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 78

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

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

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