of measuring the pendulum. This impracticability results from the difficulty in fact of finding the centre of oscillation of the bob, from which center the admeasurement is to be made. It can be easily found by calculation in a bob of a regular form. And it is from calculation and not measure that the length of the pendulum has been generally given to very minute fractions. When you come to actual mensuration no two mathematicians will put the point of their dividers on the same point of the bob.—This fact is so certain, that it is on this difficulty, and this alone, that Whitehurst was induced to propose his theory of two Pendulums, the ratio between the vibrations of which should furnish3 the standard.—But this in truth doubles the difficulty, for4 after you have got your two pendulums to vibrate in the given ratio, you have then to measure both in order to find your standard. The error from this source in the Rod, is but the 1/120 of what it is in the pendulum.
• 2. The aliquot part of the Rod (to wit ⅕ of 58.72 I.) gives 11¾ inches for our foot, which is but ¼ of an inch different from the present foot. Whereas the aliquot part of a pendulum (to wit ⅓ of 39.15 I.) gives 13. inches, which is an inch more than the present foot.—The foot is certainly the most important measure to preserve as nearly as possible.

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If the Rod be agreed to as the Standard, I do not foresee any objections to the decimal arrangement reported in the

Measures of	length
	surface
	capacity and

Weights.

except indeed the general objection of novelty and difficulty to the people, to which I need not mention the answers.

But an objection will be made to the Unit of coin, because different from what the legislature has adopted.

	dwt grs	dwt
The Dollar of Spain till 1728. had	11– 4 of pure metal to every 12 of mixed
from 1728. to 1772	10–21
since 1772.	10–17

The Dollar adopted is to have only	371¼ grs. pure metal
and	44¾ grs. alloy
which make	416  grs.

Here the alloy is nearly ⅛ of the pure metal. There is not a country under the sun which has adopted so base a mixture for it’s general standard. The alloy in England and France is less than 1/12 of the whole mass.

To bring back our Money Unit to a coincidence with the system of measures and weights, by making the Dollar weigh one ounce of rain water, let the pure metal remain at 371.25 grs. Troy, as now.

and add, of alloy, only                                 38.92

which makes the dollar of mixed metal                    410.17 grs. Troy, which is the new Ounce of rain water, as the Report proposes.

This raises our coin to a middle ground of purity between what it now is, and that of England and France. To wit

The mixed mass is to the alloy	in the dollar established as	9	to 1.
	in that I now propose	10½	to 1.
	in that of France and Engld.	12	to 1.

and it brings us back very near to the Spanish Dollar previous to 1772 which was the one we were generally acquainted with when we contracted our debt (for the subsequent ones could not then have come into general circulation) and was therefore the honest measure of that debt.

That Spanish Dollar had 22½ dwt. of alloy in the pound of mixed metal.

The one I now propose will have 22¾ dwt. alloy in the pound instead.5

Note. I have not Hamilton’s Report on the Mint. But I well remember that it proposed a *purer dollar than that adopted by the Senate. But if an attempt to alter the money unit, would endanger the making any additional enemies to the general system of weights and measures, would it not be better to omit altogether, now, whatever relates to coins? If the system passes, it will be easy hereafter to engraft the Money unit into it: and an opportunity will probably arise this Session, when the change [in the?] copper coinage shall be taken up, as I think it certainly will be.