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responding points of the horizon, and is termed east or west variation, according as the magnetic needle, or north point of the compass, is inclined to the eastward or westward of the true north point of the horizon.

The true amplitude of any celestial object is an arch of the horizon contained between the true east or west points thereof, and the centre of the object at the time of its rising or setting ; or it is the degrees and minutes, the object rises or sets to the northward or southward of the true east or west points of the horizon.

The magnetic amplitude, is an arch contained between the east or west points of the compass and the centre of the object at rising or setting ; or it is the bearing of the object, by compass, when in the horizon.

The true azimuth of an object is an arch of the horizon contained between the true meridian and the azimuth circle passing through the centre of the object.

The magnetic azimuth, is an arch contained between the magnetic meridian and the azimuth circle passing through the centre of the object; or it is the bearing of the object, by compass, at any time when it is above the horizon,

The true amplitude, or azimuth, is found by calculation, and the magnetic amplitude, or azimuth, by an azimuth compass.

THE AZIMUTH COMPASS.

From the accounts of the compasses, heretofore given in the description of surveying instruments, it is presumed that the nature and properties of the azimuth compass will be readily conceived by a contemplative inspection; the directions for its uses are as follow :

To observe the Sun's amplitude.

Turn the compass-box until the vane containing the magnifying glass is directed towards the sun : and when the bright speck, or rays of the sun collected by the magnifying glass, falls upon the slit in the other vane, stop the card by means of the nonius, and read off the amplitude.

Without using the magnifying-glass, the sight may be directed through the dark glass towards the sun ; and in this case, the card is to he stopped when the sun is bisected by the thread in the other Vane.

The observation should be made when the sun's lower limb appears somewhat more than his semi diameter above the horizon, because his centre is really then in the horizon, although it is ap

parently elevated on account of the refraction of the atmosphere; this is particularly to be noticed in high latitudes.

To observe the Sun's Azimuth.

Raise the magnifying-glass to the upper part of the vane, and move the box, as before directed, until the bright speck fall on the other vane, or on the line in the horizontal bar; the card is then to be stopped, and the divisions being read off, will be the sun's magnetic azimuth.

If the card vibrate considerably at the time of observation, it will be better to observe the extreme vibrations, and take their mean as the magnetic azimuth. When the magnetic azimuth is observed, the altitude of the object must be taken, in order to obtain the true azimuth.

It will conduce much to accuracy if several azimuths be observed, with the corresponding altitudes, and the mean of the whole taken for the observation.

To find the variationof the Compass by an amplitude.

RULE-1 To the log. secant of the latitude, rejecting the index, add the log. sine of the sun's declination, corrected for the time and place of observation; their sum will be the log. sine of the

; true amplitude, to be reckoned from the east in the morning, or the west in the afternoon, towards the north or south, according to the declination.

2. Then if the true and magnetic amplitudes, be both north or both south, their difference is the variation; but if one be north and the other south, their sum is the variation ; and to know whether it be easterly or westerly, suppose the observer looking towards that point of the compass representing the magnetic amplitude ; then if the true amplitude be to the right hand of the magnetic amplitude, the variation is east, but if to the left hand, it is west.

EXAMPLE I. July 3, 1812, in latitude 99 36' S. the Sun was observed to rise E. 12° 42' N : required the variation of the compass. Latitude 9' 36' S.

Secant 0.00613
Declination 22 59 N.

Sine 9 59158

True amplitude E. 23 20 N. Sine 9.59771
Mag amplitude E. 12 42 N.

Variation 10 38 west, because the true amplitude is to the left of the magnetic.

EXAMPLE II. September 24, 1812, in latitude 26° 32' N. and longitude 78° W. the Sun's centre was observed to set W. 6° 15' S. about 6h. P. M. required the variation of the compass. Sun's declination

0° 30' S. Corr for long. 78o W.

+ 5 Corr. for time 6h. P. M.

6

+

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Variation 5 29 east, because the true amplitude is to the right hand of the magnetic.

To find the Variation of the Compass by an Azimuth.

Rule.l.- Reduce the Sun's declination to the time and place of observation, and compute the true altitude of the Sun's centre.

2. Subtract the Sun's declination from 90°, when the latitude and declination are of the same name, or add it to 90°, when they are of contrary names ; and the sum, or remainder, will be the Sun's polar distance.

3. Add together the Sun's polar distance, the latitude of the place, and the altitude of the Sun; take the difference between half their sum and the polar distance, and note the remainder. 4. Then add together

the log. secant of the altitude rejecting their the log. secant of the latitude indices

the log. co. sine of the half sum, and thelog. co. sine of the remainder.

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rejecting their

5. Half the sum of these four logarithms will be the sine of an arch, which doubled, will be the Sun's true azimuth; to be reckoned from the south in north latitude, and from the north in south latitude : towards the east in the morning, and to wards the west in the afternoon.

6. Then if the true and observed azimuths be both on the east, or both on the west side of the meridian, their difference is the variation : but if one be on the east and the other on the west side of the meridian, their sum is the variation; and to know if it be east or west, suppose the observer looking towards that point of the compass representing the magnetic azimuth ; then if the true azimuth be to the right of the magnetic, the variation is east, but if the true be to the left of the magnetic, the variation is west.

EXAMPLE November 2, 1812, in latitude 259 32' N. and longitude 75o W. the altitude of the Sun's lower limb was observed to be 15° 36', about 4h. 10m. P. M. his magnetic azimuth at that time being S. 58° 32' W.and the height of the eye 18 feet; required the variation of the compass. Sun's de. Nov. 2, at n. 14" 48'S. Obs. alt. Sun's lower limb 15° 63 Corr. for long. 75o W.+

Semidiameter Co. for ti. 4h. 10m. af. n. +

16/2

4

Dip
Reduced declination

Refraction
Polar distance

True altitude
Altitude

Secant 0.01662
Latitude

Secant 0.04463
Sum

146 12
Half

Co. sine 9.46345
Remainder

Co, sine 9.92929

+ 12

3 14 55 90 00 104 65 15 45 25 32

15 48

3 15 45

73 6
31 49

32 14

19.45399
2

Sine 9.72699
True azimuth S. 64 28 W.
Mag. azimuth S. 32 W.
Variation

5 56 east, because the true azimuth is to the right of the magnetic.

To draw a true meridian line to a man, having the variation

and magnetical meridian given. On any magnetical meridian or parallel, upon which the 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 consti. . tutes 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 mcridian 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.

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 froin 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 de. grees 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 a true meridian line.

If the variation was casterly, 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 toward 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.

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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.

To find the difference between the present variation, and that as a time when a tract was formerly surveyed, in order to trace or run out the original lines.

If the old variation be specified in the map or writings, and the present be known, by calculation or otherwise, then the difference is im

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