Note: this document has content that may require expanded/print view for best results (icons above right)

Thomas Jefferson’s Astronomical Calculations, 5-11 February 1811

Astronomical Calculations

1811. Feb. 5
	H ′	° ′		° ′ ″
	12–14	36–42	=	36–24–3 8	S.	59356
	3– 8½	22–30	=	22–11–37	S.	37774
						21582
	4–29	19– 1	=	18–42–10
	H ′ ″					° ′
time elapsd	2–54–30			Lat. by acct		37–42–	it’s Log.	10.10170
½ ti. elapsd	1–27–15			⊙’s declin Greenw		15–56–54
				80° W		3–52
						15–53– 2	Log.	10.01691
				Log. ratio				.11861
				Log. of diff. of Sines (21582)				4.68939
	½ elapsd ti.	1–27–15		Log. of ½ elapsed time				.43015
		3–59–40		Middle time correspd				5.23815
		2–32–25		Log. rising				.20965
				Log. ratio				.11861
				Log. of 1234				.09104
				59356 S. of greatr alt.
				60590. S. of 37°–18 meridional Alt. of ⊙

Note the ⊙’s decln is here stated as at Noon. Qu should it have been adapted to the hour? it is not done in the examples of the R.T. & may probably be neglected.1

1811 Feb. 7.

		observed		true alt.
	H ′ ″	° ′ ″		° ′ ″
I.	9–17–15	23–32–30	=	23–14– 6. S. 39450	decln P.F.	15°–12′–28″
II.	10–45–	33–37–30	=	33–19–51. S 54947	Log. Sect	10.01548
III:	12–14– 0	37–19–30	=	37– 2– 9 S 60231	37°–42′ Log	10.10170
IV	1–44– 0	32–50–30	=	32–32–48 S. 53799	Log. ratio	.11718
V	3–20–45	20–50– 0	=	20–31–18 S 35056

I.II.	1–27 45	el. ti	54947	Log. ratio		.11718
			39450	Log remr		4.19004
	43–52	half do	15497	Log.		71973
				H ′ ″
	2– 8–30	middle ti				5.02695
	1–24–38	time from Noon		Log. risg		3.82908
						11718
				Log. 5151.		3.71190
				54947.
				60098	S. 36°–50′	Meridn alt.

	H ′
II.	10–45	54947		Log. ratio	.11718
IV	1–44	53799
	2–59 el. ti	1148		Log. remr	3.05994
	1–29′–30″			Log.	.41945
	4 –30				3.59657
	1 25				3.83246
			Log. 5191		11718
			54947		3.71528
			60138	S. of 36°–58′ Merid. alt.

	H ′
II.	10–45	54947			Log. ratio	.11718
V.	3–20–45	35056
	4–35–45 el. ti	19891				4.29863
	2–17–52				Log ½ el. ti	.24733
	55–10					4.66314
	1–24–42.	ti. from N.			Log. rising	3.82908
						11718
			5151			3.71190
			54947
			60098	S. of 36°–56′ merid. alt.

	H ′ ″
IV	1–44– 0	53799			Log. ratio	.11718
V	3–20–45	35056
	1–36–45	18743				4.27277
	48–22	half el. ti.			Log.	.67916
	2–23–40					5.06911
	1–35–18	ti. frm N.			Log. rising	3.93082
			6511			11718
			53799			3.81364
			60310	S. of 37°–6′ Merid. Alt.

	H ′ ″
I.	9–17–15	39450			Log. ratio	.11718
IV.	1–44–	53799
	4–26–45	14349			Log.	4.15685
	2–13–22	half el. ti.			Log.	.26003
	39–20					4.53406
	1–34– 2					3.91876
						11718
			6332			3.80158
			53799
			60131	S. 36°–58′ Merid. alt.2

	H ′ ″	° ′ ″
I.	9–17–15	23–14–6	S.	39450	Log. ratio	.11718
III.	0–14– 0	37– 2–9	S.	60231
	2–56–45			20781		4.31765
	1–28–22	half el. ti				.42487
	1–24–50					4.85970
	3–32	ti frm N.			Log. rising	1.06673
				8903		11718
				60231		.94955
				69134	S. 43°–44′ Merid. Alt.

	H ′	° ′ ″
II.	10–45	33–19–51	S.	54947	Log. ratio	.11718
III.	12–14	37– 2– 9	S.	60231
	1–29			5284		3.72296
	44–30	half el. ti.				.71455
	41–20				Log. mid. ti.	4.55469
	3–10				Log. rising	.97980
				7288
				60231		.11718
				67519	S. of 42°–28′ Merid. Alt.	.86262

the falsity in the result of these two operations shews that Noon must not be the time of either observn; and consequently not very near to Noon.

