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 72

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 72

If it is seen that Δt will be a large quantity we can shorten the labor of computation by assuming an approximate value Δt[subscript]0[/subscript] for Δt.
Then Δt = Δt[subscript]0[/subscript] + x where x is a small correction to Δt[subscript]0[/subscript].
Making this substitution in Mayer's formula and introducing the correction for rate, we obtain
α = t + Δt[subscript]0[/subscript] + x[mark?] + (t - t[subscript]0[/subscript])r[superscript]s[/superscript] + Aa + Bb +- Cc
or x + Aa +-Cc = α - [t + Δt[subscript]0[/subscript] + (t - t[subscript]0[/subscript])r[superscript]s[/superscript] + Bb], - the minus sign before Cc being used for Circle Facing (West, as reversing the axis changes, the sign of the collimation error. Let l=α-[t+Δt[subscript]0[/subscript] + (t - t[subscript]0[/subscript])r + Bb]. Then we have for our observation equation
x + Aa +- Cc = l. (1)
Each star furnishes an observation equation of the form of (1).
The time of transit of a star over a wire can be estimated more accurately for a rapidly moving star near the equator than for one of greater declination; so if we [strikethrough]can[/strikethrough] weight the observations, each observation equation should be multiplied by the square root of its weight before forming the normal equations.

If it is seen that Δt will be a large quantity we can shorten the labor of computation by assuming an approximate value Δt[subscript]0[/subscript] for Δt.
Then Δt = Δt[subscript]0[/subscript] + x where x is a small correction to Δt[subscript]0[/subscript].
Making this substitution in Mayer's formula and introducing the correction for rate, we obtain
α = t + Δt[subscript]0[/subscript] + x[mark?] + (t - t[subscript]0[/subscript])r[superscript]s[/superscript] + Aa + Bb +- Cc
or x + Aa +-Cc = α - [t + Δt[subscript]0[/subscript] + (t - t[subscript]0[/subscript])r[superscript]s[/superscript] + Bb], - the minus sign before Cc being used for Circle Facing (West, as reversing the axis changes, the sign of the collimation error. Let l=α-[t+Δt[subscript]0[/subscript] + (t - t[subscript]0[/subscript])r + Bb]. Then we have for our observation equation
x + Aa +- Cc = l. (1)
Each star furnishes an observation equation of the form of (1).
The time of transit of a star over a wire can be estimated more accurately for a rapidly moving star near the equator than for one of greater declination; so if we [strikethrough]can[/strikethrough] weight the observations, each observation equation should be multiplied by the square root of its weight before forming the normal equations.