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 54

Transcribe
Translate

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 54

Effect of the Azimuth Error
upon the Time of Transit

     Let a[superscript]s[/superscript] be the azimuth error of the instrument and let S' be a star on the instrumental meridian. [strikethrough]W[/strikethrough] [inserted]We are to[/inserted] find the effect of a[superscript]s[/superscript] upon the time of transit. First let δ < φ. We wish to measure ∠ ZPS' , which is positive when the telescope points to the east of South. Let a[superscript]s[/superscript] be positive when measured to the east of South and west of North.

     In [image: symbol of part of circle] ZPS' , we have ((sin ZPS')/(sin PZS')) = ((sin ZS')/(sin PS')) .

     Let P[superscript]s[/superscript] = ∠ ZPS' . Now ∠ PZS' = 180° - a[superscript]s[/superscript] , and PS' = co - δ
ZS' = φ - δ , approximately.

     Then ((sin P[superscript]s[/superscript])/(sin (180° - a[superscript]s[/superscript])) = ((sin P[superscript]s[/superscript])/(sin a[superscript]s[/superscript])) = ((sin (φ - δ))/(cos δ)) . 

P[superscript]s[/superscript] and a[superscript]s[/superscript] being very small, we may write ((P[superscript]s[/superscript])/(a[superscript]s[/superscript] )) = ((sin (φ - δ))/(cos δ)) and P[superscript]s[/superscript] = ((sin (φ - δ))/(cos δ)) a[superscript]s[/superscript] = Aa[superscript]s[/superscript]   (1)  where A = ((sin (φ - δ))/(cos δ)) .

Saving...

Effect of the Azimuth Error upon the Time of Transit Let a[superscript]s[/superscript] be the azimuth error of the instrument and let S' be a star on the instrumental meridian. [strikethrough]W[/strikethrough] [inserted]We are to[/inserted] find the effect of a[superscript]s[/superscript] upon the time of transit. First let δ < φ. We wish to measure ∠ ZPS' , which is positive when the telescope points to the east of South. Let a[superscript]s[/superscript] be positive when measured to the east of South and west of North. In [image: symbol of part of circle] ZPS' , we have ((sin ZPS')/(sin PZS')) = ((sin ZS')/(sin PS')) . Let P[superscript]s[/superscript] = ∠ ZPS' . Now ∠ PZS' = 180° - a[superscript]s[/superscript] , and PS' = co - δ ZS' = φ - δ , approximately. Then ((sin P[superscript]s[/superscript])/(sin (180° - a[superscript]s[/superscript])) = ((sin P[superscript]s[/superscript])/(sin a[superscript]s[/superscript])) = ((sin (φ - δ))/(cos δ)) . P[superscript]s[/superscript] and a[superscript]s[/superscript] being very small, we may write ((P[superscript]s[/superscript])/(a[superscript]s[/superscript] )) = ((sin (φ - δ))/(cos δ)) and P[superscript]s[/superscript] = ((sin (φ - δ))/(cos δ)) a[superscript]s[/superscript] = Aa[superscript]s[/superscript] (1) where A = ((sin (φ - δ))/(cos δ)) .