the difference of the heights of the two observers in feet by the difference of the observed altitude in minutes, and reserve the quotient. Divide the height of the lower observer in feet by this reserved number, and to the quotient add one quarter of the reserved number, and the sum will be the dip in minutes corresponding to the lower observer, Thus in the above example 5',6 is the reserved number, and 24. 4, to this add one fourth of 5'.6 or 1.4 and the sum will be the dip 5'.8 or nearly 6' corresponding to the lower observer, being the same as was found by the table.

68

12

TO FIND THE SUN'S DECLINATION.

THE declination of the sun is given to the nearest minute in Tab. IV. for every noon at Greenwich, from the year 1824 to 1838; and this table will answer for some years beyond that period, without any material error; if great accuracy is required, the declination may be taken from the second page of the month of the Nautical Almanac.* This declination may be reduced to any other meridian, by means of Table V. in the following

.manner.

To find the sun's declination at noon, at any place.

RULE. Take out the declination at noon at Greenwich from Table IV. (or from the Nautical Almanac;) then find the longitude from Greenwich in the top column of Table V. and the day of the month in the side column; under the former, and opposite to the latter, will be a correction in minutes and seconds, to be applied to the declination taken from Table IV: to know whether this correction be additive or subtractive, you must look at the top of the column where you found the day of the month, and you will see it noted whether to add or subtract, according as the longitude is east or west. This correction being applied, you will have the declination at noon at the given place.

EXAMPLE I.

Required the declination of the sun at the end of the sea-day, October 10, 1824, in the longitude of 1140 E. from Greenwich?

Sun's declination Oct. 10, at Greenwich, at the end of the sea-day

or beginning of the day in the N. A. by Tab. IV. . . Variation of Dec. Tab. V. Oct. 10, in 114° E. long. şub.

True dec. noon, Oct. 10. in long. 114° E.

EXAMPLE II.

..

6° 44′ S.

7

37 S.

Required the sun's declination at noon ending the sea-day of March 12, 1824, in the longitude of 750 W. from Greenwich?

Sun's declination March 12, by Tab. IV..
Var. Tab. V. March 12, long. 75° W.

sub.

True declination, noon, March 12, long. 75° W.

3° 13' S. 5

3 8 S.

The preceding correction ought always to be applied to the declination used in working a meridian observation to determine the latitude, though many mariners are in the habit of neglecting it.

* In finding the declination, or any other quantity, in the Nautical Almanac, you must be careful to note the difference between the civil, nautical, and astronomical account of time. The civil day begins at midnight, and ends the following midnight, the interval being divided into 24 hours, and is reckoned in numeral succession from 1 to 12, then beginning again at 1 and ending at 12. The nautical or sea day begins at noon, 12 hours before the civil day, and ends the following noon; the first 12 hours are marked P. M. the latter A. M. The astronomical day begins at noon, 12 hours after the civil day, and 24 hours after the sea-day, and is divided into 24 hours, numbered in numeral succession from 1 to 24, beginning at noon, and ending the following noon. All the calculations of the Nautical Almanac are adapted to astronomical time; the declination marked in the Nautical Almanac, or in Table IV. is adapted to the beginning of the astronomical day, or to the end of the sea-day, it being at the end of the sea-day when mariners want the declination to determine their latitude. It would be much better f seamen would adopt the astronomical day, and wholly neglect the old method of counting by the sexday,

To find the sun's declination at any time under any meridian. RULE. Reduce the sun's declination at noon at Greenwich to noon under the given meridian, by the preceding rule. Then enter Table V. with the time from noon at the top, and the day of the month in the side column; under the former, and opposite the latter, will be the correction to be applied to that reduced declination. To know whether this correction be additive or subtractive, you must look at the top of the column where you found the day of the month, and you will find it noted whether to add or subtract, according as the time is before or after noon.

EXAMPLE III.

Required the sun's declination October 10, 1824, sea account, at 8h. 21' in the forenoon, in the longitude of 114° E. from Greenwich?

Sun's declination Oct. 10, at Greenwich at noon, by Tab. IV. 6° 44' S. Variation for 114° E. long.

Declination at noon, October 10, in long. 114° E.
Variation of dec. for 3h. 39' from noon* Oct. 10,

sub.

7

True dec. Oct. 10, sea acc. in long. 970 E. at 8h. 21' A. M. ...6 34 S.

EXAMPLE IV.

Required the sun's declination May 10, 1824, sea account, at 5h. So' P. M. in the longitude of 17° 30′ E. from Greenwich ? Variation of declination, May 10, in long. 17° 30′ E. Variation of declination for 5h. 30' P. M. additive

.

sub.

.

