Suppose that in commencing to observe at a station the error of the chronometer is not known; then having secured for the instrument a very solid foundation, removed as far as possible level and collimation errors, and placed it by estimation nearly in the meridian, let two stars differing considerably in declination be observed--the instrument not being reversed between them. From these two stars, neither of which should be a close circumpolar star, a good approximation to the chronometer error can be obtained; thus let [epsilon]1, [epsilon]2, be the apparent clock errors given by these stars if [delta]1, [delta]2 be their declinations the real error is [epsilon] = [epsilon]1 + ([epsilon]1 - [epsilon]2) (tan [phi] - tan [delta]1) / (tan [delta]1 - tan [delta]2). Of course this is still only approximate, but it will enable the observer (who by the help of a table of natural tangents can compute [epsilon] in a few minutes) to find the meridian by placing at the proper time, which he now knows approximately, the centre wire of his instrument on the first star that passes--not near the zenith. The transit instrument is always reversed at least once in the course of an evening's observing, the level being frequently read and recorded. It is necessary in most instruments to add a correction for the difference in size of the pivots. The transit instrument is also used in the prime vertical for the determination of latitudes. In the preceding figure let q be the point in which the northern extremity of the axis of the instrument produced meets the celestial sphere. Let nZq be the azimuthal deviation = a, and b being the level error, Zq = 90 deg. - b; let also nPq = [tau] and Pq = [psi]. Let S' be the position of a star when observed on a wire whose distance from the collimation centre is c, positive when to the south, and let h be the observed hour angle of the star, viz. ZPS'. Then the triangles qPS', gPZ give -Sin c = sin [delta] cos [psi] - cos [delta] sin [psi] cos (h + [tau]), Cos [psi] = sin b sin [phi] + cos b cos [phi] cos a, Sin [psi] sin [tau] = cos b sin a. Now when a and b are very small, we see from the last two equations that [psi] = [phi] - b, a = [tau] sin [psi], and if we calculate [phi]' by the formula cot [phi]' = cot [delta] cos h, the first equation leads us to this result-- [phi] = [phi]' + (a sin z + b cos z + c)/cos z, the correction for instrumental error being very similar to that applied to the observed time of transit in the case of meridian observations. When a is not very small and z is small, the formulae required are more complicated. [Illustration: FIG. 4.--Zenith Telescope constructed for the International Stations at Mizusawa, Carloforte, Gaithersburg and Ukiah, by Hermann Wanschaff, Berlin.]