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 52

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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 52

or P[superscript]s[/superscript] = ((cos (φ - δ))/(cos δ)) * b[superscript]s[/superscript] = Bb[superscript]s[/superscript]  (1) , where B = ((cos (φ - δ))/(cos δ)). B is called Mayer's level factor.

     In the figure, b[superscript]s[/superscript] and P[superscript]s[/superscript] are both negative. The sign of B is positive, so the sign of Bb[superscript]s[/superscript] is the same as that of b[superscript]s[/superscript].

     In the case of sub-polar transits, a star will cross the instrumental meridian too soon when b[superscript]s[/superscript] is negative and the correction for level error, i.e., Bb[superscript]s[/superscript], will be positive. Let S[subscript]1[/subscript] be the position of a sub-polar star on the instrumental meridian, and S[subscript]0[/subscript] its position on the true meridian. Then the angle we wish to measure is ∠ NPS[subscript]1[/subscript] . Let P[subscript]1[/subscript] = ∠ NPS[subscript]1[/subscript] . In [image: symbol for part of circle] S[subscript]1[/subscript]PN , we have 
((sin NPS[subscript]1[/subscript])/(-sin PNS[subscript]1[/subscript])) = ((sin S[subscript]1[/subscript]N)/(sin PS[subscript]1[/subscript])) , sin NPS[subscript]1[/subscript] and sin PNS[subscript]1[/subscript] being opposite in sign; or -((sin P[subscript]1[/subscript][superscript]s[/superscript])/(sin b[superscript]s[/superscript])) = ((sin h)/(sin [co or cδ ?] - δ)) , S[subscript]1[/subscript]N being taken approximately equal to h.
Again, P[subscript]1[/subscript][superscript]s[/superscript] and b[superscript]s[/superscript] being very small, we may take ((sin P[subscript]1[/subscript][superscript]s[/superscript])/(sin b[superscript]s[/superscript])) = ((P[subscript]1[/subscript][superscript]s[/superscript])/(b[superscript]s[/superscript])) . Then we have -((P[subscript]1[/subscript][superscript]s[/superscript])/(b[superscript]s[/superscript])) = ((sin (δ - 90° + φ))/(cos δ)) .   (2)

     Let δ[subscript]1[/subscript] be the declination of the sub-polar star as measured then the zenith and pole.

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or P[superscript]s[/superscript] = ((cos (φ - δ))/(cos δ)) * b[superscript]s[/superscript] = Bb[superscript]s[/superscript] (1) , where B = ((cos (φ - δ))/(cos δ)). B is called Mayer's level factor. In the figure, b[superscript]s[/superscript] and P[superscript]s[/superscript] are both negative. The sign of B is positive, so the sign of Bb[superscript]s[/superscript] is the same as that of b[superscript]s[/superscript]. In the case of sub-polar transits, a star will cross the instrumental meridian too soon when b[superscript]s[/superscript] is negative and the correction for level error, i.e., Bb[superscript]s[/superscript], will be positive. Let S[subscript]1[/subscript] be the position of a sub-polar star on the instrumental meridian, and S[subscript]0[/subscript] its position on the true meridian. Then the angle we wish to measure is ∠ NPS[subscript]1[/subscript] . Let P[subscript]1[/subscript] = ∠ NPS[subscript]1[/subscript] . In [image: symbol for part of circle] S[subscript]1[/subscript]PN , we have ((sin NPS[subscript]1[/subscript])/(-sin PNS[subscript]1[/subscript])) = ((sin S[subscript]1[/subscript]N)/(sin PS[subscript]1[/subscript])) , sin NPS[subscript]1[/subscript] and sin PNS[subscript]1[/subscript] being opposite in sign; or -((sin P[subscript]1[/subscript][superscript]s[/superscript])/(sin b[superscript]s[/superscript])) = ((sin h)/(sin [co or cδ ?] - δ)) , S[subscript]1[/subscript]N being taken approximately equal to h. Again, P[subscript]1[/subscript][superscript]s[/superscript] and b[superscript]s[/superscript] being very small, we may take ((sin P[subscript]1[/subscript][superscript]s[/superscript])/(sin b[superscript]s[/superscript])) = ((P[subscript]1[/subscript][superscript]s[/superscript])/(b[superscript]s[/superscript])) . Then we have -((P[subscript]1[/subscript][superscript]s[/superscript])/(b[superscript]s[/superscript])) = ((sin (δ - 90° + φ))/(cos δ)) . (2) Let δ[subscript]1[/subscript] be the declination of the sub-polar star as measured then the zenith and pole.