160 PROCEEDINGS OF THE CALIFORNIA 



furnishes the maximum amounts of aziinuthal motions (in opposite direc- 

 tions), and hence most desirable, is a lower culminating circumpolar star aud 

 an equatorial star; while with a pair of circumpolars the sum of these mo- 

 tions is a minimum. And of those in class A, a close circumpolar star and 

 an equatorial star gives the greatest difference of motions; while a pair of 

 circumpolars gives the least. When the stars of a pair move in the same di- 

 rection, and at not very greatly different speeds, they will doubtless be found 

 to cling together in the telescope field a provokingly long time. 



As to the frequency of their availability, the pairs of circumpolar stars 

 stand pre-eminent; since they are on our meridian and its visible extension 

 twice in every 24 hours, they are hence doubly more available than the other 

 pairs which transit our meridian but once in that time. 



As to the amount of computation required — an element only in those pairs 

 whose stars are not exactly on the same declination circle or its visible exten- 

 sion — when a zenith star is paired with either a south or a north star tat 

 upper or lower culmination), following within a few minutes, the computa- 

 tion is a minimum, for then the difference of the times of the stars transiting 

 our meridian equals the difference of their right ascensions; and the zenith 

 star obviously transits the meridian at the exact moment it and its mate are 

 in the same vertical plane. And when its mate is a close circumpolar star 

 their mean right ascensions will prove all-sufficient because from the slowness 

 of its motion in azimuth the error of assuming the difference of their mean, 

 equal to the difference of their apparent, right ascensions will in general be 

 inappreciable. And it may often occur that the error of assuming this of two 

 stars having nearly the same precession in right ascension will enter the re- 

 sulting azimuth in so diminutive a form as to be quite allowable, except in a 

 very close work. 



If the stars chosen fall in a part of the celestial sphere illuminated by the 

 sun as they transit our meridian, they will require to be of larger magnitudes 

 than such star pairs as, being in the opposite part of the heavens, cross our 

 meridian at night. Especial effort should be made to incorporate the double 

 stars into pairs, from the facility and certainty with which they can be identi- 

 fied in the telescope field. 



And again, if tables are available giving the exact right ascensions and 

 declinations of Mars and Jupiter, they may be advantageously paired with 

 suitable stars; and their continuous motion among _the stars renders them 

 more available, since they cross successively the declination circle of every 

 star in the heavens. But the use of these planets will necessitate a more 

 accurate knowledge of our time. 



Experience has proven that, in reconnaissances, rapidity of execution in 

 finding latitude, time and azimuth, is all-important and in many cases essen- 

 tial to success; and hence methods and instruments which yield a maximum 

 amount of results in a minimum time are in especial demand. Under the 

 contingency, often arising in reconnaissance and exploration, that the latitude 

 is not known and the time only to the nearest five or ten minutes; and when 

 limited in time and facilities, as the reconnoiterer or explorer per necessitatum 

 generally is, then this method will be found most acceptable; for it is obvious 

 that by bisecting one of the stars of a pair (of identical right ascension) with 



