Calculation of the longitude from Greenwich, of Monticello, in Virginia,
from the solar eclipse of the 17th of September, 1811.
Latitude 38.° 8′ Estimated Longitude, 5. h. 14. m. 0. sec = 78.° 30.′ 0.″ West.
Ratio of the equatorial diameter to the polar axis of the earth, 320 to 319.
| Constant Log. to reduce the latitude (320 to 319) |
9.9972814. |
| Lat. of the place 38.° 8.′ 0″ |
log. tangent |
9.8948918.
|
| Lat. of Monticello, reduced, 37.° 57.′ 33.″ 341. dec |
log. tangent |
9.8921732. |
| Constant log. to reduce the Moon’s equat. hor. parallax, for lat. and ratio, |
9.9994827. |
|
|
° ′ ″ dec. |
| Apparent time of beginning of the eclipse, 0. h. 13. m. 54.0 sec. |
= |
3.28.30.000 |
| Corresponding time at Greenwich 5. h. 27. m. 54. Sec. |
| Sun’s right ascension, |
|
174.23.10.067. |
| Right ascension of the meridian from the beginning of ♈︎, |
|
177.51.40.067 |
| do do from the beginning of ♑︎, |
|
92. 8.19.933 |
The operation at large, with several rules to find the altitude and longitude
of the nonagesimal.
Rule 1.
|
° ′ ″ dec. |
| Log. versed sine R.A. meridian from ♑︎, |
92. 8.19.933 |
|
10.0159134 |
| 〃 cosine lat. place, reduced, |
37.57.33.341 |
|
9.8967732. |
| 〃 Sine obliquity of the ecliptic |
23.27.42.690 |
|
9.6000342 |
| Corresponding natural number, A. |
3256273. |
(–3 from index) |
6.5127208. |
|
° ′ ″ |
| Lat. red. |
37.57.33.341 |
| obliq. ecl. |
23.27.42.690. |
|
61.25.16.031 |
Natural sine |
8781593. |
| Nat. cosine alt. nonag. 56.° 27.′ 32″ 783 dec. |
5525320. |
|
° ′ ″ |
| Log. cosecant R.A. meridian from ♑︎, |
92. 8.19.933 |
10.0003027. |
| 〃 Secant lat. place, reduced, |
37.57.33.341 |
10.1032268. |
| 〃 Sine altitude of the nonagesimal |
56.27.32.783 |
9.9209013. |
| 〃 Secant, long. of the nonag. from ♎︎, west, |
19. 2.19.000 |
10.0244308. |
|
180. 0. 0 – |
| Long. nonag. from beginning of ♈︎, |
160.57.41.000 |
Rule 2.
|
° ′ ″ |
| Log. cotangent lat. reduced, |
37.57.33.341 |
10.1078268 |
| 〃 sine R.A. meridian from ♈︎. |
177.51.40.067 |
8.5719609 |
tangent |
8.5722636. |
| 〃 tangent arch A. |
2.44.20.111 |
8.6797877 |
cosecant, |
11.3207087. |
| obliq. ecliptic |
+23.27.42.690. |
|
| arch B |
26.12. 2.801. |
° ′ ″ dec |
Sine |
9.6449484. |
tang. |
9.6920338 |
| Longitude nonag. from ♎︎, West, |
|
19. 2.18.840 |
|
9.5379207. |
cosecant, |
10.4865100. |
|
|
|
|
° ′ ″ |
tang. |
10.1785438. |
| do from beg. of ♈︎, |
|
160.57.41.160 |
alt. nonag. |
56.27.32.733. |
| ☞ |
R.A. meridian less than 180°, the sum of arch A, and obliq: eclip = arch B, otherwise, their difference.
The supplement of R.A. meridian might have been used, as producing the same result. |
Rule 3.
