Washington. Dec. 22. 04
I return you the inclosed paper with thanks for the communication of it. I have taken the liberty of copying the result, to wit, the longitude of our place. the method of finding the longitude by observing the occultation of a star has the merit of precision in the moments of immersion & emersion in proportion to the sensibility of the eye of the observer. but the calculations are lengthy and laborious, & therefore proportionably liable to error. at land, where we can have a long meridian, the passage of the moon over that can be observed with great accuracy, and the calculations, especially with what is supplied by the Nautical almanac, are shorter; and the observations may, with the same labour be oftener repeated.
When contemplating the mission of Capt. Lewis and others to procure us the geography of the rivers of Louisiana, a sense of the importance of some method of finding longitudes without the aid of any time piece, and by measuring angles alone with an accurate instrument, led me to reflections on the subject, which suggested to me the following method.
1. Observe the moon’s distance from your meridian at any moment, & her right ascension at the same moment (by her distance from a known star.) find from the Nautical almanac her distance from the meridian of Greenwich when she had that R.A. the sum or the difference, as the case may be, is your longitude from Greenwich. this method may be varied as follows.
2. Observe the moon’s passage over your meridian, and her R.A. at the same moment (by her distance from a star). find from the Nautical almanac the time at Greenwich when she had that ascension. her distance at that moment from the meridian of Greenwich, is your distance from it.
3. find from the Nautical Almanac the R.A. of the moon when she is on the meridian of Greenwich. watch the moment she attains that R.A. with you and take her then distance from your meridian. this is your longitude.
the 2d. & 3d. observations can be made once in the 24. hours & the 1st. repeated several times, so as to furnish an average worthy of a proportional confidence. I mentioned this idea to Baron Humbold, who said it was correct, & that I should find it in 3d. Delalande. I have not the book here; but I doubt not he has given full directions for practising it. On account of the missions still meditated I wish the merit of this process were ascertained by actual trial. my time does not permit my attempting it, even were not my familiarity with the process as much weakened as it is by so long an abstraction from studies of this kind. one of the best theodolites with two telescopes, & Nonius divisions to 1’ or 2’ would I presume be sufficient for the observations. the present season however is too rigorous to undertake observations which will bear delay till a milder season. Accept my salutations & best wishes
DLC: Papers of Thomas Jefferson.