vol,. LXVI.] PHILOSOPHICAL TRANSACTIONS. 735 



this zenith distance, as soon as the star is found to come to it, it will be in the 

 proper vertical circle. 



The advantage of this method will appear in the following exarnple of equal 

 altitudes, taken July 15, 1773, at Loam-pit hill, near Deptford, in latitude 5° 

 28' 7" N. and longitude 5 " in time w. of the Royal Observatory at Greenwich. 

 The star selected was y Draconis, having 38° 28' 21" apparent north polar dis- 

 tance, being very little less than the complement of the latitude 38° 31' 53". 

 Then, 



As COS. 38' 28' 21" : rad. :: cos. 38° 31' 53" : cos. 2° 19' the zenith distance; 

 and sin. 38 31 53 : rad. :: sin. 38 28 21 : sin. 87 5 20 " the azimuth ; 



also rad. : tan. 38 28 21 :: cotan 38 31 53 : cos. 3 43 13 the horary arc = I •1'" 



52'.9 in sidereal time, or 14" 50". 5 in mean time. 



The true zenith distance being 2° IQ' the same was diminished by 1" for re- 

 fraction, and the telescope fixed to 2° 18' 58*, the apparent zenith distance; and 

 when the star came to the wires, the times by the clock, were as follow : 



Eastern altitudes. ' Western altitudes. Meridian passage. 



1st wire at.. 9" 55" 43' „„, . ,^ . 10" 29"" 4(ji' .10" 12"" 44'.5 



2d 9 57 57 % \\ \i :* 10 27 32 ..10 12 44.5 



3d 10 9 ' 10 25 20 10 12 44.5 



so that in about 34™ the complete set of altitudes was obtained near the prime 

 vertical, free from the effects of a different refraction, and any motion in azi- 

 muth. The horary arc observed by the middle wire not turning out exactly ac- 

 cording to the computation, is of no consequence to the observations. Some 

 little difference may arise in it from small inaccuracies in the estimation of the 

 star's apparent polar distance, the latitude of the place, or the error of the line 

 of collimation ; or from not setting the telescope exactly to the proper zenith dis- 

 tance; but as the chief intention of the computation is to find the vertical circles 

 in which the star has no motion in azimuth, the other parts of it need not be 

 strictly attended to. 



The following manner of inferring mean time from the star's meridian pas- 

 sage, being more convenient and concise than the usual one, may also be ac- 

 ceptable. From the star's apparent right ascension, increased by 24 hours if 

 necessary, subtract the sun's apparent right ascension for apparent noon ; dimi- 

 nish the remainder by the proportional part of the star's acceleration, at the rate 

 of 3"" 55*.91 for 24 hours, of which a table is easily computed ; to this last re- 

 mainder apply the equation of time for apparent noon, according as it is additive or 

 subtractive ; the result will be the mean time of the star's passing the meridian. 



Ex. — ^The AR apparent of y Draconis July 15, 1773, was l?"" 51"° 24'.0 



— the apparent AR of the sun at apparent noon 7 39 59.0 



. First remainder 10 11 25.0 



— thestar'saccelerationfor 10" 11"'25', at3°'55'.9l for24 hours. 1 40.2 



Second remainder 10 9 4*.8 



+ the equation of time at apparent noon, additive 5 27.7 



^ Gives the star's meridian passage in mean time 10 15 12.5 