| ° ° ′ ″ ° ′ ″ |
|
° ′ ″ |
|
° ′ ″ dec |
| 90,–37.57.33.341.–23.27.42.690. |
= |
28.34.43.969 |
half, |
14.17.21.9845. |
(B) |
| 90,–37.57.33.341.+23.27.42.690. |
= |
75.30. 9.349. |
half |
37.45. 4.6745 |
(C) |
| Right ascension meridian from ♑︎, |
= |
92. 8.19.933. |
half |
46. 4. 9.9665 |
(D) |
|
|
|
° ′ ″ |
| Sine |
of |
C, |
37.45. 4.6745. ar. comp. |
0.2130817 |
ar. comp. cosine. |
0.1020016. |
| Sine |
|
B, |
14.17.21.9845 |
9.3923811 |
Cosine |
9.9863512. |
| Cotangent |
|
D, |
46. 4. 9.9665 |
9.9837838. |
cotangent |
9.9837838. |
| tangent |
|
E, |
21.13.28.984 |
9.5892466. |
tangent F, = |
10.0721366 |
|
|
|
|
|
|
° ′ ″ |
|
|
|
|
|
|
49.44.12.139 |
|
|
|
|
|
E, |
+21.13.28.984. |
|
|
|
|
|
from [. . .], East, |
70.57.41.123. |
|
|
|
|
|
|
+90. – – – |
| Longitude of the nonag. from beginning of ♈︎, |
160.57.41.123 |
|
|
° ′ ″ |
| Log. sine |
E, |
21.13.28.984. |
arith. comp. |
0.4412594. |
| 〃 Sine |
F, |
49.44.12.139 |
|
9.8825715. |
| 〃 tang. |
D, |
14.17.21.9845 |
|
9.4060298 |
| 〃 tang. |
C, |
23.13.46.392 |
|
9.7298607. |
|
|
2 |
|
|
56.27.32.784 |
altitude of the nonagesimal. |
Rule 4. (Mr Brinkley’s.)
|
° ′ ″ dec. |
| Log. cosine lat. place, reduced, |
37.57.33.341. |
9.8967732 |
Cotangent, |
|
10.1078268. |
| 〃 cosine R.A. meridian from ♈︎, |
177.51.40.067. |
9.9996973 |
Sine, |
|
8.5719609. |
| 〃 cosine arch I, |
141.59.22.529. |
9.8964705 |
Cotangent, |
|
8.6797877. |
|
|
|
Arch II, |
|
87.15.39.889. |
|
|
Ob. Ecl. |
– |
23.27.42.690 |
|
|
Arch III |
|
63.47.57.199 |
|
° ′ ″ dec. |
| Log. sine arch I |
141.59.22.529 |
9.7894430 |
tangent |
9.8929724.
|
| 〃 Sine arch III. |
63.47.57.199 |
9.9529146 |
Cosine, |
9.6449485 |
| 〃 cosine alt. nonagesimal, |
9.7423576 |
tangent, |
9.5379209 |
| ° ′ ″ dec |
|
|
° ′ ″ |
| = 56.27.32.742. |
|
|
–19. 2.18.869. |
|
|
|
180. 0. 0. – |
| Longitude nonag. from ♈︎, |
160.57.41.131 |
| Alt. nonagesimal. |
Longitude nonagesimal. |
|
|
° ′ ″ |
|
° ′ ″ |
| By Rule |
1 |
56.27.32.783 |
|
160.57.41.000 |
|
2 |
56.27.32.783 |
|
160.57.41.160. |
|
3 |
56.27.32.784 |
|
160.57.41.123 |
|
4 |
56.27.32.742 |
|
160.57.41.131 |
| Mean, |
|
56.27.32.773. |
Mean, |
160.57.41.103. |
|
|
|
|
° ′ ″ dec. |
| Moon’s true longitude |
173.12.40.980 |
| Longitude of the nonagesimal, |
60.57.41.103. |
| Moon’s true distance from the nonagesimal. (East) |
12.14.59.877 |
|
′ ″ |
|
″ |
| Moon’s equatorial horizontal parallax, |
54. 9.366 |
= |
3249.366 |
log. |
3.5117986 |
| Constant log. for latitude and ratio |
|
|
|
|
9.9994827. |
| Moon’s hor. parallax, reduced |
54. 5.498. |
|
3245.498 |
|
3.5112813. |
| Sun’s hor. parallax, Sept. 17 |
–8.700 |
| hor. parallax ☽ à ☉, |
53.56.798 |
= |
3236.798. |
log. |
3.5101156 |
|
° ′ ″ |
| Log sine altitude of the nonag. |
56.27.32.773 |
|
|
|
9.9209013 |
| Moon’s true lat. north, asc. |
0.32.47.332 |
ar. comp. cosine, |
0.0000197 |
|
|
|
|
(a) |
3.4310366 |
| Moon’s true dist. à nonag. (East) |
12.14.59.877 |
|
(b) |
9.3266985 |
| 1st approximation, |
a+b, |
9.32.447 |
log. |
(c) |
2.7577351 |
| Sine |
b+c, |
12.24.32.324 |
|
(d) |
9.3322129 |
| 2d approximation, |
a+d, |
9.39.761 |
log. |
(e) |
2.7632495 |
| Sine |
b+e, |
12.24.39.638 |
|
(f) |
9.3322829 |
| 3d approximation, |
a+f, |
9.39.855 |
log. |
(g) |
2.7633195. |
| Sine |
b+g, |
12.24.39.732 |
|
(h) |
9.3322838 |
| 4th approximation, |
a+h |
9.39.856 |
log. |
(i) |
2.7633204 |
| Sine |
b+i, |
12.24.39.733 |
|
(k) |
9.3322838 |
| Parallax in long: |
a+k |
9.39.856 |
log. |
(l) |
2.7633204. |
Other rules to find the parallax in longitude.
