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 60

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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 60

Mayer's Formula.

     If the transit instrument were in perfect adjustment we would have, as the relation between the right ascension, the clock time of transit of a star, and Δt,  
        α = t + Δt ; 
but considering the effects of the errors in level, azimuth, and collimation, this equation become[s?]

α = t + Δt + ((sin(0-δ))/cos δ) a[superscript][s?][/superscript] + ((cos(0-δ))/cos δ)b[superscript][s?][/superscript] + (1/cos δ)c[superscript][s?][/superscript]

or α = t + Δt + Aa[superscript][s?][/superscript] + Bb[superscript][s?][/superscript] + Cc[superscript][s?][/superscript] .    (1).

     This is Mayer's formula. The constants A, B, and C have been computed and tabulated for latitude 41° 40' and for declinations from -35° to 90° for upper culminations, and from 90° to 55° for lower culminations.
     By means of the equation (1) we can find Δt by the following method: α is given by the Nautical Almanac; A, B, and C are computed when the latitude is given; b[superscript][s?][/superscript] is determined by level readings, and t is observed; so the only unknown quantities are Δt, a[superscript][s?][/superscript], and c[superscript][s?][/superscript]. Transposing the unknown quantities to the

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Mayer's Formula. If the transit instrument were in perfect adjustment we would have, as the relation between the right ascension, the clock time of transit of a star, and Δt, α = t + Δt ; but considering the effects of the errors in level, azimuth, and collimation, this equation become[s?] α = t + Δt + ((sin(0-δ))/cos δ) a[superscript][s?][/superscript] + ((cos(0-δ))/cos δ)b[superscript][s?][/superscript] + (1/cos δ)c[superscript][s?][/superscript] or α = t + Δt + Aa[superscript][s?][/superscript] + Bb[superscript][s?][/superscript] + Cc[superscript][s?][/superscript] . (1). This is Mayer's formula. The constants A, B, and C have been computed and tabulated for latitude 41° 40' and for declinations from -35° to 90° for upper culminations, and from 90° to 55° for lower culminations. By means of the equation (1) we can find Δt by the following method: α is given by the Nautical Almanac; A, B, and C are computed when the latitude is given; b[superscript][s?][/superscript] is determined by level readings, and t is observed; so the only unknown quantities are Δt, a[superscript][s?][/superscript], and c[superscript][s?][/superscript]. Transposing the unknown quantities to the