12. Our first object will be to mark the line, as it was in 1840, of no variation. For this purpose we shall make a table of places lying near this line.

At the point whose latitude is 40° 53', longitude 80° 13', the variation of the needle was nothing in the year 1840, and the direction of the line of no variation, traced north, was N 24° 35′ west. The line of no variation, prolonged, passed a little to the east at Cleveland, in Ohio— the variation there being 19 minutes east. Detroit lay still further to the west of this line, the variation there being 1° 56' east; and Mackinaw still further to the west, as the variation at that place was 2° 08′ east.

The course of the line of no variation, prolonged southerly, was S 24° 35' E. Marietta, in Ohio, was west of this line—the variation there being 1° 24' east. Charlottesville, in Virginia, was a little to the east of it-the variation there being 19' west; whilst Charleston, in South Carolina, was on the west, the variation there being 2° 44' east.

From these results, it will be easy to see about where the line of no variation is traced in our own country.

Places.

PLACES WHERE THE VARIATION WAS EAST.

Latitude. Longitude. Variation. An. Motion.

METHODS OF ASCERTAINING THE VARIATION.

14. The best practical method of determining the true meridian of a place, is by observing the north star. If this star were precisely at the point in which the axis of the earth, prolonged, pierces the heavens, then, the intersection of the vertical plane passing through it and the place, with the surface of the earth, would be the true meridian. But, the star being at a distance from the pole, equal to 1° 30′ nearly, it performs a revolution about the pole in a circle, the polar distance of which is 1° 30': the time of revolution is 23 h. and 56 min.

To the eye of an observer, this star is continually in motion, and is due north but twice in 23 h. 56 min.; and is then said to be on the meridian. Now, when it departs from the meridian, it apparently moves east or west, for 5 h. and 59 min., and then returns to the meridian again. When at its greatest distance from the meridian, east or west, it is said to be at its greatest eastern or western elongation. The following tables show the times of its greatest eastern and western elongations:

EASTERN ELONGATIONS.

Days. April. May. June. July. August.

Sept.

The eastern elongations are put down from the first of April to the first of October; and the western, from the first of October to the first of April; the time is computed from 12 at noon. The western elongations in the first case, and the eastern in the second, occurring in the daytime, cannot be used. Some of those put down are also invisible, occurring in the evening, before it is dark, or after daylight in the morning. In such case, if it be necessary to determine the meridian at that particular season of the year, let 5 h. and 59 min. be added to, or subtracted from, the time of greatest eastern or western elongation, and the observation be made at night, when the star is on the meridian.

15. The following table exhibits the angle which the meridian plane makes with the vertical plane passing through the pole-star, when at its greatest eastern or western elongation such angle is called the azimuth. The mean angle only is put down, being calculated for the first of July of each year:

Year.

AZIMUTH TABLE.

Lat. 32° Lat. 34° Lat. 36° Lat. 88° Lat. 40° Lat. 42° Lat. 44°
Azimuth. Azimuth. Azimuth. Azimuth. Azimuth. Azimuth. Azimuth.

1851 1° 45′ 1° 48′

1852 1° 45′ 1° 47

1/

1° 50' 1° 53′ 1° 56′2° 00′2° 041′

1° 50' 1° 53′ 1° 56' 1° 593/2° 033'

1853 1° 441° 47' 1° 493 1° 52' 1° 55′ 1° 591 2° 03′

4931°

1854 1° 44'1° 46′ 1° 49′ 1° 52′ 1° 55' 1° 59′ 2° 023'

1855 1° 4331° 46' 1° 4831° 5131° 543 1° 58′ 2° 02' 1856 1° 4311° 453' 1° 481'1° 51'1° 54' 1° 58' 2° 013 1857 1° 43′ 1° 45'1° 48′ 1° 5031° 54′ 1° 57' 2° 01' 1858 1° 42' 1° 4431° 47'1° 50' 1° 53' 1° 57' 2° 003 1859 1° 42′ 1° 44' 1° 47' 1° 493 1° 53′ 1° 56′ 2° 00′ 1860 1° 4131° 44' 1° 46'1° 4911° 52' 1° 56' 2° 00'

The use of the above tables, in finding the true meridian, will soon appear.

TO FIND THE TRUE MERIDIAN WITH THE THEODOLITE.

16. Take a board, of about one foot square, paste white paper upon it, and perforate it through the centre; the diameter of the hole being somewhat larger than the diameter of the telescope of the theodolite. Let this board be so fixed to a vertical staff, as to slide up and down freely: and let a small piece of board, about three inches square, be nailed to the lower edge of it, for the purpose of holding a candle.

About twenty-five minutes before the time of the greatest eastern or western elongation of the pole-star, as shown by the tables of elongations, let the theodolite be placed at a convenient point and levelled. Let the board be

placed about one foot in front of the theodolite, a lamp or candle placed on the shelf at its lower edge; and let the board be slipped up or down, until the pole-star can be seen through the hole. The light reflected from the paper will show the cross hairs in the telescope of the theodolite.

Then, let the vertical spider's line be brought exactly upon the pole-star, and, if it is an eastern elongation that is to be observed, and the star has not yet reached the most easterly point, it will move from the line towards the east, and the reverse when the elongation is west.

At the time the star attains its greatest elongation, it will appear to coincide with the vertical spider's line for some time, and then leave it, in the direction contrary to its former motion.

As the star moves towards the point of greatest elongation, the telescope must be continually directed to it, by means of the tangent-screw of the vernier plate; and when the star has attained its greatest elongation, great care should be taken that the instrument be not afterwards moved.

Now, if it be not convenient to leave the instrument in