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 53

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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 53

     Then delta[subscript]1[/subscript] = 180degrees - delta . Substituting in (2) for delta , we have 

{-(P[subscript]1[/subscript][superscript]s[/superscript])/(b[superscript]s[/superscript])} = {(sin(90degrees - delta[subscript]1[/subscript] + [symblo]))/(cos(180degrees - delta[subscript]1[/subscript]))} = {(cos([symbol] - delta[subscript]1[/subscript]))/(- cos delta[subscript]1[/subscript])} ; 

or P[subscript]1[/subscript][superscript]s[/superscript] = {(cos ([symbol] - delta[subscript]1[/subscript]))/(cos delta[subscript]1[/subscript])} b[superscript]s[/superscript] .  (3)

     It is evident that we can just as well use formula (1) instead of (3) for subpolar transits if we use for delta in (1) its supplementary value, and consider P[superscript]2[/superscript] the supplement of the star's hour angle.

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Then delta[subscript]1[/subscript] = 180degrees - delta . Substituting in (2) for delta , we have {-(P[subscript]1[/subscript][superscript]s[/superscript])/(b[superscript]s[/superscript])} = {(sin(90degrees - delta[subscript]1[/subscript] + [symblo]))/(cos(180degrees - delta[subscript]1[/subscript]))} = {(cos([symbol] - delta[subscript]1[/subscript]))/(- cos delta[subscript]1[/subscript])} ; or P[subscript]1[/subscript][superscript]s[/superscript] = {(cos ([symbol] - delta[subscript]1[/subscript]))/(cos delta[subscript]1[/subscript])} b[superscript]s[/superscript] . (3) It is evident that we can just as well use formula (1) instead of (3) for subpolar transits if we use for delta in (1) its supplementary value, and consider P[superscript]2[/superscript] the supplement of the star's hour angle.