|
° ′ ″ |
| Log. cosine ☽’s true latitude. |
0.32.47.332 |
|
9.9999803. |
| 〃 cosine true dist à nonag. |
12.14.59.877 |
+ |
9.9899974 |
|
Log. (A) |
|
9.9899777 |
natural number, |
9771870. |
|
° ′ ″ |
| hor. parallax ☽ à ☉, |
0.53.56.798 |
Sine |
8.1956726 |
| altitude of the nonag. |
56.27.32.773 |
Sine, |
9.9209013 |
|
(B) |
|
8.1165739. |
natural num. |
–0130790. |
| Corresponding log. of C |
|
9.9841257 |
(C) |
9641080. |
| arith. comp. |
|
0.0158743 |
| Cosine Moon’s true latitude |
9.9999803. |
| Sine Moon’s true dist. à nonag |
° ′ ″ |
|
9.3266985 |
| tang. ☽’s apparent dist. à nonag. |
12.24.39.710. |
|
9.3425531 |
| true dist do |
12.14.59.877. |
| Parallax in longitude, |
9.39.833. |
|
° ′ ″ |
| Log. sine hor. parallax ☽ à ☉, |
0.53.56.798. |
Sine |
8.1956726. |
| 〃 Sine alt. nonagesimal. |
56.27.32.773. |
Sine, |
9.9209013. |
|
|
(x) |
8.1165739. |
| 〃 Cosine ☽’s true dist. à nonag. |
9.9899974. |
|
|
(y) |
8.1065713 |
nat: number, |
0127812 |
| Natural cosine Moon’s true latitude |
9999546. |
| Corresponding log. (z) |
9.9943931 |
(z) |
9871734. |
|
ar. comp. |
|
0.0056069 |
|
log. (x) |
|
8.1165739. |
| Log. sine ☽’s true dist. à nonagesimal, |
9.3266985 |
| tangent parallax in longitude 9.′ 39.″ 834 |
7.4488793 |
| Parallax in long. |
apparent dist. ☽ à nonag. |
|
|
′ ″ |
|
|
° ′ ″ |
|
| Rule |
1 |
9.39.856 |
|
|
12.24.39.733 |
|
2 |
9.39.833 |
|
|
12.24.39.710 |
|
3 |
9.39.834 |
|
|
12.24.39.711 |
| Mean |
|
9.39.841. |
Mean |
|
12.24.39.718. |
For the Moon’s parallax in latitude.
Rule 1. (M. de la Lande’s.)
|
° ′ ″ |
| hor. parallax ☽ à ☉, |
0.53.56.798 |
|
Sine, |
8.1956726. |
| altitude of the nonagesimal |
56.27.32.773. |
|
Cosine, |
9.7423575 |
| Moon’s true dist. à nonag |
12.14.59.877. |
ar. |
comp. sine |
0.6733015 |
| 〃 apparent distance do |
12.24.39.718 |
|
Sine |
9.3322837 |
| first part parallax in lat. |
0.30.11.532 |
|
Sine, |
7.9436153 |
| Moon’s true latitude |
0.32.47.332. |
|
Sine |
7.9794460. |
| 〃 true dist. à nonag |
12.14.59.877. |
ar. |
co. sine |
0.6733045. |
| 〃 parallax in long. |
0. 9.39.841 |
|
sine |
7.4487832 |
| true dist. à nonag. + par. in long⁄2 |
12.19.49.797. |
|
cosine |
9.9898644 |
| Second part |
–0. 0.25.464 |
|
sine – |
6.0914951 |
| First part |
0.30.11.532 |
| Parallax in lat. approximated |
29.46.068 |
|
Sine |
7.9374675. |
| Moon’s true latitude |
32.47.332 |
| 〃 apparent lat. approxim |
3. 1.264. |
|
Cosine |
9.9999998 |
| Parallax in latitude, (correct) |
0.29.46.067 |
|
Sine |
7.9374673 |
2. Dr Maskelyne’s rule
| hor. parallax ☽ à ☉, |
0.53.56.798 |
Sine, |
8.1956726. |
| altitude nonagesimal |
56.27.32.773 |
cosine |
9.7423575. |
| ☽’s apparent lat. (found above) |
0. 3. 1.265 |
cosine |
9.9999998 |
| 1st part parallax in lat. |
0.29.48.383 |
Sine |
7.9380299 |
| hor. parallax ☽ à ☉, |
0.53.56.798 |
Sine |
8.1956726. |
| altitude of nonagesimal |
56.27.32.773 |
Sine |
9.9209023 |
| Moon’s apparent lat. |
0. 3. 1.265 |
Sine |
6.9438888 |
| true dist. à nonag + par. in long.⁄2 |
12.19.49.797 |
cosine |
9.9898644 |
| Second part |
0. 0. 2.316 |
Sine |
5.0503271. |
| first part |
0.29.48.383 |
| Parallax in latitude |
0.29.46.067 |
Rule 3. (Mr Seth Pease’s.)
