ACADEMY OF SCIENCES. 159 



with the collimation line equal to one-half of the supplement of the algebraic 

 difference of the north polar distances of the two stars, and bring the more 

 readily identified one of them into the field of view, and follow it till its mate 

 appears there, either meeting, chasing or fleeing from it. We then " pick the 

 beat" of the watch or chronometer, and beginning to count the beats at the 

 instant the stars coiucide in the telescope field, follow the hinder star till the 

 moment its " tabular hour angle" expires, and clamp, and our instrument is 

 in the meridian. 



A pair of fast-moving stars will give an accurate meridian, yet practically 

 it will in general be found preferable to have one of the pair a star of slow 

 motion, so that it can be readily bisected and followed until the instant its 

 fast-moving mate strikes the middle wire, thus enabling the observer to clamp 

 his instrument at exactly the right time without hesitation or doubt. 



If the table gives the hour angle in time of the hinder star at the instant 

 the two stars and our zenith are in the same vertical plane, then their relative 

 right ascensions and positions with reference to the zenith must be as follows, 

 viz: 1. If both stars are on the same side of the zenith then the star having 

 the greater zenith distance must have the smaller right ascension, and this 

 rule holds when one is a zenith star. 2. But if one star is south and the other 

 north of the zenith then either maybe in advance, but practically it is prefer- 

 able that the slow mover "bring up the rear." 3. When a star south of or in 

 the zenith is paired with a sub-polar, then the latter should not be quite twelve 

 hours in advance of the former. 4. If a star north of the zenith has a sub- 

 polar mate, then the upper culminating star should transit the meridian first, 

 if it is the lower culminating star that we are following with the cross thread, 

 and vice versa. 



But if our table gives the azimuthal deviation, in degrees, minutes and 

 seconds, of our instrument at the instant two such stars coincide in the field 

 of its telescope (its plane of motion being, of course, vertical) then it is a 

 matter of indifference which star precedes, d!nce this angular deviation can 

 be turned off either backward or forward on the horizontal limb of the instru- 

 ment. 



Within the latitudes of the United States the following varieties of pairs 

 will offer, viz: 



Class A. Pairs whose stars have the same, or differ but a few minutes, in 

 right ascension. 1. Two circumpolar stars. 2. A circumpolar star and a 

 time star, the latter being either in the zenith or south or north thereof. 3. 

 Two time stars, either one north and one south of the zenith, or both north 

 or both south thereof, or one star in and the other star either north or south 

 of it. 



Class B. Pairs, the stars of which differ exactly 12 hours in right ascen- 

 sion, or lack but a few minutes thereof. 1. Two circumpolar stars. 2. A 

 circumpolar star and a time star either in or south or north of the zenith. 



With respect to the relative motions of the stars of a pair most important 

 to the observer in deciding upon the exact instant of their coincidence, class 

 B is in general more favorable than class A. And the pair in class B which 



Pboo. Cal. Aoad. Sci., Vol. VII.— 12. 



