Hagen.] 218 [Feb. 3, 



the time and latitude of tlie place being known. First d may be deter- 

 mined, as in former cases, either by the striding level, which will give the 

 angle 



^ d = b + ,S, 

 or by observing the direct and reflected image of a star either in west or 

 in east. By subtracting the two corresponding equations we find 



d Ti — T 



2 = yS -f b = 2 — tan z sm cr, 



where stars are to be chosen, that pass near the zenith. The collimation 

 constant c may be determined by reversing the axis and observing in both 

 cases the time of transit. As in this case the sign of c alone is changed, 

 we find by subtracting the two corresponding equations 



T^ — T . 

 c = o — sm z sm cp, 



where stars passing near the zenith are again preferable. Both operations 

 may be performed by first observing the transits over some threads and 

 then, after having moved the instrument, over the rest, and by reduc- 

 ing them to the middle thread, or if the observations are taken on diflfer- 

 ent days, the rate of the clock must be known and added to the observed 

 time. 



Let us now suppose the time T being already corrected as to the collima- 

 tion, then by observing the same star east and west we may find both con- 

 stants b and k. In this case the equations are 



^ = T + J T + t-^-^^ + ,^^ Star west, 



,^ = T^ + JT-,-^^-^-fsir^ "east. 

 By subtracting we have 



b = tan z sin ^ [ H^ — (>') — HT — T')]- 

 Should the clock corrections not be the same T^ were to be corrected by 

 the rate. Now ^ (o — 0^) = i is the hour-angle of the star in the moment 

 when it passes over the true prime vertical and may be computed from the 

 latitude of the place and the star's declination by the formula 



tan d 



cos t = 



tan tp 



or better still from the formula 



, , ,, sin (^ — 5) 

 tan ^ t' = — / , - . 

 sm (^ -f d) 



The errors in the observation of T — T^ will also here be the smaller, 

 the smaller tan z, i. e. the nearer the star passes the zenith. Now d and b 

 being known we find the north inclination of the apparent horizon 

 /3 = i d - b. 



