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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 82

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IV. Again, we have [ns] = [an] + [cn] + [dn] - [nn]. (23). In accordance with (6) let [ns1] = [ns] - (([an][as])/([aa])) (24). Substituting in (24) the values of [ns] and [as] we obtain [ns1] = [an] + [cn] + [dn] - [nn] - ((([an])/([aa]))[aa]) - ((([an])/([aa]))[ac]) - ((([an])/([aa]))[ad]) + (([an][an])/([aa])) , or [ns1] = ([cn] - ((([an])/([aa]))[ac])) + ([dn] - ((([an])/([aa]))[ad])) - ([nn] - (([an][an])/([aa]))) or [ns1] = [cn1] + [dn1] - [nn1] (25). In accordance with (10) let us write [ns2] = [ns1] - (([cs1][cn1])/([cc1])) (26). Substituting in (26) the values of [ns1] and [cs1] we get [ns2] = [cn1] + [dn1] - [nn1] - (([cn1]/[cc1])[cc1]) - (([cn1]/[cc1])[cd1]) + (([cn1][cn1])/[cc1]) , or [ns2] = [dn2] - [nn2] . (27)
 
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