To Thomas Jefferson from Andrew Ellicott, 11 May 1802
From Andrew Ellicott
Lancaster May 11th. 1802
Dear Sir
I ask pardon for not furnishing you sooner with the method I use for calculating the rising and setting of the heavenly bodies.
In almost every one of our popular books of navigation, we find the declinations of the principal fixed stars, with that of the sun for every day in the year, and a table of logarithms, which is all that is necessary for calculating the semi-diurnal arcs.
The rule is
Add the tangent of the sun’s or star’s declination, and the tangent of the latitude of the place of observation together, and take 10 from the index, the remainder will be the sine of an arch, which converted into time, and added to six hours if the declination is north, or taken from six hours if the declination is south, will give the semi-diurnal arch.
Example
Suppose on the first day of May the sun’s declination to be 14.° 57′, and the latitude of the place of observation to be 38.° 53″ north.1
| Then | Tangent of the declin. | log. | 9.42653 |
| + Tangt. latitude | log. | 9.90656 | |
| 19.33309 | |||
| − | 10. | ||
| equal the S. of 12.° 26″ | log. | 9.33309 |
To convert degrees, minutes, and seconds into time, divide by 15, and multiply the remainder, if any, by 4 and place the product one denomination lower, that is, if the remainder is degrees, call the product minutes and so on let the above 12.° 26′ be the
Example2
| 15) 12°. 26′ | |||
| 0.48 | |||
| 1.44 | |||
| 0.49.44 |
This 49′. 44″ added to 6 hours will give 6.h 49.′ 44″ for the semi-diurnal arc of that day, and be the time of sun setting, and taken from 12h will leave 5.h 10.′ 16″ for the time of sun rising.—
Suppose the declination of the sun to be 23.° 28′ north, and the latitude the same as above
| Then | Tangent 23.° 28.′ | log | 9.63761 | |
| + Tangent 38. 53 | log | 9.90656 | ||
| 19.54417 | ||||
| − 10 | 10. | |||
| equal the sine of 20.° 30′ | 9.54417 | then |
| 15) 20°. 30′ |
| 1. 20 |
| 2 |
| 1. 22 |
which added to 6.h will give 7.h 22′ for the semi-diurnal arc of that day, and be the time of sun setting, and taken from 12 will leave 4.h 38′ for the time of sun rising and when doubled will give 14.h 44′ for the length of the longest day in the City of Washington.
When the declination of the sun or star is south the sine found by the logarathims is to be deducted from 6.h to obtain the semi-diurnal arc, As for
Example
On the 1st. day of November when the sun’s declination is 14.° 25′ south,—the semi-diurnal arc will be had as follows.
| Sun’s decli S. | 14.° 25′ log. Tgt. | 9.41005 | ||
| + Latd. | 38.° 53 log. Tgt. | 9.90656 | ||
| 19.31661 | ||||
| − | 10. | |||
| S. | 11.° 58′ log. S. | 9.31661 | then |
| 15) 11°. 58′ | |
| 0. 44 | |
| 3.52 | |
| 0. 47.52 |
which taken from 6 hours will leave 5.h 12.′ 8″ for the semi-diurnal arc, and be the time of sun setting, and the semi-diurnal arc taken from 12.h will give3 6.h 47.′ 52″ for the time of sun rising,—and the semi-diurnal arc doubled will give 10.h 24.′ 16″ for the length of that day.—
This method may seem tedious to those not in the habit of making such calculations but after working a few examples it will be found to take so little time as to render an Almanac unnecessary and has moreover the advantage of being made for the precise latitude of the place.—The rising of the sun or stars in the U.S. will be accelerated nearly 3 minutes from the effect of refraction, and their setting equally retarded, which when the horizon is tolerably good may be allowed for.—But when the horizon is broken by hills the correction will be very difficult, as the effect of the altitude of the hills will be combined with that of the refraction.—
A few days ago I received a letter from the ingenious Mr. William Jones of London informing me that the new Planet lately discovered by Mr. Piazzi at Palerme has been observed in England by Doctr. Maskelyne Mr. Herschel and others; but he does not inform me in what part of the heavens it is to be seen.—
I expect to get my transit instrument set up in three, or four weeks, by which I shall be able to increase the number, and value of my observations.—I have with great difficulty, and patience, placed a reticule of spider’s web, (the first ever executed) in the focus of this instrument: and intend accomodating my large Telescope with a diaphram, to observe the eclipses of Jupiters satellites,—this precaution appears necessary, and is strongly recommended by de la Lande in a late work.—
The Legislature of this Commonwealth has complimented me with the use of the large reflecting Telescope, which was executed, and imported, for the purpose of observing the Transit of Venus in the year 1769,—it is much the best instrument of the kind upon this continent, and is sent to London to be put in complete repair, at public expense.—The duties of my office prevented me from doing it myself.—
Some time next month, I shall have another paper relating to the eclipses of Jupiter’s satellites ready for Delambre* one of the Secretaries of the National Institute, which I shall have to request my friend Mr. Madison to forward to our Minister Mr. Livingston at Paris—
I have the honour to be with the greatest respect, and esteem, your sincere friend
Andw; Ellicott
RC (DLC); at foot of text: “Thomas Jefferson President of the U.S. and of the A.P.S.”; with notations by TJ (notes 1–2 below); endorsed by TJ as received 31 May and so recorded in SJL. PrC (DLC: Ellicott Papers).
TJ was acquainted with WILLIAM JONES of London, the maker of precision instruments (Vol. 14:346, 411–12; TJ to Robert Patterson, 22 Mch. 1802).
The NEW PLANET was Ceres, first observed by Giuseppe PIAZZI early in 1801. Calculations of its orbit by Carl Friedrich Gauss enabled astronomers to find the object in the sky again later that year. Nevil MASKELYNE had been astronomer royal and director of the observatory at Greenwich since 1765. In 1802, William HERSCHEL, who had discovered the planet Uranus in 1781, coined the term “asteroid” for bodies such as Ceres that orbited the sun but were neither comets nor, in Herschel’s opinion, planets (, 5:299–300; 6:328–9, 334; 10:591–2; , s.v. “Maskelyne, Nevil”).
By a joint resolution approved 6 Apr., the Pennsylvania General Assembly agreed to have the REFLECTING TELESCOPE that had been obtained to observe the 1769 TRANSIT OF VENUS put into good repair and made available for Ellicott’s use (Acts of the General Assembly of the Commonwealth of Pennsylvania: Passed at a Session, Which was Begun and Held at the Borough of Lancaster on Tuesday the First Day of December, in the Year of Our Lord One Thousand Eight Hundred and One [Lancaster, Pa., 1802], 285).
Joseph Jérôme Le Français de Lalande’s comment about his protégé and collaborator, Jean Baptiste Joseph DELAMBRE, appeared in the third edition of Lalande’s text, Astronomie (, 4:14, 17n). Translated, it says in reference to Delambre’s birth at Amiens on 19 Sep. 1749 that “I put the date here because I consider it to mark an era in the history of astronomy.”
1. Here in margin TJ wrote: “lat. of Washn.”
2. Here in margin TJ wrote: “another method is, as every degree is 4.′ of time, and 15′ of a circle is 1′=60″ of time, multiply the degrees & minutes by 4. & the result will be minutes & seconds of time. thus 12°–26′ × 4 = 49′–44″.”
3. Word lacking in MS.