to the Legislature of the State of New York. 263 
By this process it is found that the angle aPz is 3 degrees and 11 
minutes, which is equal to 12 minutes and 44 seconds of time; 
showing that in latitude 43° N. on the Ist 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 
ursve 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 Connatssance de Tems 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- 
Jation, in order to establish a true meridian line. 
Given, the latitude of the place and the north polar distance of 
the north star. Requirep, the angle Pzd, 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 ses 
will not sensibly affect the result. 
The north polar distance is given in the annual Nautical Alesis 
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 Ohicher: 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 Ist 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 Ist 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 beat 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 
