DIY History | Transcribe | Scholarship at Iowa | Theory of the astronomical transit instrument applied to the portable transit instrument Wuerdemann no.26: a compilation from various authorities, with original observations by Harry Edward Burton, 1903 | Theory of the astronomical transit instrument applied to the portable transit instrument Wuerdemann no. 26: a compilation from various authorities, with original observations by Harry Edward Burton, 1903, Page 74

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Theory of the astronomical transit instrument applied to the portable transit instrument Wuerdemann no.26: a compilation from various authorities, with original observations by Harry Edward Burton, 1903

Theory of the astronomical transit instrument applied to the portable transit instrument Wuerdemann no. 26: a compilation from various authorities, with original observations by Harry Edward Burton, 1903, Page 74

     Multiplying (1) by (square root of (pP)) gives the general weighted equation of condition, which is

(square root of (pP))(x + Aa +- Cc) = (square root of (pP)) b .   (2)

     The observations show that ∆t=-29s, approximately, so we shall assume ∆t[subscript]0[/subscript] = -29s .

     Now we shall compute and tabulate the values of b , (square root of (pP)) , and (b * square root of (pP)) for each star as follows:

[table]
Star   |   b   |   (square root of (pP))   |   (b * square root of (pP))   |   

(1)   |   +0.9   |   0.7   |   +6.63
(2)   |   0.0   |   0.9   |   0
(3)   |   -0.1   |   0.9   |   -0.09
(4)   |   +3.7   |   0.3   |   +1.11
(5)   |   +0.3   |   0.8   |   +0.24
(6)   |   +0.1   |   0.9   |   +0.09
(7)   |   -0.3   |   0.8   |   -0.24
(8)   |   -1.8   |   0.4   |   -0.72
(9)   |   -0.7   |   0.8   |   -0.56
(10)   |   -0.2   |   0.9   |   -0.18
[/table]

     Substituting in (2) the values of (square root of (pP)) , A , C , and [?b?] for each star we obtain the following equations:

(1) -0.21s a + 1.14s c + 0.7s x = +0.6s

(2) +0.20s a + 1.04s c + 0.9s x = 0

(3) +0.25s a + 1.02s c + 0.3s x = -0.1

(4) -0.61s a + 1.13s c + 0.8s x = +1.1

(5) +0.02s a + 1.06s c + 0.8s x = +0.2

(6) +0.15s a + 1.08s c + 0.9s x = +0.1

(7) +0.22s a - 0.9s c + 0.8s x = -0.2

(8) +1.14s a + 1.23s c + 0.4s x = -0.7

(9) +0.48s a - 0.8s c + 0.8s x = 
-0.6
(10) +0.25s a - 1.01s c + 0.9s x = -0.2

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Multiplying (1) by (square root of (pP)) gives the general weighted equation of condition, which is (square root of (pP))(x + Aa +- Cc) = (square root of (pP)) b . (2) The observations show that ∆t=-29s, approximately, so we shall assume ∆t[subscript]0[/subscript] = -29s . Now we shall compute and tabulate the values of b , (square root of (pP)) , and (b * square root of (pP)) for each star as follows: [table] Star | b | (square root of (pP)) | (b * square root of (pP)) | (1) | +0.9 | 0.7 | +6.63 (2) | 0.0 | 0.9 | 0 (3) | -0.1 | 0.9 | -0.09 (4) | +3.7 | 0.3 | +1.11 (5) | +0.3 | 0.8 | +0.24 (6) | +0.1 | 0.9 | +0.09 (7) | -0.3 | 0.8 | -0.24 (8) | -1.8 | 0.4 | -0.72 (9) | -0.7 | 0.8 | -0.56 (10) | -0.2 | 0.9 | -0.18 [/table] Substituting in (2) the values of (square root of (pP)) , A , C , and [?b?] for each star we obtain the following equations: (1) -0.21s a + 1.14s c + 0.7s x = +0.6s (2) +0.20s a + 1.04s c + 0.9s x = 0 (3) +0.25s a + 1.02s c + 0.3s x = -0.1 (4) -0.61s a + 1.13s c + 0.8s x = +1.1 (5) +0.02s a + 1.06s c + 0.8s x = +0.2 (6) +0.15s a + 1.08s c + 0.9s x = +0.1 (7) +0.22s a - 0.9s c + 0.8s x = -0.2 (8) +1.14s a + 1.23s c + 0.4s x = -0.7 (9) +0.48s a - 0.8s c + 0.8s x = -0.6 (10) +0.25s a - 1.01s c + 0.9s x = -0.2