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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 78

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Then (4) and (5) may be written ([cc1]c) + ([cd1]x) = [cn1] (7) and ([cd1]c) + ([dd1]x) = [dn1] . (8) From (7) we have c = ([cn1]/[cc1]) - (([cd1]/[cc1])x) . Substituting this value of c in (8) we get ([dd1] - (([cd1]/[cc1])[cd1]))x = [dn1] - (([cd1]/[cc1])[cn1]) . (9) Let [dd1] - (([cd1]/[cc1])[cd1]) = [dd2] } (10). and [dn1] - (([cd1]/[cc1])[cn1]) = [dn2]. } (10). Then (9) because [dd2]x = [dn2] , whence x = ([dn2]/[dd2]) . (11) Check-Formulae. I. Let [cs1] = [cs] - (([ac]/[aa])[as]) , in accordance with (6). Substituting in this equation the values of [cs] and [as] as given by the former check equations, we have
 
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