|
° ′ ″ |
| hor. parallax ☽ à ☉ |
0.53.56.798 |
Sine, |
8.1956726. |
| altitude nonagesimal |
56.27.32.773 |
Cosine, |
9.7423575 |
Nat. number1 |
|
0.32.47.332 |
|
7.9380301. |
0086702. |
| Natural Sine Moon’s true lat. |
0095377 |
| Corresponding log |
6.9382695. |
Nat. no |
0008675. |
| Moon’s true dist. à nonag |
Cosecant, |
10.6733015. |
| 〃 apparent distance |
Sine |
9.3322837. |
| 〃 true latitude |
′ ″ |
Secant |
10.0000197 |
| 〃 apparent lat. |
3. 1.259. |
tangent |
6.9438744 |
| true lat |
32.47.332 |
|
|
° ′ ″ |
| Parallax in lat |
29.46.073 |
|
By rule 1. |
0.29.46.067. |
|
|
|
2 |
0.29.46.067. |
|
|
|
3. |
0.29.46.073. |
|
|
|
Mean, |
0.29.46.069. |
|
° ′ ″ dec |
| Moon’s true longitude |
173.12.40.980 |
| 〃 Parallax in longitude, (mean result) |
+9.39.841. |
| 〃 apparent longitude do |
173.22.20.821. |
| Sun’s longitude |
173.53. 1.967. |
| difference of apparent longitude ☉ and ☽, |
30.41.146. |
| Moon’s true latitude, North, |
0.32.47.332. |
| 〃 Parallax in latitude (mean result) |
– 0.29.46.069. |
| 〃 apparent latitude, north, |
0. 3. 1.263. |
|
|
° ′ ″ dec |
| Apparent time of the end of the eclipse, 3. h 29. m. 4. sec. 4 d |
= |
52.16. 6.000 |
| Corresponding time at Greenwch 8. h. 43. m 4. sec 4 Sun’s Right ascension, |
|
174.30.28.191 |
| Right ascension of the meridian from beginning of ♈︎, |
|
226.46.34.191. |
| ditto from the beginning of ♑︎, (west) |
|
43.13.25.809 |
Rule 1.
|
° ′ ″ |
| Log. versed sine R.A. meridian from ♑︎. |
43.13.25.809. |
(–3 from index) |
6.4334758. |
| 〃 Cosine latitude place, reduced, |
37.57.33.341 |
|
9.8967732. |
| 〃 Sine obliquity of the ecliptic, |
23.27.42.690 |
|
9.6000342 |
| corresponding natural number |
– 851693 |
(A) |
5.9302832. |
|
° ′ ″ |
| Lat. reduced |
37.57.33.341 |
| Obliq: eclip |
23.27.42.690. |
| Sum, |
61.25.16.031 |
Natural sine |
8781593. |
| Nat. cosine altitude nonag. |
37.° 32.′ 3.″ 047. |
7929900. |
|
° ′ ″ |
| Log. cosant R.A. meridian from ♑︎ |
43.13.25.809 |
|
10.1644044. |
| 〃 Secant lat. place, reduced, |
37.57.33.341 |
|
10.1032268 |
| 〃 Sine altitude of the nonagesimal |
37.32. 3.047 |
|
9.7847845 |
| 〃 Secant long. nonag. from ♎︎, (East) |
27.35.13.818 |
|
10.0524157 |
|
+180. 0. 0 – |
| Longitude of the nonag. from ♈︎ |
207.35.13.818. |
Rule 2.
|
° ′ ″ dec. |
| Lat. place, reduced, |
37.57.33.341 |
cotangent |
10.1078268. |
| R.A. meridian from ♎︎, |
46.46.34.191 |
sine |
9.8625391 |
tang. |
10.0269434 |
| arch A |
43. 2.48.214. |
tang. |
9.9703659 |
cosec. |
10.1658372. |
| obliq. eclip. |
–23.27.42.690. |
| (B) |
19.35. 5.524 |
Sine |
° ′ ″ |
|
9.5253076. |
|
|
|
27.35.13.823. |
tang. |
9.7180882 |
|
|
|
180. 0. 0 |
| Longitude of the nonag. |
207.35.13.823. |
|
° ′ ″ |
| arch B |
19.35. 5.524 |
tangent |
9.5511894. |
|
27.35.13.823 |
cosecant, |
10.3343274. |
| altitude of the nonag. |
37.32. 3.046 |
tangent |
9.8855168. |
Rule 3.
