TO FIND THE VARIATION OF 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 west in the afternoon, towards the north or south according to the decknation.

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.

E e

EXAMPLE 1.

July 3, 1812, in latitude 9° 36' S. the sun was observed to rise E. 22° 42′ N. required the variation of the

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

TO FIND THE VARIATION OF THE COMPASS

BY AN

AZIMUTH.

RULE 1. 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 of the 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,

The log. secant of the latitude, rejecting their indices.

The log. co-sine of the half sum,

And the log. co-sine of the remainder.

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 north in south latitude, towards the west in the afternoon.

6. Then, if the true and observed azimuths be bot on the east and on the west side of the meridian, their

difference is the variation: but if one be on the east and 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 25° S2 N. and longitude 75° W. the altitude of the sun's lower limb was observed to be 15° 36' about 4 h. 10 m. P. M. his magnetic azimuth being S. 58° 32′ W. and the height of the eye 18 feet, required the variation of the compass.

TO ENLARGE OR DIMINISH

MAPS.

To enlarge a Map to Two, Three, or four times the Size.

LET the dotted lines a, b, c, &c. represent a Map, or Survey, laid down by a scale of 40 perches to an inch, and it be required to enlarge it to one laid down by a scale of 20 perches to an inch.

Pitch upon any convenient place, within the Map, for a centre, as ; then lay a straight edged ruler on the centre, and point a; take in the compasses, the distance from this centre to a, and set it from a to A; then lay the ruler on the centre and b, and the distance from the centre to b, lay from b to B; join AB. Thus proceed with every station, and the Map ABCDEFGHIKL, will be double the size of the other.

If it were required to enlarge the Map three or four times the size, then the distances from the centre to each station, must be laid over as many times, &c.

If it be required to reduce a Map from 20 to 40 perches to an inch, then half the distance from the centre to each