158 PROCEEDINGS OP THE CALIFORNIA 



other to a double reflection, by using an additional mirror, as in the sextant, 

 or employing the principle embodied in the Steinheil heliotrope. We may, 

 however, avoid this double reflection of either of the stars of such a pair by 

 pointing the telescope on the artificial horizon image of one of them, and 

 thus get the other into the telescopic field by a single reflection. 



When the stars of a pair have the same right ascension, we will have them 

 enter the field of the telescope on the same side and move across in the same 

 direction, the faster mover, as it were, chasing the slower, and catching up 

 with it at the instant of their simultaneous passage Of the meridian. But 

 with a pair of stars differing twelve hours in right ascension, i. e., one of them 

 culminating sub polo, they will enter the telescope field on opposite sides, move 

 across and meet exactly on the meridian. It is hence obvious that a pair 

 whose stars differ 12 hours in right ascension offers the advantageous feature 

 of the sum of their motions to aid the observer in deciding upon the exact in- 

 stant of their coincidence in the telescope field, whereas with a pair having 

 the same right ascension he has only the difference of its stars' motions to as- 

 sist him in gxing upon this instant. 



But when the catalogues do not offer star pairs culminating at desirable 

 times, of suitable magnitudes and declinations, and of the same or exactly 12 

 hours different right ascensions, and thus permitting the application of the 

 method in its greatest perfection, we may yet find our meridian most accu- 

 rately by selecting and observing suitable pairs, the right ascension of whose 

 stars differ but a few minutes frorn being identical, or exactly 12 hours differ- 

 ent. Now the zenith of a position is a point common to all its vertical planes, 

 and since the plane passing through the earth's center and any two stars dif- 

 fering more in declination than in right ascension, is, by the diurnal revolu- 

 tion of the earth, made to coincide successively with one of the vertical planes 

 of every point on the earth's surface, we hence have but to observe two such 

 stars at the instant they and our zenith are in the same vertical plane, and 

 clamp, and we have our instrument in a vertical plane whose deviation in azi- 

 muth is determined by, and easily derived from, the north polar distances of 

 the two stars, the difference of their right ascensions, and the co-altitude of 

 one of the stars (or our co-latitude;, we can observe the co-altitude of one of 

 the stars at the instant of their coincidence , in the telescope field. Having 

 selected a list of such star pairs, we can readily compute a table from which 

 an observer at any known latitude can pick out the azimuthal deviation of his 

 instrument in degrees, minutes and seconds, at the instant two such stars 

 coincide in his telescope field. Or, instead of using the co-latitude, which 

 must then be known, we can use, in the preparation of such a table, the 

 zenith distance of one of the stars; otherwise we may tabulate the hour angle 

 in time (minutes and seconds) of the hinder of the two stars at the instant of 

 their coincidence in the field of the telescope, either for the different altitudes 

 of this star or for the different latitudes. 



The method of observing such a pair with the aid of the last named table 

 will be as follows : Having taken care in selecting to have one of the pair a 

 star of such magnitude and position as to be readily identified by a stellar 

 chart or allineation, we set the mirror in front of the object glass, at an angle 



