24 A MANUAL OF TOPOGRAPHIC METHODS. 



by observing- the transits of some close circumpolar star, when near elonga- 

 tion, across the movable thread, setting the thread repeatedly at regular 

 intervals in advance of the star, and taking the time of its passage, with the 

 reading of the micrometer. The precaution should be taken to read the 

 latitude level occasionally and correct for it if necessary. This correction, 

 which is to be applied to the observed time, is equal to one division of the 

 level, in seconds of time, divided by the cosine of the declination of the 

 star and multiplied by the level error, the average level reading being 

 taken as the standard. 



The time from elongation of the star requires a correction in order to 

 reduce the curve in which the star apparently travels to a vertical line. 

 The hour angle of the star is first obtained from the equation, 



cos t u — cot S tan <p, 

 S being the star's declination and q> the latitude. 



The chronometer time of elongation, T„ rr a — t — St, a being the 

 right ascension of the star obtained from the Nautical Almanac, and St the 

 error of the chronometer. 



Having thus obtained the chronometric time of elongation, the correc- 

 tion in question is obtained from the observed interval of time of each ob- 

 servation before or after elongation, from tables in Appendix No. 14, U. S. 

 Coast and Geodetic Survey Report for 1880, pp. 58 and 59. A discussion 

 of this subject will be found in the appendix above referred to, and in 

 Chauvenet's Practical Astronomy, vol. u, pp. 360 to 3G4. 



The times of observation thus corrected for level, and distance from 

 elongation, are then grouped in pairs, selected as being a certain number of 

 revolutions of the micrometer apart, and the time intervals between the 

 members of each pair obtained. The mean of these, divided by the sum of 

 revolutions which separate the members of each pair, is yet to be corrected 

 for differential refraction, which is derived from the following equation: 



Ref. — 57" .7 sin B sec 2 Z. 

 R being the value of a division of the micrometer and Z the zenith distance of 

 the star. Four-place logarithms are sufficient for computing this correction, 

 as it is small. Below is given an example of record and computation of the 

 value of a revolution of the micrometer of combined instrument No. 534, 

 one of the two in possession of the Geological Survey. 