48" S' 44

256

Diff. is additive because the greatest number is so
May 10, sea account, is May 9, by N. A. at which time sun's
declination

Frue declination May 10, 5h. 30' P. M. sea account in long. 17° 30' E.

170 25 10

17 28 GN.

EXAMPLE V.

Required the sun's declination March 26, 1824, sea account, at 3h. P. M. in the longitude of 120° E. from Greenwich? Variation of declination, March 26, in long. 120° E. Variation for 3h. P. M.

sub.

add

7' 50" 2.56

Diff. is subtractive because the greatest number is so
March 26, sea acc. is Mar. 25, by N. A. at which time sun's dec. 1 54 41 N.

IT was many years after the discovery of the compass, before it was suspected that the magnetic needle did not point accurately to the north pole of the world; but about the middle of the sixteenth century, observations were made in England and France, which fully proved that the needle pointed to the eastward of the true north. This difference is called the variation of the compass, and is named east when the north point of the compass (or magnetic north) is to the eastward of the true north; but west when the north point of the compass is to the westward of the true north. The quantity of the variation may be found by observing with a compass the bearing of any celestial object when in the horizon (or, as it is called, the magnetic amplitude) the difference between this and the true amplitude found by calculation, will be the variation. The same may be obtained by observIn the present example, the time is Oct. 10, 8h. 21'. A. M. which evidently wants Sh. 39′′ of the cys If the sea day Oct 10, for which time the declination is marked in Table IV.

ing the magnetic azimuth of any celestial object (that is, its bearing by a compass when elevated above the horizon;) the difference between this and the true azimuth found by calculation will be the variation.

Some years after the discovery of the variation, it was found that it did not remain constant: for the easterly variation observed in England gradually decreased till the needle pointed to the true north, and then increased to the westward, and is now above two points.

As all the courses steered by a compass must be corrected for the variation to obtain the true courses, it is of great importance to the navigator to know how to find the variation at any time; to do this it is necessary to find the magnetic amplitude or azimuth of a celestial object, which may be done as follows:

To observe an amplitude by an azimuth compass.

When the centre of the sun is about one of his diameters above the hori zon, turn the compass round in the box, until the centre of the sun is seen through the narrow slit which is in one of the sight vanes, exactly on the thread which bisects the slit in the other ; at that instant push the stop which is in the side of the box against the edge of the card, and the degree and parts of a degree which stand against the middle line on the top will be the magnetic amplitude of the sun at that time, which is generally reckoned from the east or west point of the compass.

To observe an azimuth by an azimuth compass.

Turn the compass round in the box until the centre of the sun is scen through the narrow slit which is in one of the sight vanes, exactly on the thread which bisects the slit on the other, or until the shadow of the thread falls directly along the line of the horizontal bar,‡ the card is then to be stopped, and the degree and parts of a degree which stand against the middle line of the stop, will be the magnetic azimuth of the sun at that time, which is generally reckoned from the north in north latitude, and from the south in south latitude.§ At the time of making this observation, you must. also observe the altitude of the sun, in order to obtain the true azimuth. What is here said of the sun, is alike applicable to the moon, planets, and .stars.

TO FIND THE TRUE AMPLITUDE.

RULE.

BY LOGARITHMS.-To the log-secant of the latitude (rejecting 10 in the inder) add the log. sine of the sun's declination;|| the sum will be the log. sine of the true amplitude or distance of the sun from the east or west point, towards the north in north declination, but towards the south in south declination.

BY INSPECTION.-Find the declination at the top of Table VII. and the latitude in the side column; under the former, and opposite the latter, will be the true amplitude. When great accuracy is required, you may proportion for the minutes of latitude and declination.

The figure of an azimuth compass, furnished with sight vanes, is given in Plate VI. fig. 5. The card of this compass is similar to that of a common compass.

The observation is to be taken at that altitude on account of the dip, refraction and parallax, the correction of altitude depending on these causes being in general nearly equal to the sun's diameter. If the instrument is furnished with a magnifying glass fixed to one of the vanes, you may (instead of proceeding as above) turn the compas--box until the vane is directed towards the sun, and when the hright speck (or rays of the sun collected by the maguitying glass) falls upon the slit of the other vane, or upon the line in the horizontal bar, the card is to be stopped, and the divisions read off as above.

§ If the compass vibrate considerably at the time of making the observations, it would be condurive to accuracy to take several azimuths and altitudes, and to take the mean of all the azimuths and all the altitudes, and work the observation with the mean azimuth and altitude. The same is to be observed in taking an amplitude.

The declination of the sun at noon is given in the Nautical Almanac, and in Table IV. and must be corrected for the longitude of the ship and the hour of the day, by means of Table V.