Thomas Jefferson’s Calculations for a Horizontal Sundial at Poplar Forest, [ca. 23 August 1811]
Calculations for a Horizontal Sundial at Poplar Forest
[ca. 23 Aug. 1811]
Hour lines of horizontl dial for Lat 37°–22′–26″1
| Hour | horary angle | Logarithm Tangt | Hourline2 |
| H ′ | ° ′ | ° ′ ″ | |
| 0–5. | 1–15 | 8.1220547 | 0–45–32 |
| 10 | 2–30 | 8.4232915 | 1–31– 5 |
| 15 | 3–45 | 8.5997278 | 2–16–41 |
| 20 | 5– 0 | 8.7251502 | 3– 2–24 |
| 25. | 6–15. | 8.8226832 | 3–48–12 |
| 30. | 7–30 | 8.9026275 | 4–34– 8 |
| 35 | 8–45 | 8.9704786 | 5–20–15 |
| 40 | 10– 0 | 9.0295171 | 6– 6–33 |
| 45 | 11–15 | 9.0818602 | 6–53– 5 |
| 50 | 12–30 | 9.1289536 | 7–39–52 |
| 55. | 13–45 | 9.1718296 | 8–26–55 |
| I. XI. | 15– 0 | 9.2112508 | 9–14–18 |
| 5. | 16–15 | 9.2477974 | 10– 2– 0 |
| 10. | 17–30 | 9.2819207 | 10–50– 5 |
| 15. | 18–45 | 9.3139797 | 11–38–35 |
| 20. | 20– 0 | 9.3442643 | 12–27–31 |
| 25. | 21–15 | 9.3730126 | 13–16–54 |
| 30. | 22–30 | 9.4004227 | 14– 6–48 |
| 35. | 23–45 | 9.4266615 | 14–57–15 |
| 40. | 25– 0 | 9.4518709 | 15–48–15 |
| 45. | 26–15– | 9.4761734 | 16–39–53 |
| 50. | 27–30 | 9.4996751 | 17–32–10 |
| 55. | 28–45. | 9.5224691 | 18–25– 7 |
| II. X. | 30– 0 | 9.5446378 | 19–18–49 |
| 5. | 31–15. | 9.5662546 | 20–13–15 |
| 10. | 32–30 | 9.5873857 | 21– 8–31 |
| 15. | 33–45 | 9.6080910 | 22– 4–38 |
| 20. | 35– 0 | 9.6286940 | 23– 2–24 |
| 25. | 36–15 | 9.6484388 | 23–59–34 |
| 30. | 37–30 | 9.6681789 | 24–58–30 |
| 35. | 38–45 | 9.6876894 | 25–58–28 |
| 40. | 40– 0 | 9.7070119 | 26–59–30 |
| 45. | 41–15 | 9.7261863 | 28– 1–41 |
| 50. | 42–30 | 9.7452509 | 29– 5– 8 |
| 55. | 43–45 | 9.7642427 | 30– 9–37 |
| III. IX. | 45– 0 | 9.7831984 | 31–15–30 |
| 5. | 46–15. | 9.8021541 | 32–22–49 |
| 10. | 47–30. | 9.8211459 | 33–31–19 |
| 15. | 48–45 | 9.8402105 | 34–41–23 |
| 20. | 50– 0 | 9.8593849 | 35–52–57 |
| 25. | 51–15 | 9.8787074 | 37– 6– 4 |
| 30. | 52–30 | 9.8982179 | 38–20–48 |
| 35. | 53–45 | 9.9179580 | 39–37–12 |
| 40. | 55– 0 | 9.9379716 | 40–55–20 |
| 45. | 56–15 | 9.9583058 | 42–15–14 |
| 50. | 57–30 | 9.9790111 | 43–36–58 |
| 55. | 58–45 | 10.0001414 | 45– 0–33 |
| IV. VIII. | 60– 0 | 10.0217590 | 46–26– 5 |
| 5. | 61–15 | 10.0439277 | 47–53–34 |
| 10. | 62–30 | 10.0667217 | 49–23– 3 |
| 15. | 63–45 | 10.0902234 | 50–54–33 |
| 20. | 65– 0 | 10.1145259 | 52–28– 7 |
| 25. | 66–15 | 10.1397353 | 54– 3–45 |
| 30. | 67–30 | 10.1659741 | 55–41–28 |
| 35. | 68–45 | 10.1[ ]35842 | 57–21–17 |
| 40. | 70– 0 | 10.2221325 | 59– 3–10 |
| 45. | 71–15 | 10.2524171 | 60–47– 7 |
| 50. | 72–30 | 10.2844761 | 62–33– 5 |
| 55. | 73–45 | 10.3185994 | 64–21– 3 |
| V. VII. | 75– 0 | 10.3551459 | 66–10–56 |
| 5. | 76–15 | 10.3945672 | 68– 2–41 |
| 10. | 77–30 | 10.4374432 | 69–56–12 |
| 15. | 78–45 | 10.4845366 | 71–51–24 |
| 20. | 80– 0 | 10.5368796 | 73–48– 8 |
| 25. | 81–15 | 10.5959182 | 75–46–19 |
| 30. | 82–30 | 10.6637693 | 77–45–46 |
| 35. | 83–45 | 10.7437136 | 79–46–22 |
| 40. | 85– 0 | 10.8412466 | 81–47–56 |
| 45. | 86–15 | 10.9666690 | 83–50–14 |
| 50. | 87–30 | 11.1431053 | 85–53– 9 |
| 55. | 88–45 | 11.4443421 | 87–56–29 |
| VI. | 90– 0 | infinite | 90– 0– 03 |
As Radius :
to the Sine of the latitude ::
so is the tangt of the horary angle :
to the tangt of ∠ of hourline with ye meridn
MS (MHi); entirely in TJ’s hand; undated; written on both sides of a small scrap; one number illegible. Tr (ViU: TJP); entirely in TJ’s hand; undated; written on one side of a small scrap; lacking heading, middle two columns, and concluding section; with TJ’s notation perpendicular to text: “Hour lines for an horizontal dial for Lat. 37.°–22′–26″”; enclosed in TJ to Charles Clay, 23 Aug. 1811.
1. MS: “37″–22′–26″’.”
2. Tr: “horizontl angle.”
3. Tr ends here, as does recto of MS.