| Sine of C, |
ar. comp. |
|
0.2130817 |
cosine, ar. co. |
|
0.1020016. |
| Sine B, |
|
|
9.3923811 |
cosine |
|
9.9863512. |
| Cotangent D,= |
21.° 36.′ 42.″ 9045 |
|
10.4021199 |
cotangent |
|
10.4021199. |
|
tang. |
|
10.0075827 |
tang. |
|
10.4904727. |
|
|
|
° ′ ″ |
|
|
E. |
45.30. 0.571. |
|
E. |
72. 5.13.222 |
|
|
|
|
|
E. |
45.30. 0.571 |
| E, ar. comp. sine |
0.1467568 |
|
|
90 – – |
| F, Sine |
9.9784201 |
Long. nonag. |
|
207.35.13.793 |
| B tangent |
9.4060298 |
| G. tang. 18.° 46.′ 1.″ 522 |
9.5312067 G × 2 = 37.° 32.′ 3.″ 044. |
|
altitude nonag. |
Rule 4.
|
° ′ ″ |
| Log. cosine lat. reduced, |
37.57.33.341 |
9.8967732 |
co-tangent |
10.1078268 |
| 〃 cosine R.A. mer. from ♎︎, |
46.46.34.191 |
9.8355957 |
Sine |
9.8625391. |
| 〃 cosine arch I |
57.19.06.484 |
9.7323689 |
cotang |
9.9703659 |
|
|
|
|
° ′ ″ |
|
|
|
Arch II. |
46.57.11.786. |
|
|
|
Obl. ecl. |
+23.27.42.690 |
|
|
|
Arch III, |
70.24.54.476 |
|
° ′ ″ |
| arch I |
57.19. 6.484. |
Sine |
9.9256695. |
tangent |
10.1927806 |
| arch III |
70.24.54.476. |
Sine |
9.9741183 |
cosine |
9.5253076 |
| alt. nonag. |
37.32. 3.000 |
|
9.8992678 |
|
|
|
|
|
|
tang |
9.7180882 |
|
|
|
|
|
° ′ ″ |
|
|
|
|
|
27.35.13.823 |
|
|
|
|
|
+180 |
|
|
|
|
Long. nonag. |
207.35.13.823 |
|
|
Altitude nonag. |
Longitude nonag. |
|
|
° ′ ″ |
|
By rule 1 |
37.32.3.047 |
|
207.35.13.818. |
|
2 |
37.32.3.046 |
|
207.35.13.823 |
|
|
37.32.3.046 |
|
3 |
|
|
207.35.13.793 |
|
4 |
|
|
207.35.13.823 |
|
|
|
Mean result |
207.35.13.814. |
| Longitude of the nonagesimal |
207.35.13.814. |
| Moon’s true longitude |
174.49.20.531. |
| ☽’s true distance à nonagesimal, (west) |
32.45.53.283. |
| Moon’s equatorial horizontal parallax 54.′ 10.″ 179 = 3250.″ 179. log. |
3.5119073. |
| Constant logarithm for latitude and ratio |
9.9994827 |
| Moon’s horizontal parallax, reduced |
3246.310 |
3.5113900. |
| Sun’s horizontal parallax |
–8.700 |
| horizontal parallax, ☽ à ☉, |
3237.610 log. |
3.5102245. |
|
° ′ ″ |
| Sine altitude of the nonagesimal |
37.32. 3.046 |
|
9.7847845 |
| ar. comp. cosine Moon’s true lat. north |
0.41.38.115 |
|
0.0000318 |
|
|
(a) |
3.2950408. |
| Sine Moon’s true distance à nonagesimal, |
32.45.53.283 |
(b) |
9.7333511 |
| 1st approximation, |
a+b, |
17.47.559 |
(c) |
3.0283919. |
| Sine |
b+c, |
33.3.40.842 |
(d) |
9.7368240 |
| 2d approximation, |
a+d |
17.56.130 |
(e) |
3.0318648 |
| Sine |
b+e |
33.3.49.413 |
(f) |
9.7368517. |
| 3d approximation |
a+f, |
17.56.199 |
(g) |
3.0318925. |
| Sine |
b+g |
33.3.49.482 |
(h) |
9.7368519 |
| 4th approximation, |
a+h |
17.56.200 |
(i) |
3.0318527. |
| Sine |
b+i, |
33.3.49.483 |
(k) |
9.7368519 |
| Parallax in long. |
a+k |
17.56.200 |
(l) |
3.0318527. |
Rule 2.
