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 70

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 70

Rate.
The clock should be regulated so as to have a losing rather than a gaining rate. If the rate is appreciable, it should be taken into consideration for an accurate determination of Δt. In that case it will be convenient to determine Δt for some time, t[subscript]0[/subscript], chosen near the middle of the observing list.
Let r[superscript]s[/superscript] be the hourly rate. Then to correct an observation equation, corresponding to the time t, to what it would have been if the clock's error had been constantly Δt, we must add to t the value (t - t[subscript]0[/subscript])r[superscript]s[/superscript]. therefore in general
α=t+(t-t[subscript]0[/subscript])r[superscript]s[/superscript] + Δt + Aa + Bb + Cc, where Δt is the error of the clock at the time t[subscript]0[/subscript].
A single observation upon β Bootis gave, not considering the errors of the instrument, Δt = - 42.7[superscript]s[/superscript]; and a second observation taken upon the same star a week later, the instrument not having been disturbed, gave Δt= - 29.1[superscript]s[/superscript]. So in the seven sidereal days the clock lost 13.6[superscript]s[/superscript]. Therefore the daily rate was + 13.6[superscript]s[/superscript]/7 = + 1.94[superscript]s[/superscript]; and the hourly rate was r[superscript]s[/superscript] = +13.6[superscript]s[/superscript]/7x[24 or 2.4?] = + 0.081[superscript]s[/superscript].

Rate.
The clock should be regulated so as to have a losing rather than a gaining rate. If the rate is appreciable, it should be taken into consideration for an accurate determination of Δt. In that case it will be convenient to determine Δt for some time, t[subscript]0[/subscript], chosen near the middle of the observing list.
Let r[superscript]s[/superscript] be the hourly rate. Then to correct an observation equation, corresponding to the time t, to what it would have been if the clock's error had been constantly Δt, we must add to t the value (t - t[subscript]0[/subscript])r[superscript]s[/superscript]. therefore in general
α=t+(t-t[subscript]0[/subscript])r[superscript]s[/superscript] + Δt + Aa + Bb + Cc, where Δt is the error of the clock at the time t[subscript]0[/subscript].
A single observation upon β Bootis gave, not considering the errors of the instrument, Δt = - 42.7[superscript]s[/superscript]; and a second observation taken upon the same star a week later, the instrument not having been disturbed, gave Δt= - 29.1[superscript]s[/superscript]. So in the seven sidereal days the clock lost 13.6[superscript]s[/superscript]. Therefore the daily rate was + 13.6[superscript]s[/superscript]/7 = + 1.94[superscript]s[/superscript]; and the hourly rate was r[superscript]s[/superscript] = +13.6[superscript]s[/superscript]/7x[24 or 2.4?] = + 0.081[superscript]s[/superscript].