I am sensible that in addressing a letter to you, as the first political Character, in the United States; I might be accused of unjustifiable Confidince. But, I have been taught to believe, from your own writings, and Common fame; that you, unite the Philosopher with the States-man. And I am the more readely induc’d, to troble you, with the result of my rescearches for obtaining an univercal Standard of Measure; as yourself have employ’d at times, your thoughts on the same subject.

I Confess that on account of the obscurity of my situation in life, I have been able only, to obtain a superfical knowledge of your scheme of the Pendulum. which has incline’d me to raise objections to it. those objections, I have, myself been able, so far to remove, as very much to discorage me in offering mine to the Public. for, I Concider that if the first Philosophical Character, in Our Country, Cannot introduce an improvement, that is a good one; I may well despair of gaining patronage for mine, tho I may think it more iligible.

But I will troble you no farther with tiresom observations. If you have never thought of the same thing yourself; nor read a description of it in the Monthly Magezine, Publish’d in N. york, it will be new to you, and I hope suficently entertaining to plead my excuse for the troble I give you.

I take for granted, that we agree upon the principles of Central forces; that when a body of matter, is made to revolve round its Centre, it is acted upon by two powers opposed to each other. It is an establish’d theorem, that these powers are subject to Certain Laws, of variation; but if I am not mistaken, what is said of Centripetal force is only true in theory, and when reduce’d to practice will be found to be the same in all Cases where there is but one Common Centre; and that the point where the Centrifugal force acts. as supose you suspend a weight, by a line held in your hand, and Cause it to revolve round your hand, in a vertical direction, your hand will be the Centre; and the Centrifugal force incras’d with the velocity, either by increacing the length of the line or the number of periodic movements, or both. but the Centripetal force is neither more nor less than its own specific gravety, notwithstanding different velocities.

If you lay the weight on a whirling table, and Cause it to revolve horizontaly, it will be found in practice to have no Centripetal inclination at all.

But if you hang the weight pendulous and Cause, it to move spiraly, then what is said in theory is also true in practice—I have been the more minute on this subject, as my scheme, has been Condemn’d on account of my asserting that Centripetal force was invariable under the fore-mention’d Circumstances. Least you should anticipate me I will come imediately to the point.

If the Centripetal force is invariable, and the Centrifugal dependant on the velocity; then by fixing the revolutions arbitrary, we Cause the increace of Centrifugal force to depend on the distance from the Centre. And visa versa, if the distance is determinate, the force is as the periodic movements. so that if a distance is giveen, there is (tho yet unknown) a Certain rate of movement, necessary to produce, a Centrofugal power equal to the Centripetal, or gravety of the weight employ’d. This being once assertain’d in all future experiments, the distance will be governed by the number of revolutions. To Conceive a just idea of my scheme, it is necessary to use in imagination, a Common whirling table, in a groove on which, place a weight, at, supose one yard from the Centre; let a line pass from this through the Centre of the table; to this line under the table, suspend another weight equaly pondurous. sit the table in motion and increace the velocity of the weight on the table, untill it acquires Centrifugal force sufficent to preponderate the weight oppos’d to it. then note the times of its movement, to govern the distance in other experiments. I trust that the differance of magnetude in bodies of equal ponderocity, will not vary the result in diferant experiments as the same meterials Cannot be used at all times. but I Confess this is a subject I want advice upon, altho it appears Clear to me that it is no objection, at least it is none to the plan I had first invented. but My favourite scheme, may possebly be affected by it,

This I propose to your better judgement as most worthy attention being more simple. in this I would make use of liquid in stead of solid weights.

But the Machines, for realizeing these theorems, Cannot be explain’d within the Compass of this letter, and my principle object, is to ascertain if I Can your opinion, of the theoretical principles of my scheme. And Conclude that if it should be so fortunate as to meet your approbation, you will Condecend to lay your Commands on me, for an explaination of the machanical part.

I feel the impropriety of attempting [to] draw you into a Corespondance, with an obscure Mill-wright, but believe, if there is real merit in the discovery, the importance of the subject, will excuse the attempt. for I feel at the same time, that if this is new to you, it will not be me but my proposal you will Contemplate.

I am with unfeigned respect, for you; and sincear happiness, on the fair prospect, that the day is at hand, when the improvement of Arts & Manufactures shall take place of Political intrigue

Yours &c.