|
° ′ ″ |
| Log. cosine Moon’s true latitude, |
0.41.38.115 |
|
9.9999682. |
| 〃 cosine ☽’s true dist. à nonag. |
32.45.53.283 |
|
9.9247439. |
|
|
|
9.9247121. |
Nat. num. 8408375. |
| Sine, hor. parallax ☽ à ☉, |
0.53.57.610 |
|
8.1957816. |
| Sine altitude of the nonagesimal, |
37.32. 3.046 |
|
9.7847845 |
|
|
|
7.9805661. |
nat. num. 0095624. |
|
Corresponding log. |
|
9.9197448 |
8312751. |
|
arith. comp. |
|
0.0802552 |
| Cosine Moon’s true latitude |
|
|
9.9999682. |
| Sine Moon’s true dist. à nonagesimal |
° ′ ″ |
|
9.7333511. |
| tangent ☽’s apparent dist. |
33. 3.49.457. |
|
9.8135745. |
| true dist. |
32.45.53.283. |
| Parallax in longitude |
– 17.56.174 |
Rule 3.
|
° ′ ″ |
| hor. parallax ☽ à ☉, |
0.53.57.610, |
Sine |
|
8.1957816. |
| Altitude nonagesimal |
37.32. 3.046. |
Sine |
|
9.7847845 |
|
|
(x) |
|
7.9805661 |
| Moon’s true distance à nonag. |
32.45.53.283 |
Cosine, |
|
9.9247439 |
|
|
(y) |
|
7.9053100 |
nat: number, 0080410 |
| Natural cosine Moon’s true latitude |
|
|
|
9999267. |
| corresponding log. |
(z) |
|
9.9961656. |
nat num. 9918857. |
| arith. comp |
|
|
0.0035354 |
|
|
(x) |
|
7.9805661. |
| Moon’s true distance à nonagesimal Sine |
|
|
9.7333511. |
|
′ ″ |
| tangent parallax in longitude |
17.56.160 |
|
|
7.7174556. |
|
|
Parallax in longitude |
☽’s apparent dist. à nonagesimal. |
|
|
′ ″ |
|
° ′ ″ dec |
|
| Rule |
1 |
17.56.200 |
|
33.3.49.483. |
|
2 |
17.56.174 |
|
33.3.49.457. |
|
3 |
17.56.160 |
|
33.3.49.443. |
| Mean, |
|
17.56.178 |
Mean, |
33.3.49.461 |
|
|
|
° ′ ″ |
|
|
Moon’s true longitude |
174.49.20.531. |
|
|
Parallax in longitude, (☽ West of nonag.) |
– 0.17.56.178. |
|
|
Moon’s apparent longitude |
174.31.24.353. |
|
|
Sun’s longitude |
174. 0.58.817. |
| difference of apparent longitude, ☽ East of ☉, |
30.25.536 |
For the Moon’s parallax in latitude.
Rule 1. (M. de la Lande’s)
|
° ′ ″ |
| hor. parallax ☽ à ☉, |
0.53.57.610 |
|
sine |
8.1957816. |
| altitude of the nonagesimal |
37.32. 3.046 |
|
cosine |
9.8992677 |
| ☽‘s true dist. à nonagesimal |
32.45.53.283 |
ar. |
comp. sine |
0.2666489. |
| 〃 apparent dist. do |
33. 3.49.461 |
|
Sine |
9.7368518. |
| 1st part parallax in latitude, |
0.43. 8.133 |
|
Sine |
8.0985500. |
| Moon’s true latitude |
0.41.38.115 |
|
Sine |
8.0831707. |
| 〃 true dist. à nonag. |
32.45.53.283 |
ar. |
comp. sine |
0.2666489. |
| 〃 Parallax in longitude |
0.17.56.178 |
|
Sine |
7.7174570 |
| 〃 true dist. à nonag. + par. in long⁄2 |
32.54.51.372 |
cosine |
9.9240127 |
| Second part parallax |
– 0. 0.20.217 |
|
Sine |
5.9912953 |
| First part do |
0.43. 8.133 |
| Parallax in lat. approximated |
0.42.47.916 |
| Moon’s true latitude, north |
0.41.38.115 |
| 〃 apparent lat. south, |
1. 9.801. |
(co-sine nearly equal to radius.) |
The approximated parallax and apparent lat. in this case, may be considered as correct.
