Two methods of using Polaris for finding latitude

Those of us sailing in the northern hemisphere have a great advantage
because we can use Polaris, or the North Star, to easily obtain a latitude
position.
Polaris lies above the axis of the earth, about 1Â° away from the
imaginary celestial North Pole. Because it is slowly revolving around that
point, a Polaris sight requires some corrections to yield an accurate
latitude sight.
There are two methods for correcting the sight and I shall compare
them. One comes from the Nautical Almanac and is probably most familiar to
the readers. The other correction tables can be found at the rear of H.O.
249 Vol. 1 Selected Stars, which is published every five years.
In both cases the entering arguments is LHA Aires, and the sight
reduction is from Hs to Ho. Once the sight has been reduced, including
entering the 3rd correction, then the corrections can be added to the H.O.
and the latitude can be found. Because Polaris is moving so slowly, the
seconds of the sight time are not required.
As with any star sight, unless there is a full moon illuminating the
horizon, the shots have to be taken either at civil, or nautical twilight.
Let’s do a problem.
It is December 10, 2008. The Hs of Polaris is 42Â° 25.2′. The height
of eye is 10 feet. The time of the sight is 16 hrs 52 min. The DR is 43Â°
50′ N by 73Â° 15′ W.

First we have to find the GHA Aires for the time of the sight:

16 hrs    319Â° 45.1′
52 min    13Â° 02.1′
GHA Aires 332Â° 47.2′
-Ass long    73Â° 47.2′
LHA Aires    259Â°

Next we reduce the Hs to Ho:

Hs        42Â° 25.2′
-dip        3.1′
Ha        42Â° 22.1′
3rd corr –    1.1′
Ho        42Â° 21.0′

Now we are ready to enter the Polaris correction tables in the rear of the
Nautical Almanac, page 276. The directions for use require that we take our
Ho and first subtract 1Â° and then add back the three corrections. They are
as follows:

Ho            42Â° 21.0′
-1Â°
41Â° 21.0′
LHA Aires 259Â°  ao +1Â° 31.6′
+ Lat            (a1) +0.6′
+ Month        (a2) +0.5′
Latitude        42Â° 53.7′

Now let’s compare that with the results we get from using HO 249 Vol.1:

First we will use H.O. 249 to find GHA Aires. We go to the rear of the
volume and find a table for GHA Aires For the Years 2001-2008. We then just
make our entries:

Dec. 2008            70Â° 13′
Inc for days and hours  +249Â° 32′
Min of time+        13Â° 02′
GHA Aires            332Â° 46′
-Ass long            73Â° 46′
LHA Aires            259Â°

Next we go to the last page of H.O. 249 to the table for correction (Q)
For Polaris. We go to the column that includes LHA Aires 259Â° and find a
critical table. The Q correction is +33′ and we add that to the Ho:

Ho    42Â° 21.0′
+    33′
Lat:    42Â° 54′

So we have a difference of 0.3′ between the two techniques. Take your
pick and have fun.