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 |
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′ |
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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.