to the Legislature of the State oj New York. 263 



By this process it is found that the angle aPz is 3 degrees and 1 1 

 minutes, which is equal to 12 minutes and 44 seconds of time ; 

 showing that in latitude 43° N. on the 1st of January, 1833, the 

 pole star came to the meridian 12 minutes and 44 seconds after it 

 was in the same vertical, or cut the same plumb line with epsilon 

 ursse majoris or Alioth. The lower the latitude of the place, or the 

 greater the distance between the zenith and the pole, the greater 

 will this interval be. This fact alone shows how vague the rule is 

 which has been recommended without due qualifications. 



The place of Alioth is taken from the Connaissance de Terns of 

 1830, and corrected for January, 1833; and the place of the pole 

 star is taken from the Nautical Almanac of this year. 



In preference to this method, the following is recommended as 

 that most commonly used by astronomers, and requiring less calcu- 

 lation, in order to establish a true meridian line. 



Given, the latitude of the place and the north polar distance of 

 the north star. REq,uiRED, the angle Pzb, its greatest azimuth. 



The latitude of the place may be taken from the map of the State 

 with sufficient accuracy for the purpose, for a small variation in this 

 will not sensibly affect the result. 



The north polar distance is given in the annual Nautical Almanac. 

 From these data, find the pole star's greatest azimuth thus: 

 As the cosine of the latitude of the place is to radius, so is the 

 sine of the north polar distance of the pole star to the sine of its 

 greatest azimuth, the angle Pzb. 



The latter part of September, or the beginning of October, is the 

 most convenient time for making the observation, for then the pole 

 star will reach the place required soon after it becomes visible in 

 the evening ; and, as a direction about the time, it may be observed 

 that on the 1st of October next it will be in that position about 50 

 minutes after sun-set, to which may be added about two and a half 

 minutes for every day back, and about as much deducted for every 

 day forward. On the 1st of October, the pole star will be at its 

 greatest azimuth at about 38 minutes after 6 o'clock in the evening, 

 apparent time, or 28 minutes after 6 o'clock, mean time ; that is, 

 the time shown by a well regulated clock, and four minutes earlier 

 on each succeeding day. 



The time when the polar star will be at its greatest azimuth, on 

 any given day, is found thus. Subtract the right ascension of the 

 sun from the right ascension of the star. This will give the time 



