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1. As the tangent of half the complement of the altitude,

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

So is the tangent of half the difference between the distance of the sun from the pole, and complement of the altitude,

To the tangent of a fourth arc.

Add this fourth arc and half the complement of the latitude together, their sum will give a fifth arc; from which if the complement of the latitude be taken, the remainder will give a sixth arc.

Then say,

As radius
Is to the tangent of the altitude,
So is the tangent of the sixth arc
To the co-sine of the sun's true azimuth.

Which is counted from the north or south, to the east or west, according to the sun's situation at the time and place of observation.

If the latitude of the place, and the sun's declination be both north or both south, the declination taken from 90°, give the sun's distance from the pole, but if one be north and the other south, the declination added to 90°, will give the sun's distance from that pole which is nearest the observer.

If both azimuths are east or west, their difference is the variation ; but if one be east, and the other west, their sum is the variation.

To know whether the variation be easterly or

westerly.

Just as with the amplitudes, let the observer's face be turned to the sun; then if the true azimuth be to the right hand of the magnetical one, the variation is easterly; but if to the left, westerly.

EXAMPLE I.

In the latitude 53° 20' N. the sun's declination being 19° 03' N. I find by observation the sun's altitude to be 37° 30', and its magnetical azimuth to be SE, 51o. Required the variation.

90° 59° 20'=36° 40', the compt. of the latitude

18 20 } the compt. of the latitude

90°—37 30 – 52o. 30', the compt. of the altitude.

90°— 19° 03' 70° 57', the sun's dist. from the pole

52 30 compt. of the altitude

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As the tang. of the

18° 23' 9.52031 compt. of the latitude

Is to the tangent of the sum of the distance of the

61° 43'-- 10.26916 sun from the pole and complement of the altitude.

:: tang. of their difference 9° 13 9.21022

19.47938

To a tangent of a fourth arc, 42° 18'— 9.95007

Half the compt. of the latitude
The 4th arc

18° 20'
62 18

Their sum is the 5th arc

60 38 Complement of the lat. subtract. 36 40

Gives the 6th arc

23 58

As radius
Is to the tang. of the alt.
: : tangent of the 6th arc

90° 00-10.00000 37 30 — 9.88498 23 58 0.64790

Co-sine of the sun's true azim. 70 04-9.53288

True azimuth
Magnetical azimuth

S. 700 04' E.
S. 51 00 E.

Variation

19 04 W.

The true azimuth being to the left of the magnetical one, the variation is westerly.

EXAMPLE II.

Suppose the sun's true azimuth N. 830. 20. E. but the magnetical one N. 70° 30. E. Required the variation.

True azimuth
Magnetical azimuth

N. 83o. 20 E
S. 70. 30 E.

Variation

12. 50 E.

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

EXAMPLE III.

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

True azimuth
Magnetical azimuth

S. 370. 15' W.
S. 44. 20 W.

Variation

6. 05 W

The true azimuth being to the left of the mag. netical one, the variation is westerly.

EXAMPLE IV.

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

True azimuth
Magnetical azimuth

S. 4°. 05' W..
S. 3. 30 E.

Variation

7. 35 E

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 upon the true meridian, 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 4o. 00 W. at. London ; in 1722 it was at Dublin found to be 11° 15' W. and in 1751 it was there found to be 199.00' W. but how far it will continue to move more westerly, time and observations will probably be the only means to discover.

At Paris in 1640, the variation was 3o. 00' E. in 1666 there was no variation ; but in 1681 it was 2o. 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

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