Rule 2. (Dr Maskelyne’s)
|
° ′ ″ dec |
| hor. parallax ☽ à ☉ |
0.53.57.610 |
|
Sine |
8.1957816. |
| altitude of the nonagesimal |
37.32. 3.046 |
|
Cosine |
9.8992677 |
| Moon’s apparent lat. S (as above) |
0. 1. 9.801 |
ar. |
comp. cosine, |
0.0000000 |
| 1st part parallax in latitude, |
0.42.47.353 |
|
Sine |
8.0950493. |
| hor. parallax ☽ à ☉ |
0.53.57.610 |
|
Sine |
8.1957816. |
| altitude of the nonagesimal |
37.32. 3.046 |
|
Sine |
9.7847845 |
| ☽’s apparent lat. South (as above) |
0. 1. 9.801 |
|
Sine |
6.5294365. |
| true dist. à nonag + par. in long⁄2 |
32.54.51.372 |
|
Cosine |
9.9240127 |
| Second part parallax |
0. 0. 0.560 |
|
Sine |
4.4340153. |
| First part (☽’s apparent lat. S.) |
+0.42.47.353. |
| Parallax in latitude, |
0.42.47.913. |
Rule 3. (Mr Seth Pease’s.)
|
° ′ ″ |
| hor. parallax ☽ à ☉, |
0.53.57.610 |
|
Sine |
8.1957816. |
nat. number |
| altitude of the nonagesimal, |
37.32.03.046. |
|
cosine |
9.8992677 |
|
|
|
|
8.0950493. |
0124465.6. |
| Moon’s true latitude, north |
0.41.38.115 |
|
Natural sine |
–0121109.1 |
| corresponding log. |
|
6.5258867 (South) |
0003356.5. |
| Moon’s true dist. à nonag. |
co-secant |
|
10.2666489 |
| 〃 apparent dist. do |
Sine |
|
9.7368518. |
| 〃 true latitude |
Secant |
|
10.0000318. |
|
′ ″ |
|
6.5294192. |
| tangent, ☽’s apparent lat. south, |
1. 9.798. |
| ☽’s true latitude, north |
+41.38.115 |
| Parallax in latitude |
42.47.913. |
| Parallax in latitude |
|
|
° ′ ″ dec. |
| Rule |
1 |
0.42.47.916 |
|
2 |
0.42.47.913. |
|
3 |
0.42.47.913 |
|
° ′ ″ dec |
| Mean |
|
0.42.47.914 |
Mean Moon’s apparent S. |
0. 1. 9.799 |
| at the beginning of the eclipse north, |
+0. 3. 1.263. |
| Moon’s motion in apparent lat. during the transit, |
4.11.062. |
|
′ ″ |
| difference of apparent longitude, at the beginning |
30.41.146 |
| ditto do at end of eclipse |
+30.25.536 |
| ☽’s motion in apparent longitude à ☉, during the transit |
61. 6.682. |
The Moon’s distance from the meridian at the beginning of the eclipse was 3.° 52.′ 35.″ 344 dec
declination north 3.° 11.′ 56.″ 974 dec at the end, the Moon’s horary angle was
51.° 15.′ 38.″ 415 dec declination, north, 2.° 41.′ 53.″ 065 hence, by calculation allowing for the
spheroidal figure of the Earth, according to the ratio 320 to 319.—
|
|
° ′ ″ dec. |
| The |
Moon’s true altitude at the beginning, was |
55. 3.33.493 |
| |
Parallax in altitude |
0.31.22.998. |
|
apparent altitude, exclusive of refraction |
54.32.10.495. |
| 〃 |
true altitude, at the end of the eclipse |
31.27.31.269. |
|
Parallax in altitude |
0.46.31.833. |
|
apparent altitude, exclusive of refraction, |
30.40.59.436. |
An allowance of –1.″ 623. dec. for irradiation of the Sun’s light, and –2.″ 977,
for inflexion of the Moon’s light, as stated by Mr Ferrer, in his calculation of the longitude of
Kinderhook, in the State of New-York, from the solar eclipse of June 16th 1806, will be made
in the present case.
