246 Mr Freeman, On a table showing the time and place [May 29, 



that its line of collimation describes the plane of the piime vertical 

 circle, that is, moves so as to be always in the vertical plane at 

 right angles to the meridian. It is an additional advantage if 

 the horizontal axis of the instrument be easily reversible on the 

 fixed north and south supports of its pivots. 



Transits of the same star across the east and west portions 

 of the prime vertical are to be observed ; the latitude may then 

 be inferred if the declination be known ; or the declination and 

 right ascension of unregistered stars may be found from noting the 

 times of their transits, if the latitude has been already determined 

 from the transits of known stars. 



If the vertical circle be large and well graduated, and if a 

 micrometer eye-piece be employed, observations of the zenith 

 distances of stars at their east and west passages will show the 

 effects of refraction. For the true zenith distances may be calcu- 

 lated if we know two of the three quantities, latitude, declination, 

 hour-angle of transit ; and with these the observed zenith distances 

 may be compared. 



Preliminary to a series of such observations it is productive of 

 great saving of time to tabulate at close intervals of north polar 

 distance the corresponding hour-angles and zenith distances with 

 their corresponding mean refractions at transit over the east or 

 west portions of the vertical circle. 



We are thus enabled to set the instrument sufficiently near 

 to its proper position to find the star in the field of view at a 

 sidereal time determined beforehand from the known li. A. of 

 the star and the hour-angle interpolated from the table. 



The formulae on which the table depends are extremely simple. 

 If A be the polar distance of the star, h its hour-angle from the 

 meridian at transit over the prime vertical, z the zenith distance 

 at the same instant, and c the complement of the latitude, we 

 have 



and 



cos z = 



cos h = 



cos A 

 cose 

 tan c 

 tan A 



■(1). 

 .(2). 



