This section is from "Scientific American Supplement Volumes 275, 286, 288, 299, 303, 312, 315, 324, 344 and 358". Also available from Amazon: Scientific American Reference Book.
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,