one of which culminates on one side of the zenith and the other at nearly the same distance on the opposite side of the zenith, by means of an eye-piece micrometer rather than a graduated circle, and herein lies the chief advantage of the Talcott method over all others, the micrometer being a much more delicate and accurate instrument than the graduated circle.
The program of work calls for sixteen determinations of the latitude each night, which means the observation of sixteen pairs of stars. Particular stars have been chosen in such a way as to give convenient intervals between the culmination times of each and the work consumes four hours of time each night. As the stations are all located on the same parallel of latitude the zenith of each observatory will traverse the same path in the sky and the same stars may therefore be observed at each station. Exactly the same program of work, weather and other conditions permitting, is carried out at each station every night of the year. About 12,000 determinations of the latitude are obtained each year, the total to the beginning of 1908 being 99,313. The greatest number of observations are obtained at the Italian station, the next greatest at Ukiah as may be seen from the following table:
Total of Latitude Observations up to 1908
| Mizusawa | 13,561 | Cincinnati | 12,190 | |
| Tschardjui | 14,901 | Ukiah | 18,676 | |
| Carloforte | 25,302 | Total | 99,313 | |
| Gaithersburg | 14,683 |
middle is measured by means of the micrometer. The instrument is then reversed about its vertical axis, without disturbing the setting, and the telescope will then point as far south as it did north of the zenith before reversal, or vice versa. The second star will then pass through the field of view as far below or above as the first star was above or below the center, and this distance from the center is again measured by means of the micrometer. The proper combination of the micrometer settings on the two stars gives the actual difference of their zenith-distances, which may be turned into arc measure, provided the value of one revolution of the micrometer-screw be known. The latitude, φ, of the place of observation is computed by means of the formula, , in which the first term of the right-hand member of the equation represents one half the sum of the declinations of the two stars of the pair observed; the second term one half the difference of the zenith-distances of the two stars as measured by means of the micrometer; the third term a small correction for any change in the pointing of the telescope after reversal, detected by means of two very delicate levels attached to the telescope; and the last term a small correction for the difference in the atmospheric refraction affecting the rays of light coming from the two stars. It might be noticed that if the two stars are at exactly the same zenith-distance, and the instrument is reversed without disturbing the pointing, then the second, third and fourth terms each become zero in the equation above, and the latitude is simply the mean of the declinations of the two stars, or the declination of the zenith, as may be seen by referring to Fig. 1.
