National Institute of Informatics - Digital Silk Road Project
Digital Archive of Toyo Bunko Rare Books

SPECIMEN COPY OF COMPUTATION OF ONE DAY'S
Computation of Longitude fr
At Kashghar (Yangi-Shahr) Station, on

Moon { West of Meridian.
Lower Limb observed. Lat. N. = φ = 39 24 32 Assumed

Ref.
No. No. of observation (Mean of F. L. and F. R.) 1 2 3

(1) Chronometer Time of observation ... 10 47 55·2 10 52 31·3 10 57 26·2
(2) Correction ... – 22 20·4 22 20·4 22 20·4
(3) Local Mean Time (Ast. D.) = 28 days ... + 10 25 34·8 10 30 10·9 10 35 5·8
(4) Approx. Gr. Mean Time = (3) + L₁ = 28 days + 5 20 34·8 5 20 10·9 5 30 5·8
(5) ☽'s observed Zenith Distance ... = ζ₁ 46 56 38 47 43 14 48 33 30
(6) Refraction (for B and T) = r ... – 57 59 1 0
(7) ☽'s Semi-diameter at (4) from N. A. = S ... – 16 2 16 2 16 2
(8) From Table I Δ S ... – 11 11 11
(9) (5) + (6) + (7) + (8) = ζ₂ 46 41 22 47 28 0 48 18 17
(10) ☽'s Horizontal Parallax at (4) from N. A. = π' + 58 45 58 44 58 44
(11) From Table II Δ π' + 5 5 5
(12) Log. π₁' = log. (π + Δ π)' ... { 3·54777 3·54765 3·54765
(13) Log. ζ₂ ... { 1·86192 1·86740 1·87314
(14) (12) + (13) = log. (π₁ sin ζ₂)' ... { 3·40969 3·41505 3·42079
(15) π₁ sin ζ₂ ... 42 49 43 20 43 55
(16) (9) − (15) = ζ₂ − π₁ sin ζ₂ = ... ζ₁ 45 58 33 46 44 40 47 34 22
(17) ☽'s Declination at (4) from N.A. = δ 11 57 8 11 58 15 11 59 27
(18) Δδ from Table III ... + 15 15 15
(19) (17) + (18) = δ + Δ δ = δ₁ ... + 11 57 23 11 58 30 11 59 42
(20) φ − (19) = (φ − δ₁) ... 27 27 9 27 26 2 27 24 50
(21) (16) + (20) = ζ₁ + (φ − δ₁) = 2 σ₁ ... 73 25 42 74 10 42 74 59 12
(22) (16) − (20) = ζ₁ − (φ − δ₁) = 2 σ₂ ... 18 31 24 19 18 38 20 9 32
(23) σ₁ ... 36 42 51 37 5 21 37 29 36
(24) σ₂ ... 9 15 42 9 39 19 10 4 46
(25) Log. sin σ₁ ... 1·7765729 1·7803585 1·7843813
(26) Log. sin σ₂ ... 1·2066735 1·2245847 1·2430716
(27) Log. sec φ ... 0·1120256 0·1120256 0·1120256
(28) Log. sec δ₁ ... 0·0095255 0·0095554 0·0095876
(29) (25) + (26) + (27) + (28) = log. sin 2½ t' 1·1047975 1·1265242 1·1490661
(30) Log. sin ½ t ... 1·5523988 1·5632621 1·5745331
(31) t (in arc) ... + 41 48 18 42 54 56 44 6 8
(32) S. T. Gr. Mean Noon on 28 days (see (4)) ... 18 28 5·8 18 28 5·8 18 28 5·8
(33) Local Mean Time (same as (3)) ... 10 25 34·8 10 30 10·9 10 35 5·8
(34) Acceleration for (4) ... 52·7 53·4 54·2
(35) (32) + (33) + (34) = local S. T. of observation = θ 4 54 33·3 4 59 10·1 5 4 5·8
(36) t (in time) deduced from (31) ... + 2 47 13·2 2 51 39·7 2 56 24·5
(37) ☽'s Right Ascension or AR = θ − t ... 2 7 20·1 2 7 30·4 2 7 41·3
(38) Greenwich Mean Time for (37) from N. A. ... 5 21 1·1 5 25 47·8 5 30 51·2
(39) (38) − (33) = Approx. Long. = L₂ ... – 5 4 33·7 5 4 23·1 5 4 14·6
(40) (39) − L₁ = L₂ = L₁ ... = β' + 26·3 36·9 45·4
(41) At (38) change in ☽A R for increment of 1ᵐ = λ' + 2·155 2·155 2·156
(42) Do. Do. Deen. Do. = β' + 14·621 14·615 14·609
(43) Log. cos φ (see (27)) ... 1·8880 1·8880 1·8880
(44) Log. sin t (see (31)) ... 1·8239 1·8331 1·8426
(45) Log. cosec ζ₁ (see (16)) ... 0·1432 0·1377 0·1319