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 85

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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 85

We now determine c from the equation

[cc1]c + [cd1]x = [cn1] .

Solving for c we get 

c = ([cn1] - [cd1]x) / ([cc1]) .

lg [cd1] =     0.45367
lg x =           9.09341
                  --------------
lg x [cd1] =  9.54708


x [cd1] =            0.3524
[cn1] =               2.4051
                       --------------
[cn1] - x[cd1] =  2.0527     :

lg 2.0527 = 0.31233
lg [cc1] =     1.03879
                 -------------
lg c =          9.27354

c =            +0.1877

We determine a from the equation

a = ([an] - [ac]c - [ad]x) / [aa] .

lg [ac] = 9.45515[repeating decimal 5]
lg c = 9.27354
        -------------
lg [ac]c = 8.72869
[ac]c = 0.0535
[ad]x = 0.1819
           ----------
[ac]c + [ad]x = 0.2354
[an] = -1.9830
         ------------
[an] - [ac]c - [ad]x = -2.2184

lg [ad] = 0.16143
lg x = 9.09341
        ------------
lg [ad]x = 9.25984
[ad]x = 0.1819

lg -2.2184 = 0.34604n
lg [aa] = 0.33895
             -------------
lg a = 0.00709n
a = -1.0165 .

   We have therefore for the results of our observations, Δt = Δt[subscript]0[/subscript] + x = -29s + 0.1s = -28.9s ; 

c = +0.19s and a = -1.0s .

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We now determine c from the equation [cc1]c + [cd1]x = [cn1] . Solving for c we get c = ([cn1] - [cd1]x) / ([cc1]) . lg [cd1] = 0.45367 lg x = 9.09341 -------------- lg x [cd1] = 9.54708 x [cd1] = 0.3524 [cn1] = 2.4051 -------------- [cn1] - x[cd1] = 2.0527 : lg 2.0527 = 0.31233 lg [cc1] = 1.03879 ------------- lg c = 9.27354 c = +0.1877 We determine a from the equation a = ([an] - [ac]c - [ad]x) / [aa] . lg [ac] = 9.45515[repeating decimal 5] lg c = 9.27354 ------------- lg [ac]c = 8.72869 [ac]c = 0.0535 [ad]x = 0.1819 ---------- [ac]c + [ad]x = 0.2354 [an] = -1.9830 ------------ [an] - [ac]c - [ad]x = -2.2184 lg [ad] = 0.16143 lg x = 9.09341 ------------ lg [ad]x = 9.25984 [ad]x = 0.1819 lg -2.2184 = 0.34604n lg [aa] = 0.33895 ------------- lg a = 0.00709n a = -1.0165 . We have therefore for the results of our observations, Δt = Δt[subscript]0[/subscript] + x = -29s + 0.1s = -28.9s ; c = +0.19s and a = -1.0s .