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 81

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 81

[nn] - (([an]/[aa])([an])) + (([an]/[aa])([ac]c)) + (([an]/[aa])([ad]x)) - ([cn]c) - ([dn]x) = [vv] (18)
Let [nn] - (([an]/[aa])([an])) = [nn1] in accordance with (6).
Then (18) becomes
[nn1] - ([cn1]c) - ([dn1]x) = [vv]. (19)
From (7) we have c = ([cn1]/[cc1]) - (([cd1]/[cc1])(x)).
Substituting this value of c in (19) we get
[nn1] - (([cn1]/[cc1])[cn1]) + (([cn1]/[cc1])[cd1]x) - ([dn1]x) = [vv]. (20).
Now [nn1] - (([cn1]/[cc1])[cn1]) = [nn2] , in accordance with (10).
Therefore, (20) may be written
[nn2] - ([dn2]x) = [vv]. (21)
Substituting in (21) the value of x from (11) we have
[nn2] - (([dn2][dn2])/[dd2]) = [vv] = [nn3] (22).

[nn] - (([an]/[aa])([an])) + (([an]/[aa])([ac]c)) + (([an]/[aa])([ad]x)) - ([cn]c) - ([dn]x) = [vv] (18)
Let [nn] - (([an]/[aa])([an])) = [nn1] in accordance with (6).
Then (18) becomes
[nn1] - ([cn1]c) - ([dn1]x) = [vv]. (19)
From (7) we have c = ([cn1]/[cc1]) - (([cd1]/[cc1])(x)).
Substituting this value of c in (19) we get
[nn1] - (([cn1]/[cc1])[cn1]) + (([cn1]/[cc1])[cd1]x) - ([dn1]x) = [vv]. (20).
Now [nn1] - (([cn1]/[cc1])[cn1]) = [nn2] , in accordance with (10).
Therefore, (20) may be written
[nn2] - ([dn2]x) = [vv]. (21)
Substituting in (21) the value of x from (11) we have
[nn2] - (([dn2][dn2])/[dd2]) = [vv] = [nn3] (22).