18°23'-9.52031

As the tang. of the compt. of the latitude,

Is to the tangent of the sum of the distance of the sun from the pole and complement of the altitude,

:: tang. of their difference

61.43-10.26916

9.13-9.21022

19.47938

To a tangent of a fourth arc. 42. 18-9.95907

Co-sine of the sun's true azim. 70.04— 9.53288

The true azimuth being to the left of the magnetic

one, the variation is westerly.

EXAMPLE II.

Suppose the sun's true azimuth N. 83°. 20′ E. but the magnetical one N. 70°.30' E. Required the variation.

The true azimuth being to the right of the magne tical one, the variation is easterly.

EXAMPLE III.

Suppose the sun's true azimuth was S. 37°. 15W. and the magnetical one S. 44°.20W. Required the

The true azimuth being to the left of the magneti

EXAMPLE IV.

Suppose the sun's true azimuth be S. 4°.05 W. and the magnetical one S. 3°.30 E. Required the varia

The true azimuth being to the right of the magnetical, the variation is easterly.

The variation of the compass was first observed at London in the year 1580, to be one point of the compass easterly, or 11°.15' E. after which time it became less; for in the year 1622 it was 6°.00' E. in 1634 it was 4°05' E. and so continued to decrease till the needle coincided with the true meridian, and then there was no variation; after which the variation became westerly, and has ever since increased to the westward; for in the year 1672 it was 2o.33′ W. in the year 1683 it was 40.30' W. at London; in 1722 it was at Dublin found to 11°.15' W. and in 1751 it was there found to be 19°.00′ W. At London, in the year 1800, it was about 23°.30', and still continues to increase westerly at the rate of 11 or 12' every year.

At Paris in 1640, the variation was 3°.00' E. in 1666 there was no variation; but in 1681 it was 20.30′ W. and still continues to go on westerly.

How to draw a true meridian line to a map, having the variation and magnetical meridian given.

On any magnetical meridian or parallel, upon which your map is protracted, set off an angle from the north towards the east, equal to the degrees or quantity of variation, if it be westerly, or from the north towards the west if it be easterly, and the line which constitutes such an angle with the magnetical meridian, will be a true meridian line.

For if the variation be westerly, the magnetical meridian will be the quantity of variation of the west side of the true meridian, but if easterly on the east side, therefore the true meridian must be a like quantity on the east side of the magnetical one, when the variation is westerly, and on the west side when it is easterly.

How to lay out a true meridian line by the circumferentor.

If the variation be westerly, turn the box about till the north of the needle points as many degrees from the flower-de-luce towards the east of the box, or till the south of the needle points the like number of degrees from the south towards the west, as are the number of degrees contained in the variation, and the index will be then due north and south; therefore, if a line be struck out in the direction thereof, it will be

If the variation was easterly, let the north of the needle point as many degrees from the flower-de-luce towards the west of the box, or let the south of the needle point as many degrees towards the east, as are the number of degrees contained in the variation, and then the north and south of the box will coincide with the north and south points of the horizon, and consequently a line being laid out by the direction of the index, will be a true meridian line.

This will be found to be very useful in setting an horizontal dial, for if you lay the edge of the index by the base of the stile of the dial, and keep the angular point of the stile towards the south of the box, and allow the variation as before, the dial will then be due north and south, and in its proper situation; provided the plane upon which it is fixed be duly horizontal, and the sun be south at noon; but in places where it is north at noon, the angular point of the index must be turned to the north.

How maps may be traced by the help of a true meridian line.

If all maps had a true meridian line laid out upon them, it would be easy by producing it, and drawing parallels, to make out field notes; and by knowing the variation, and allowing it upon every bearing, and having the distances, you would have notes sufficient for a trace. But a true meridian line is seldom to be met with, therefore we are obliged to have recourse to the foregoing method. It is therefore advised to lay out a true meridian line upon every map.