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 79

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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 79

[cs1] = [ac] + [cc] + [cd] - [cn] - (([ac]/[aa])[aa]) - (([ac]/[aa])[ac]) - (([ac]/[aa])[ad]) + (([ac]/[aa])[an])

= ([cc] - (([ac]/[aa])[ac])) + ([cd] - (([ac]/[aa])[ad])) - ([cn] - (([ac]/[aa])[an]))

or
[cs1] = [cc1] + [cd1] - [cn1].   (12)

     In like manner

[ds1] = [ds] - (([ad]/[aa])[as])
= [ad] + [cd] + [dd] - [dn] - (([ad]/[aa])[aa]) - (([ad]/[aa])[ac]) - (([ad]/[aa])[ad]) + (([ad]/[aa])[an])

= ([cd] - (([ad]/[aa])[ac])) + ([dd] - (([ad]/[aa])[ad])) - ([dn] - (([ad]/[aa])[an])) , 

[missing edge?][or?][/missing edge?]

[ds1] = [cd1] + [dd1] - [dn1].   (13)

II. Let [ds2] = [ds1] - (([cd1]/[cc1])[cs1]) , in accordance with (10).
     Substituting in this equation the values of [cs1] and [ds1] as given by (12) and (13) we have
[ds2] = [cd1] + [dd1] - [dn1] - (([cd1]/[cc1])[cc1]) - (([cd1]/[cc1])[cd1]) + (([cd1]/[cc1])[cn1])

= [dd1] - (([cd1]/[cc1])[cd1]) - ([dn1] - ([dn1] - (([cd1]/[cc1])[cn1]) ; 
or [ds2] = [dd2] - [dn2] .   (14)

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[cs1] = [ac] + [cc] + [cd] - [cn] - (([ac]/[aa])[aa]) - (([ac]/[aa])[ac]) - (([ac]/[aa])[ad]) + (([ac]/[aa])[an]) = ([cc] - (([ac]/[aa])[ac])) + ([cd] - (([ac]/[aa])[ad])) - ([cn] - (([ac]/[aa])[an])) or [cs1] = [cc1] + [cd1] - [cn1]. (12) In like manner [ds1] = [ds] - (([ad]/[aa])[as]) = [ad] + [cd] + [dd] - [dn] - (([ad]/[aa])[aa]) - (([ad]/[aa])[ac]) - (([ad]/[aa])[ad]) + (([ad]/[aa])[an]) = ([cd] - (([ad]/[aa])[ac])) + ([dd] - (([ad]/[aa])[ad])) - ([dn] - (([ad]/[aa])[an])) , [missing edge?][or?][/missing edge?] [ds1] = [cd1] + [dd1] - [dn1]. (13) II. Let [ds2] = [ds1] - (([cd1]/[cc1])[cs1]) , in accordance with (10). Substituting in this equation the values of [cs1] and [ds1] as given by (12) and (13) we have [ds2] = [cd1] + [dd1] - [dn1] - (([cd1]/[cc1])[cc1]) - (([cd1]/[cc1])[cd1]) + (([cd1]/[cc1])[cn1]) = [dd1] - (([cd1]/[cc1])[cd1]) - ([dn1] - ([dn1] - (([cd1]/[cc1])[cn1]) ; or [ds2] = [dd2] - [dn2] . (14)