Thomas Jefferson Papers
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Enclosure: William Lambert’s Calculation of Monticello’s Longitude from Greenwich, 14 November 1811

Enclosure

William Lambert’s Calculation of Monticello’s Longitude from Greenwich

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 long2  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 long2 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 long2 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.

MS (DLC); written entirely in Lambert’s hand on five folio sheets; with one small hole.

1Manuscript: “numbe.”

Index Entries

  • astronomy; and calculations of Monticello’s longitude search
  • astronomy; and solar observations search
  • astronomy; solar eclipse of1806 search
  • Ferrer, José J. de; calculates longitude search
  • Kinderhook, N.Y.; longitude of search
  • Lalande, Joseph Jérôme Le Français de; and W. Lambert’s calculations search
  • Lambert, William; calculates Monticello’s longitude search
  • Maskelyne, Nevil; W. Lambert uses rules of search
  • Monticello (TJ’s estate); longitude of search
  • New York (state); longitude of Kinderhook search
  • Pease, Seth; and W. Lambert’s calculations search
  • sun; and calculation of longitude search
  • sun; annular eclipse of1811observed search