					Log. Sec. 37°–42′=			10.10170
					Log. Sec. ⊙’s decln			10.01368
			observd		Log. ratio			.11538
		H ′ ″	° ′
	<~~Feb. 9.~~>	<~~2–24–15~~>	<~~22–30~~>		° corrected
I	Feb. 10.	9–13	25–24–30	=	25– 6–25	S	42433
II		10– 5	31–32– 3	=	31–14–22	S.	51860
III		11– 1	36–35–	=	36–17–38	S.	59190
IV.		1–21	34–37	=	34–19–33	S.	56390
V		2– 2	30–31–30	=	30–13–49	S	50339
VI.		2–58	20–31	=	20–12–24	S	34541

Feb. 11.
	H ′		° ′
I.	10–3	Observd Alt.	32– 8	=	31–50–24	S.	52755	<~~Log S. lat~~>	<~~.10170~~>
II	11–9–20		37–27–30	=	37–10	S.	60414		<~~.02601~~>
								<~~Log rat~~>	<~~.11671~~>
								<~~do decln~~>	<~~.01475~~>
								Log. sec.	.10170
								do decln	.01305
								Log. rat.	.11475

error of instrumt
	′ ″
Feb. 11.	8–3–30
14.	0–5
	8–6–30
	0–5
	8–53

Feb. 10. 1811.

	H ′	° ′ ″
I.	9–13	25– 6–25	S.	42433	Log. ratio	.115384
III.	11– 1	36–17–38	S.	59190
				16757	Log.	4.22419
	1–48
	54	½ el. ti			Log.	.63181
	1–51–40					4.97138
	51–40				Log. risg	3.39816
						11538
				24145		3.382786
				59190

				61644	S. of 37°–3′ merid alt. ⊙ 7

	H ′	° ′ ″
I	9–13	25– 6–25	S.	42433	Log. ratio	.11538
IV	1–21	34–19–33	S.	56390
	4– 8			13957	Log.	4.14479
	2– 4	½ eld ti			Log	.28816
	40–46					4.54833
	1–23–14				Log. rising	3.81453
						11538
				5002		3.69915
				56390
				61392	S. 37°–52′ Mer. alt.

	H ′	° ′ ″
II.	10– 5	31–14–22	S.	51860	Log. ratio	.11538
III.	11– 1	36–17–38	S.	59190
	–56			7330	Log	3.86510
	28	½ el. ti.			Log	.91411
	1–32–24					4.89459
	1– 4–24				Log. risg	3.59351
						11538
				3007		3.47813
				59190
				62197	S. 38°–27′ Mer. alt.

	H	° ′ ″
II	10– 5	31–14–22	S.	51860		Log. ratio	.11538
IV	1–21	34–19–33	S.	56930
	3–16			4530			3.65610
	1–38	H. el. ti.				Log.	.38227
	16–20						4.15375
	1–22–40					Log. risg	3.80855
				4934			11538
				56390			3.69317
				61324	S. 37–49

Feb. 10.
° ′ ″
37–58–43.		Noon
<~~37– 3–~~>		<~~I.III.~~>
37–52		I.IV
<~~38–27~~>		<~~II.III~~>
37–49		II.IV
37–42		II.V
<~~35– 4~~>	<~~IV.VI.~~>
37–56	III.IV.
37–56	III.V
<~~37–14~~>	<~~III.VI.~~> 8

	Feb. 10	° ′ ″
II.	10– 5	31–14–22	S.	51860	Log. ratio	.11538
V.	2– 2	30–13–49	S	50339
	3–57			1521		3.18213
	1–58–30	H. el. ti.			Log.	.30599
	4–36				Log. mid	3.60350
	1–53–54				Log. risg	4.08393
						11538
				9301		3.96855
				51860
				61161	S. 37°–42′ Merid. Alt.

	H ′	° ′ ″
IV.	1–21	34–19–33	S.	56390		Log. ratio	.11538
VI.	2–58	20–12–24	S.	34541
	1–37			21849		Log.	4.33945
	48–30	H. el. ti.				Log	67769
	2–50–53					Log. mid. ti.	5.13252
	2– 2–23					Log. risg	4.14374
							11536
				1067			4.02836
				56390
				57457	S. 35°–4′	Merid. Alt

	H ′	° ′ ″
III.	11– 1	36–17–38	S.	59190		Log. ratio	.11538
IV.	1–21	34–19–33.	S	56390
	2–20			2800		Log.	3.44716
	1–10	H. el. ti.				Log.	.52186
	13–54″					Log. mid. ti	4.08440
	56– 6					Log. risg	3.47432
							.11538
				2285.		Log.	3.35894
				59190
				61475	S. 37°–56	Mer. alt.

