If the assumed latitude and watch error were correct, all the stars would give the same value for h. If not, each star would give an equation of the form
h + cos A dφ + cos φ sin A dT − h0 = 0
where A is the star’s azimuth, dφ the required correction to the assumed latitude, dT the required correction to the assumed watch times, and h0 the true altitude common to the three stars. The values of cos A and cos φ sin A were calculated from the ordinary formula
sin A = cos δ sin tcos h
by four-place logarithms (using the approximate values for φ, t, and h, since these are quite sufficiently accurate for the purpose) and inserted into the three star-equations.[66] By then solving the three simultaneous equations for dφ, the required correction to the assumed latitude was at once obtained.
As the method is one not usually treated of in books on practical astronomy, I give on the following pages the reduction of an observation worked out in full.
Latitude by Equal Altitudes of Three Stars.
Station on Gebel Um Heshenib. January 30, 1906.
| Approximate | φ | = | 24° | 20′ | 50″ | N. |
| „ | λ | = | 34° | 51′ | 0″ | E. |
Sidereal watch U. and C. 30811, approximately 2m 22s fast on L.S.T., rate negligible.