Having been informed of your Wish that a method should be devised for finding the Longitude of a Place without a Timepiece, the principal Datum of which should be a marked Meridian; I went into the Investigation nearly persuaded that the Problem could be solved in the precise manner originally suggested.—I find, however, that either I have not been able to seize on that View of the Subject which would lead to it; or that it cannot be so solved.

In the Attempt I was involved in a Difficulty which compelled me very laboriously to examine the Effects produced by almost every Element concerned in the Problem; in order to see which of them would best help me out. Each Conclusion commonly suggested other ways; & at length, after the rejection of three or four methods, I rested upon the one now submitted.

My Hope is that it may be useful, or give rise to other Solutions which will be so; and that it will be accepted as an Expression of my Desire to exert my portion of Faculties for the benefit of the Community.—

I am, Sir, With the utmost Respect, Your most obedient Servant,