4. If a circle be supposed to pass round the globe of the earth, so as to be equi-distant from each pole, it is called the equator, or equinoctial line, and by some the line only.

And if the plane of the equator be produced to the heavens, it will lay out the celestial equator.

5. The latitude of any place, is its nearest distance to, and counted from the equator in degrees and minutes, and is north or south as it lies on the north or south side of the equator.

6. The poles are 90 degrees from the equator; therefore the complement of the latitude of any place, is the latitude taken from 90 degrees, or the distance of the place from its nearest pole.

7. The declination of the sun, is the nearest distance thereof from the celestial equator counted in degrees and minutes; and is north or south, as it lies on the north or south side of the equator.

8. The sun's declination taken from 90, leaves the complement thereof; or its distance from the nearest celestial pole.

9. The sun's altitude, is the number of degrees and minutes the sun is above the horizon, and is easily found by a quadrant, as before.

10. What the sun's altitude wants of 90, or the sun's distance from the zenith or point of the heavens perpendicularly over you, is the complement of the altitude.

11. The magnetical amplitude, is the complement of the sun's bearing at rising or setting, taken by the quartered compass; on it is the number of degrees the sun is from the east or west point of the compass, at rising or setting.

12. The true amplitude, is the complement of degrees the sun would rise or set on if the compass did not vary; or it is the number of degrees the sun is from the east or west point of the horizon, at rising or setting; and this true amplitude is always north, if the sun's-declination be south.

To find the variation by the amplitudes.

Having the latitude of the place, and the sun's declination given, the true amplitude is found by this astronomical proportion, viz.

As the co-sine or sine complement of the latitude Is to the sine of the sun's declination,

So is radius

To the sine of the true amplitude.

Then if both amplitudes be north, or both south, their difference is the variation, but if one be north and the other south, their sum is the variation.

To know whether the variation be easterly or

westerly.

Let the observer turn his face to the sun, then if the true amplitude be to the right hand of the

magnetical one, the variation is easterly, but if to the left, westerly.

EXAMPLE I.

On the 28th day of May, 1789, the sun's bearing at rising being N. 71° E. in the latitude 53° 20 N. required the true amplitude, and the variation of the needle.

Find the sun's declination by the annexed table and then to find the true amplitude, say,

As the co-sine of the latitude 36° 40′

9.77609 Is to the sine of the declination 21° 34 N. 9.56536

So is radius

To the sine of the true amplitude

90°

10,00000

38° 9.978927

90-71° 19° the mag. amp. from the east. True amplitude E. 38°.00 N. for decl. is N. Magnetical ampl. E. 19°.00 N.

Variation 19.00' W. because the true

amplitude is to the left of the magnetical.

EXAMPLE II.

Suppose the sun's true amplitude is found to be W. 42° 00 S. and the magnetical amplitude W. 23. 00 S. the sun's bearing at setting being SW. 67. Required the variation.

90°-67° 23° the magnetical amplitude from the west.

True amplitude

W. 42° 00' S.

Magnetical amplitude W. 23 00 S.

Variation 19 00 W.

In this case also the true amplitude is to the left of the magnetical; and therefore the variation is westerly.

EXAMPLE III.

Sun's bearing at rising being SE 771°, and the true amplitude being found to be 10°. 12. N. required the variation.

The true amplitude being still to the left, the va

riation is westerly.

EXAMPLE IV.

Sun's bearing at setting is SW. 81°, and the true amplitude is found to be W. 6. 16' N. Required the variation.

90°-81-8 the magnetical amplitude from the west.

True amplitude W. 6°. 16 N. Magnetical amplitude W. 8. 30 S.

Variation 14. 46 E.

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

2. To find the variation of azimuths.

13. The sun's magnetical azimuth is the bearing thereof at any time of the day, taken by the quartered compass; that is, counted from the north or south towards the east or west points of the box.

14. The sun's true azimuth is the point of the compass it would bear from you upon, if there were no variation; or it is the distance intercepted between the north or south points of the horizon and a vertical circle, or circle drawn from the zenith through the sun to the horizon.

Having the latitude of the place, the sun's declination, and its altitude given, the true azimuth is obtained by the following astronomical proportions.