MERIDIAN LINE.

[Footnote: From Proceedings of the Association of County Surveyors of Ohio, Columbus, January, 1882.]

The following process has been used by the undersigned for many years. The true meridian can thus be found within one minute of arc:

Directions.--Nail a slat to the north side of an upper window--the higher the better. Let it be 25 feet from the ground or more. Let it project 3 feet. Kear the end suspend a plumb-bob, and have it swing in a bucket of water. A lamp set in the window will render the upper part of the string visible. Place a small table or stand about 20 feet south of the plumb-bob, and on its south edge stick the small blade of a pocket knife; place the eye close to the blade, and move the stand so as to bring the blade, string, and polar star into line. Place the table so that the star shall be seen very near the slat in the window. Let this be done half an hour before the greatest elongation of the star. Within four or five minutes after the first alignment the star will have moved to the east or west of the string. Slip the table or the knife a little to one side, and align carefully as before. After a few alignments the star will move along the string--down, if the elongation is west; up, if east. On the first of June the eastern elongation occurs about half-past two in the morning, and as daylight comes on shortly after the observation is completed, I prefer that time of year. The time of meridian passage or of the elongation can be found in almost any work on surveying. Of course the observer should choose a calm night.

In the morning the transit can be ranged with the knife blade and string, and the proper angle turned off to the left, if the elongation is east; to the right, if west.

Instead of turning off the angle, as above described, I measure 200 or 300 feet northtward, in the direction of the string, and compute the offset in feet and inches, set a stake in the ground, and drive a tack in the usual way.

Suppose the distance is 250 feet and the angle 1° 40', then the offset will be 7,271 feet, or 7 feet 3¼ inches. A minute of arc at the distance of 250 feet is seven-eighths of an inch; and this is the most accurate way, for the vernier will not mark so small a space accurately.

ANGLE OF ELONGATION.

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:

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,