| At the beginning. |
End of the Eclipse. |
|
′ ″ |
|
|
|
′ ″ |
| Sun’s semidiameter, |
15.57.227. |
|
|
Sun’s semid. |
15.57.250 |
| Irradiation of light |
– 1.623. |
′ ″ |
|
Irrad: of light |
– 1.623 |
|
|
15.55.604 |
|
|
|
15.55.627 |
| ☽’s horiz. semidiam. |
14.45.455. |
|
|
☽’s hor. sem. |
14.45.726 |
| augmentn for altitude, |
+11.533. |
|
|
augment. |
+ 7.253 |
| Inflexion of light |
– 2.977 |
|
|
Inflexion, |
– 2.977 |
|
|
14.54.011. |
|
|
|
14.50.002 |
| Sum of ☉ and ☽’s semidiameters, |
30.49.615. |
|
Sum of semidiameters, |
30.45.629. |
| corrected. |
|
|
corrected. |
|
″ |
| Moon’s motion in apparent lat. |
251.062 |
log. + 10. = |
12.3997810. |
| 〃 motion in apparent long. |
3666.682 |
log. |
3.5642733 |
| angle of inclination, |
tangent, 3.° 55.′ 1.″ 181. |
8.8355077. |
| Moon’s motion in apparent longitude |
3666.″ 682. log |
3.5642733. |
| angle of inclination |
3.° 55.′ 1.″ 181 ar. comp. cos. |
0.0010156 |
| chord of transit, or line of |
 |
61.′ 15.″ 267 = 3675.″ 267 |
3.5652889. |
| ☽’s path in the apparent orbit. |
|
″ |
| Chord of transit |
3675.267. |
ar. co. log. |
6.4347111. |
| Sum of semidiameters |
3695.244 |
log |
3.5676432 |
| difference of ditto |
3.986 |
log |
0.6005373. |
|
(x) 4.007 |
log |
0.6028916. |
| |
|
|
|
″ |
|
3675.267 + 4.007 |
= 3679.274 |
half = |
1839.637. |
|
3675.267 – 4.007 |
= 3671.260. |
half = |
1835.630 |
| ″ |
| 1839.637 |
log |
|
3.2647321. |
| 1849.615. |
(Sum of Semrs at beg.) ar. co. log. |
|
6.7329187. |
| cosine angle of conjunction 5.° 57.′ 14.″ 500 |
|
9.9976508 |
|
° ′ ″ dec. |
| Angle of conjunction, at the beginning of the eclipse, |
5.57.14.500. |
| Angle of inclination of the ☽, in the apparent orbit, |
–3.55. 1.181. |
| Central angle, at the beginning |
2. 2.13.319. |
| 1835.630 |
log. |
|
3.2637851 |
| 1845.629. |
ar. co. log. |
|
6.7338556. |
|
° ′ ″ |
| Cosine angle of conjunction, at the end |
5.58. 0.500 |
|
9.9976407. |
| Angle of inclination, |
+3.55. 1.181 |
|
9.53. 1.681. |
| Sum of Semidiameters at beginning |
1849.″ 615. dec log. |
3.2670813. |
| Central angle |
2.° 2.′ 13.″ 319. cosine, |
9.9997255 |
| diff. apparent long. ☉ & ☽, 30.′ 48.″ 446 = 1848.″ 446 |
3.2668068. |
| |
| Sum of Semidiameters at the end of eclipse, 1845.″ 629. log. |
3.2661444. |
| Central angle, at end of the eclipse, 9.° 53.′ 1.″ 681. cosine |
9.9935062 |
| diff. apparent long. ☉ and ☽, 30.′ 18.″ 237 = 1818.″ 237 |
3.2596506. |
|
′ ″ |
| diff. of apparent long. at the beginning, |
+30.48.446. |
| Parallax in longitude, |
+ 9.39.841 |
| True difference long. ☉ and ☽, at the beginning |
+40.28.287 |
| |
′ |
| diff. of apparent longitude at the end |
– 30.18.237 |
| Parallax in longitude, |
– 17.56.178 |
| True difference longitude ☉ and ☽, at the end, |
– 48.14.415. |
The hourly velocity in longitude ☽ à ☉, at a middle time between the beginning of the eclipse
and the estimated time of true conjunction at Monticello, was 27.′ 5.″ 7572 dec, and between
the end and true conjunction, 27.′ 6.″ 3006. dec
As 27.′ 5.″ 7572 dec. to one hour or 60 minutes, so is 40.′ 28.″ 287 to 1. h. 29. m. 37. Sec. 084. dec.
which added to 0. h. 13. m. 54. sec the apparent time of beginning, gives 1. h. 43. m 31. Sec. 084 dec.,
the time of true conjunction at Monticello, by the beginning of the eclipse.
As 27.′ 6.″ 3006 dec., to one hour or 60 minutes, so is 48.′ 14.″ 415. to 1. h. 46. m. 47. Sec. 114. dec
which subtracted from 3. h. 29. m. 4. Sec. 400. dec., gives 1. h. 42. m. 17. sec. 286. dec., the time of true
conjunction, by the end of the eclipse.
|
|
h. m. Sec. dec |
|
By the beginning |
1.43.31.084 |
|
〃 the end, |
1.42.17.286 |
| Mean, |
True conjunction at Monticello, |
1.42.54.185. |
|
Do at Greenwich, |
6.57.14.915 |
|
Longitude in time, west, |
5.14.20.730. |
= |
78.° 35.′ 10.″ 950. dec. |
|
City of Washington,
|
|
|
November 14th 1811. |
William
Lambert.
