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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–  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 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).

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

2Recto of second sheet ends here.

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

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

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

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

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

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

9Third sheet ends here.

10Number reworked from illegible number.

11Omitted 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