This should be computed by the surveyor for each observation. The
distance between the star and the pole is continually diminishing, and
on January 1, 1882, was 1° 18' 48".
There is a slight annual variation in the distance. July 1, 1882, it
will be 1° 19' 20". If from this latter quantity the observer will
subtract 16" for 1883, and the same quantity for each succeeding year
for the next four or five years, no error so great as one-quarter of a
minute will be made in the position of the meridian as determined in the
summer months. If winter observations are made, the distance in January
should be used. The formula for computing the angle of elongation is
easily made by any one understanding spherical trigonometry, and is
this:
R x sin. Polar dist.
--------------------- = sin. of angle of elongation.
cos. lat.
As an example, suppose the time is July, 1882, and the latitude 40°.
Then the computation being made, the angle will be found to be 1° 43'
34". A difference of six minutes in the latitude will make less than
10" difference in the angle, as one can see by trial. Any good State
or county map will give the latitude to within one or two miles--or
minutes.
The facts being as here stated, the absurdity of the Ohio law,
concerning the establishment of county meridians, becomes apparent. The
longitude has nothing at all to do With the meridian; and a difference
of _six miles_ in latitude makes no appreciable error in the meridian
established as here suggested, whereas the statute requires the latitude
within _one half a second_, which is _fifty feet_. There are some other
things, besides the ways of Providence, which may be said to be "past
finding out." It is not probable that a surveyor would err so much as
_three_ miles in his latitude, but should he do so, then the error in
his meridian line, resulting from the mistake, will be _five seconds_,
and a line _one mile_ long, run on a course 5" out of the way, will vary
but _an inch and a half_ from the true position. Surveyors well know
that no such accuracy is attainable. R. W. McFARLAND,
* * * * *