which, being added to 19° 41', will give 20° 3′ for the meridian altitude, or 69° 57′ for the zenith distance, being the same as in that example.

It is very advantageous in this method to observe as many altitudes in the afternoon as before noon, and at nearly the same distances from noon; for in this case a small error in the regulating of the watch will not materially affect the calculation. This will appear evident by supposing, in the preceding example, that the watch was 11m 2 too slow, instead of 10TM 2; by this means the times and numbers will be as in the adjoined table, and the mean of all the numbers, taken from Table XXXIII., will be 8.15, which, being multiplied by 1.6, will give 13' nearly, for the correction, instead of 11', so that in this case an error of one minute in the regulation of the watch would only cause an error of 2 seconds in the meridian altitude.

But it must be carefully observed, that, in using this method, you must not take the observation more than 2 or 3 minutes from noon, when the sun passes within 10° or 12° of the zenith.

Times.

In Tab. XXXIII.

3.15 10.6

2.00

4.0

1.06

1.2

0.08

0.0

0.30

0.2

1.50

3.4

2.12

4.8

3.15

10.6

4.10

17.4

5.25 29.3

TO DETERMINE THE LATITUDE ON SHORE BY MEANS OF AN ARTIFICIAL HORIZON.

It frequently happens that the latitude of a place on shore cannot be determined by the usual methods, by a quadrant, sextant, or circle, on account of not having an open horizon. In this case it is customary to make use of an artificial horizon formed by the surface of a vessel filled with inercury, water, Barbadoes tar, very clear molasses, or any other fluid of sufficient consistency not to be affected by the wind.* With this apparatus an observation may be taken on shore when the altitude of the object does not exceed 60°, with as much ease as at sea. Thus, if an altitude of the sun was required to be taken, the observer must place the vessel containing the mercury (or other fluid) in a firm position on the ground, and in a few minutes the surface of the liquor will attain a horizontal situation; the observer must then place himself in a situation so as to see the image of the sun, formed by the fluid, which image will evidently be depressed as much below the horizon as the sun is elevated above it, so that, to obtain the double of the sun's altitude, it is only necessary for the observer to bring the image of the sun, formed by the instrument, down to the image formed by the artificial horizon, and the angle then pointed out by the index will be double of the altitude of the sun; the half of which will be the apparent altitude. If the nearest limbs of the two images are brought in contact, the half of the angle obtained by the instrument will be the altitude of the sun's lower limb, but if the farthest limbs are brought in contact, the half angle will be the altitude of the upper limb. The altitude thus obtained must be corrected for semidiameter, parallax, and refraction, as usual, but not for dip, because a truly horizontal surface is obtained by means of the artificial horizon. In this manner the altitude of the sun, or any other bright object may be obtained when the altitude is less than 60°; at higher altitudes the angle corresponding would be above 120°, which cannot be measured by a sextant on account of the length of the arc, nor by any other instrument of reflection, in a convenient manner, with a sufficient degree of accuracy. To illustrate this method we shall here add the following examples:

* In case the wind blows fresh, you must use a screen formed of two plates of talc or glass whose surfaces are ground perfectly parallel, and connected together in a frame so as to make an angle of about 90° with each other. This frame is to be placed over the box containing the fluid, and the rays of the sun, passing through one of the plates, are reflected from the surface of the liquor, and pass through the other plate to the eye of the observer. The use of these plates is to be avoided, when it can possibly be done, on account of the defect of parallelism of the surfaces. This error is generally greatest near the border of the glass, so that it has been recommended to cover the edge of the glass with a paper or some paint, to the distance of or inch from the frame. If the surfaces of the glass are perfectly parallel, the observed angle will be the same as if the screen had not been used. Instead of using the screen we may place one of the glasses of the screen upon the surface of the fluid, which will prevent it from being agitated by the wind, or other similar causes. If the reflecting fluid is molasses, air-bubbles will sometimes rise on the surface by the sun's heat; this may in some measure be avoided by heating the molasses before using it.

If the instrument has an index error, it must be applied to the observed angle, or the half of the index

The latitude may be determined on shore by this method to a great degree of accuracy by means of a circle of reflection, by taking several altitudes a few minutes before and after the sun passes the meridian, and estimating the correction to be applied to the altitude by means of Tables XXXII. and XXXIII. Thus, if, in the example page 202, the observations had been taken in this manner, the number of degrees denoted by the circle after taking ten observations, would have been 595° 20' ; this, being divided by 20, (twice the number of observations,) will give for the observed altitude 29° 46 and by adding the semidiameter 16', parallax 8', and the correction found by Tables XXXII. and XXXIII., viz. 11 seconds, and subtracting the refraction 1' 39', the cen tral altitude will be obtained, 30° 0′ 40′′, as in the page before mentioned.

