In my last I informed you that I had invented a Machine which with great accuracy would Determine the Longitude, or departure from any given Meridian, and Promised to lay before you the System upon which the same is founded. I do myself the Honor to lay said System before you.

This System is founded on three of the Heavenly Bodies which have regular motions round their Axis or Orbits, and which they continue until they return to their first Meridians, and which is considered as the Period of the System. The whole work done by Observation, the Bodies being Subject to one General Law, Viz The Earth makes 1456 compleat revolutions in four Years, the Sun makes 4 in the same time round the Earth, the great Bear which has the Pointers for Leaders makes 4 in the same space of time round the Polar Star, during which Period we have 1461 days, or an interferrance, of Light and Darkness, which is one day more than the Earths and Suns compleat revolutions, which being the reason for adding 1 day each Leap Year to bring said Bodies to their first or primary Meridian. From which day I commence my calculations, and finding by taking the Sun on the Meridian and giving any time so as the great Bear become Visible, and taking the bearing of it’s pointers, or any other Star thereof making the Poll Star the Centre, we will find the Machine to Show their regular Progression by keeping in the same Meridian, and is fully calculated as Such. And by leaving the first Meridian, and going Westerly, And taking the Suns Meridian and Strictly adhering to the first given time, (which must be measured by a sand Glass made for that purpose to run 9, 10, 11 or 11½ Hours, which glass need not be made to run Strictly for Hours and Minutes, so it only runs Equally at all times), and then taking the bearing of the Pointers, the Pol Star the Centre, as afors[ai?]d, and looking to the Seals on the Machine and Seeing what the Index cut for my departure from the first Meridian, deducting one gratuation for every day from my first Observation, for their dayly progression, the remainder is the true departure in Time or degrees. If I go Easterly, what I want of the number of days from one Observation to the next, allowing one graduation on the Machine for every day will be the departure Eastward. Note that the same Machine and glass must always be wrought together as the will admit of no Seperation. And should any Observer be under an Error at any time, as soon as he can make good Observations the Machine will correct all former Errors, by observing the foregoing rules.

As the System and Machine are not calculated on any Ancient or Mondern Hypothisis that ever I could find, But by the Machine do find that I am able to reduce this System to a certainty, therefore think it my duty to lay the same before you, and request the favour that you would be pleased to lay the same before the Honorable Philosophical Society of Pennsylvania, making not the least doubt but meeting with your and their full approbation, as I have now in Possession two Machines one for Land and the other for the Sea, and am ready if thereto desired, fully to demonstrate the Same and prove the certainty of both. With the Highest Esteem I remain Honored Sir Your Obedient and most Humble Servant