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 61

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 61

left side and the known to the right, the equation becomes, changing the signs,
Δt + Aa[superscript]s[/superscript] + Cc[superscript]s[/superscript] = α - t - Bb[superscript]s[/superscript] .
Now it takes three equations to determine three unknown quantities. Hence, the values of Δt, a[superscript]s[/superscript], and c[superscript]s[/superscript] may be determined by observing the transits of three stars which differ little in right ascension but considerably in declination, and substituting the values of a, t, A, B, C, and b in the equation. Each observation furnishes an equation of condition. Solving the three equations gives Δt, a, and c.
For greater accuracy we can increase the number of observations, and hence of the equations, and combine the equations by the Method of Least Squares.
For a least square solution it is customary to observe the transits of ten or twelve stars. The observing list with the "settings" should be made out carefully in advance. "At about the middle of the set of observations, the axis should be reversed, so that the

left side and the known to the right, the equation becomes, changing the signs,
Δt + Aa[superscript]s[/superscript] + Cc[superscript]s[/superscript] = α - t - Bb[superscript]s[/superscript] .
Now it takes three equations to determine three unknown quantities. Hence, the values of Δt, a[superscript]s[/superscript], and c[superscript]s[/superscript] may be determined by observing the transits of three stars which differ little in right ascension but considerably in declination, and substituting the values of a, t, A, B, C, and b in the equation. Each observation furnishes an equation of condition. Solving the three equations gives Δt, a, and c.
For greater accuracy we can increase the number of observations, and hence of the equations, and combine the equations by the Method of Least Squares.
For a least square solution it is customary to observe the transits of ten or twelve stars. The observing list with the "settings" should be made out carefully in advance. "At about the middle of the set of observations, the axis should be reversed, so that the