Altitudes may be observed in this way in taking an azimuth for determining the variation, or for regulating a watch, in the manner explained in this work; observing, in all cases, that the half of the observed angle is to be corrected for refraction, parallax, and semidiameter, but not for the dip of the horizon, and that half tho index error only is to be applied.

TO FIND THE POSITION* OF A SHIP ON A LINE OF BEARING.

CASE I

When the position of a ship is unknown, the latitude by account being uncertain, assume two or more latitudes, and work out the longitudes corresponding thereto. A line drawn on a chart through the two points thus determined, will represent the line of equal altitudes. The place of the ship will be somewhere on this line; and if it passes through the land, the bearing of the land will be known. If the coast should run parallel to this line, you will have the distance of the ship from the land, but of course not the absolute position.

December 17th, 1837.-The latitude, by account, being 51° 37' N., the Greenwich time 10h. 47m. 13s. A. M., the true altitude of the sun's centre was found to be 12° 10′. Required the true bearing of the land.

Let the assumed latitudes be 51 and 52°, sun's declination 23° 23' S., and the equation of time

-3m. 37s.-The longitude corresponding to 51° latitude will be about 8° 42′ W. The longitude corresponding to 52° latitude will be about 4° 50' W. A line drawn through these positions A A', will represent the line of equal altitudes, and will also pass through "Small Lights," and run parallel to the S. E. coast of Ireland.

The light was seen in the course of an hour, and the error in latitude ascertained to be 8', C being the position of the ship.

CASE II.

When a double altitude is taken, the position of the ship may be found by working the longitude for each altitude, as in Case I., and then drawing two lines of equal altitudes through the four points A A' and B B' thus determined. The point of intersection of said lines will give the position of the ship. The necessary correction for the change of position, when the second altitude was taken, must be made as explained on page 183, or by moving the line A A' projected (parallel to itself) along the course and distance made good by the ship. Thus, suppose between the observations the ship had sailed E. N. E. 25 miles. Then move the first line A A' parallel to itself on this course 25 miles, and draw a line whose intersection with the second line B B' will give the position required.

The assumed latitude must be near the truth, to give value to this method. When the altitude is high, an error in the assumed latitude is of greater importance than when it is low.

• From Sumper's work.

TO FIND THE LATITUDE BY AN ALTITUDE OF THE POLE STAR.

In northern climates, the Atitude may be determined by means of an observed altitude of the pole star; provided the apparent time of observation can be ascertained within a few minutes.* This method might be frequently used at sea, when the horizon is well defined, if that star were of the first magnitude; but being only of the second or third magnitude, it is sometimes so dim that it is rather difficult to determine the altitude with precision. How. ever, as there are times when it would be of great importance to determine the latitude within 8 or 10 miles, it was thought advisable to explain this method, which may be used when observations of the sun or moon cannot be obtained.

Having, therefore, the apparent time of observation (which must be reckoned from noon to noon in numerical succession, that is, 6h, A. M., must be called 18h, &c.), and the observed altitude of the star determined by a fore observation, you must subtract from the altitude the dip, which is in general 4 minutes, and the refraction, and you will obtain the true altitude of the star. Then the sun's right ascension corresponding to the given day, must be found in Table VI.,t and added to the apparent time of observation (rejecting 24 hours when the sum exceeds 24 hours); with that sum enter the adjoined table, and take out the corresponding correction, which must be added to, or subtracted from, the true altitude, according to the directions in the table; the sum or difference will be the latitude of the place of observation.

If the star be not far from the meridian, an error of half an hour in the time would not affect the altitude above 1 or 2 miles.

TO FIND THE LATITUDE BY AN ALTITUDE OF THE POLE STAR. 207

EXAMPLE I.

At 7 9m P. M., June 3, 1848, the observed altitude of the pole star was 16° 10′, the dip 4'. Required the latitude of the place of observation.

On the 14th September, 1848, at 2 2m A. M., the altitude of the pole star was 24° 16′, when the dip was 4'. Required the latitude.

At 5 P. M., December 5, 1848, the observed altitude of the pole star was 25° 15′, the dip 4. Required the latitude of the place of observation.

to be taken from the Nautical Almanac, for the hour of observation, reduced to Greenwich time, by adding or subtracting the longitude turned into time.

This table will require a correction after a few years, on account of the variation of declination, and right ascension of the star. It corresponds nearly to the year 1860; for every year after that time you must add one quarter of a minute to the times in the side columns, and decrease the tabular corrections of altitude about part. Thus for the year 1872 the times must be increased 3m for the 12 years, so that 108 must be called 1 11m, and all the corrections of altitude must be decreased so that 1° 15′ must be 1° 12′ nearly, and 0° 35' must be 0° 33 nearly.

part,