	H ′
III.	11– 1	36–17–38	S.	59190		Log. rat	.11538
V	2– 2	30–13–49	S.	50339
	3– 1			8851		Log.	3.94699
	1–30–30.	H. el. ti				Log	.41488
	34–30					Log. mid. ti	4.47725
	56					Log. risg	3.47282
				2277	61467. S. 37°–56′	Mer. alt.	11538
				59190	61467. S. 37°–56′	Mer. alt.	3.35744

	H ′	° ′ ″
III.	11– 1	36–17–58	S.	59190		Log. ratio	.11538
VI.	2–58	20–12–24	S	34541
	3–57			24649		Log.	4.39182
	1–58–30	H. el. ti				Log	.30599
	1–16– 0					Log. Mid. ti	4.81319
	42–30					Log risg	3.23414
							11538
				1314			3.11876
				59190
				60504	S. 37–14 Mer. alt.9

	Observns of Feb. 11. 1811.
	H ′	° ′ ″
I.	10– 3	31–50–24.	S.	52755		Log. ratio	.1147510
II.	11– 9–20	37–10– 0	S.	60414
	1– 6–20			7659		Log.	<~~3.88417~~>
	33–10	H. el. ti.				Log.	<~~.84160~~>
						Log. mid	<~~4.84188~~>
						Log. risg	<~~3.34250~~>
							<~~11611~~>
				<~~1680~~>			<~~3.22579~~>
				60414
				<~~63096~~>	<~~S. 38°–23′ Mer Alt.~~>

(the above Log. rat. being wrong, made the work false)11				Log. ratio	.11475
it is here corrected
I. and II.				Log.	3.88487
	33–10			Log. H. el. ti	84100
	1–20–50			log. mid. ti.	4.83992
	47–40				3.33347
					11475
					3.21872
		1655
		60414
		62069	S 37°–22′

MS (MHi [sheets 1, 3–4] and ViU: TJP-ER [sheet 2]); written entirely in TJ’s hand on sheets of varying sizes, two of them parts of reused address covers to TJ.

The calculations given above are evidently related to thirteen noontime observations of the sun’s altitude that TJ made at Poplar Forest between 31 Jan. and 26 Feb. 1811. He averaged the results to calculate a latitude of 37–22–26 for this plantation and then discovered an error and corrected it to 37–19–56 (1811 Poplar Forest observations, MS in TJ’s hand forming part of his Weather Memorandum Book, 1802–16, MHi). TJ may have been inspired to make these observations by the similar data he periodically received from William Lambert. He used an address cover from Lambert for the first set of calculations printed above (Lambert to TJ, 23 July, 4, 19 Sept., 8 Dec. 1809).

1. First sheet ends here, with part of address cover from Lambert on verso.

2. Recto of second sheet ends here.

3. Preceding six lines written perpendicularly at foot of verso of second sheet, which ends here.

4. Number reworked from illegible number and recopied above the line by TJ for clarity.

5. Number reworked from illegible number and recopied above the line by TJ for clarity.

6. Number reworked from illegible number and recopied below the line by TJ for clarity.

7. Numbers reworked from illegible number and line recopied by TJ for clarity.

8. Preceding eleven lines written perpendicularly at foot of recto of third sheet, which is part of a reused address cover to TJ reading only “Free.”

9. Third sheet ends here.

10. Number reworked from illegible number.

11. Omitted opening parenthesis editorially supplied.

Index Entries

astronomy; and calculations of Poplar Forest’s latitude search
geography; and TJ’s calculations of latitude search
Greenwich Observatory, England; and prime meridian search
Jefferson, Thomas; Writings; Astronomical Calculations search
Lambert, William; and latitude calculations search
Lambert, William; and prime meridian search
latitude; calculations for Poplar Forest search
Poplar Forest (TJ’s Bedford Co. estate); astronomical observations at search
Poplar Forest (TJ’s Bedford Co. estate); latitude of search
sun; and astronomical calculations search

You Are Looking At

Source Project: Jefferson Papers
Title: Thomas Jefferson’s Astronomical Calculations, 5-11 February 1811
Author: Jefferson, Thomas
Date: 5–11 February 1811

Reference

Cite as: “Thomas Jefferson’s Astronomical Calculations, 5-11 February 1811,” Founders Online, National Archives, https://founders.archives.gov/documents/Jefferson/03-03-02-0274. [Original source: The Papers of Thomas Jefferson, Retirement Series, vol. 3, 12 August 1810 to 17 June 1811, ed. J. Jefferson Looney. Princeton: Princeton University Press, 2006, pp. 361–367.]