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 57

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 57

Effect of the Collimation Error upon the Time of Transit
Let BZA be the true meridian and B'S'A' the instrumental meridiatn. Let S' be the position of a star on the instrumental meridian and S its position on the true meridian. Let S'S1 be an arc of a great circle thru s' (perpendicular) to the meridian PQ. Then S'S1 = A'A = B'B = C(to the)(s), the collimation error.
In rt. [triangle] PS1S',
[sin(ZPS')]/[sin(S'S)] = [sin(PS1S')]/[sin(PS')]
Let P(to the)(s) = (angle) ZPS'. Then the equation becomes
[sin(P(to the)(s))]/[sin(c(to the)(s))] = 1/cos(delta).
P(to the)(s) and c(to the)(s) being very small, we may write:
[sin(P(to the)(s))]/[sin(c(to the)(s))] = P(to the)(s)/c(to the)(s) = 1/cos(delta).
or P(to the)(s) = [1/cos(delta)] * c(to the)(s) = C'c(to the)(s), where C = 1/cos(delta).
P(to the)(s) is positive when the instrumental meridian lies to the east of the true meridian and as C is positive, c(to the)(s) must be taken positive to the east of the true meridian.
Let S0 be a sub-polar star on the meridian and S1 the position it will have on the instrumental meridian.

Effect of the Collimation Error upon the Time of Transit
Let BZA be the true meridian and B'S'A' the instrumental meridiatn. Let S' be the position of a star on the instrumental meridian and S its position on the true meridian. Let S'S1 be an arc of a great circle thru s' (perpendicular) to the meridian PQ. Then S'S1 = A'A = B'B = C(to the)(s), the collimation error.
In rt. [triangle] PS1S',
[sin(ZPS')]/[sin(S'S)] = [sin(PS1S')]/[sin(PS')]
Let P(to the)(s) = (angle) ZPS'. Then the equation becomes
[sin(P(to the)(s))]/[sin(c(to the)(s))] = 1/cos(delta).
P(to the)(s) and c(to the)(s) being very small, we may write:
[sin(P(to the)(s))]/[sin(c(to the)(s))] = P(to the)(s)/c(to the)(s) = 1/cos(delta).
or P(to the)(s) = [1/cos(delta)] * c(to the)(s) = C'c(to the)(s), where C = 1/cos(delta).
P(to the)(s) is positive when the instrumental meridian lies to the east of the true meridian and as C is positive, c(to the)(s) must be taken positive to the east of the true meridian.
Let S0 be a sub-polar star on the meridian and S1 the position it will have on the instrumental meridian.