relative position with respect to each other that the points corresponding to them do on the surface of the globe, the distance between any points A and O, and A and F must be increased in the same proportion as the distance FO has been increased. The true difference of latitude, AO, is thus projected on the chart into what is called the meridional difference of latitude (see pp. 46-47), and the departure BH + CI+DK, &c., into the difference of longitude, and the representation is called a Mercator's projection. It is evidently a true representation as to form of every particular small tract, but varies greatly as to point of scale in its different regions, each portion being more and more enlarged as it lies farther from the equator, and thus giving an appearance of distortion.*

(1.) In charts generally, the upper part as the spectator holds it, is the North, and that towards his right hand, the East, as on the compass card.

(2.) On Mercator's chart the parallel lines from North to South (from top to bottom) are termed meridians, and they are all perpendicular to the equator, the meridians on the extreme right and left are the graduated meridians-so called from showing the divisions for degrees and minutes. The latitude is measured on the graduated meridians, and also the distance.

*It is plain from the principles of Mercator's projection, and from the diagram (page 89) which connects the enlarged meridian with the difference of longitude, that if a ship set out from any point on the globe, and sail on the same oblique rhumb towards the pole, it can reach it only after an infinite number of revolutions round it. For from any point to the pole, the projected meridian is infinite in length, and so, therefore, is the difference of longitude due to this advance in latitude upon an oblique course. Consequently, this latitude can be reached only after the ship has circulated round the pole an infinite number of times.

These endless revolutions, however, are all performed in a finite time, the entire track of the ship being of limited extent. This, however, paradoxical it may appear, is necessarily true from the principles of plane sailing, which shows that any finite advance in latitude is always connected with a finite length of track; this length being diff. lat.

cos. course.

The apparent paradox of the infinite number of revolutions about the pole being performed in a finite time, becomes explicable when we consider that, whatever be the progressive rate of the ship along its undeviating course, the times of performing the successive revolutions continually diminish as the ship approaches the pole, both the extent of circuit and the time of tracing it tending to zero, the limit actually attained at the pole itself; hence there must ultimately be an infinite number of such circuits to occupy a finite time.

When the pole is reached the direction all along preserved may still be continued ; and a descending path will be described similar to that just considered, and which will conduct the ship to the opposite pole, after an infinite number of revolutions round it, as in the former case. In receding from this pole the track described will at length unite with that at first traced, the point of junction being that from which the ship originally departed. But for the strict mathematical proof of these latter circumstances the student may consult Professor Davies' curious and instructive papers on spherical co-ordinates in the Edinburgh Transactions, vol. XII.

(3.) The parallel lines from West to East (from left to right) are called parallels, and they are all parallel to the equator, the parallels at the top and bottom are graduated to degrees and minutes-and longitude is measured on the graduated parallel.

(4.) The numerals in harbours, bays, channels, &c., indicate soundings reduced to low water spring tides.

(5.) When the true course between two places is known, it must be remembered that Westerly variation is allowed to the RIGHT, and Easterly to the LEFT hand of the true course, in order to obtain the cOMPASS

COURSE.

(6.) With respect to the method of determining the ship's position by cross bearings, it may be observed that this is the most complete of all methods when the difference of bearings is near 90°; but if the difference is small-as, for example, less than 10° or 20°, or near 180°-the ship's position will be uncertain, because a small error in the bearing will cause a great error in the distance.-(Raper, page 120, No. 367.)

English and Bristol Channels, and South Coast of Ireland.

Required the latitude and longitude of ship; also the course and distance to Hartlepool Light.

Required the latitude and longitude of ship; also the course (by compass) and distance to the Staples.

The Skerries, North, by compass.
Sumburgh Head, W. S.,

Required the latitude and longitude in; also the compass course and distance to Peterhead,

(4.)

The Dudgeon Light, W. by N., by compass.
Hasbro' Sand-end Light, S.S.W.,

Required the latitude and longitude of ship; also the compass course and distance to Flambro' Head.

(1.)

English and Bristol Channels, and South Coast of Ireland.

Longships Light, bearing by compass E.N.E.

St. Agnes' Light,

N.N.W.

W.

Required the latitude and longitude in; also the compass course and distance to the Lizard.

Required the latitude and longitude of ship; also the compass course and distance to Cape de la Heve.

(3.) Bembridge Light Vessel, bearing by compass N. W.

Owers Light Vessel,

East.

Required the latitude and longitude of ship; also the compass course and distance to St. Catherine's Point.

Required the latitude and longitude of ship; also the compass course and distance to St. Alban's Head.

Required the latitude and longitude of ship; also the compass course and distance to the Smalls.

Required the latitude and longitude of ship; also the compass course and distance to St. Agnes' Light.

(7.)

Mine Head Light, bearing by compass N.E. N.
N.W.
""

Ballycotton Light,

Required the latitude and longitude of ship; also the compass course and distance to Old Head of Kinsale.

TO FIND THE COURSE TO STEER IN ORDER TO MAKE GOOD ANY COURSE IN A KNOWN CURRENT, AND ALSO THE DISTANCE MADE GOOD.

Draw a line on a chart to represent the course to be made good; from the ship's place on the chart lay off a line in the direction of the set of the current, on which mark off from the ship's place the rate of the current per hour; then take in the compasses the distance the ship sails in an hour by log, and put one foot on the last-named mark, and from the point where the other foot reaches the first line draw a line to the mark on the line representing the direction of the current. The

course to be steered is represented by the line last drawn, and the parallel ruler being placed to it, and moved to the centre of the compass on the chart, will give the course of the ship; and that portion of the first line drawn, intersected by the last line drawn, will be the distance the ship will make good per hour.

B

E

B

On a chart, suppose A to be the place of the ship, B the port of destination; also A C the set of the current, the rate per hour being taken from the scale of miles and laid off in the direction of the line. Take the distance sailed by the ship per hour from the scale of miles, and with one foot of the dividers at C, make an arc cutting A at D. Join C D, and move the parallel ruler from C D to A, drawing A E parallel to CD: then A E will be the direction of the ship's head. And the parallel ruler being moved to the centre of the compass on the chart, will give the course of the ship on the chart; and A D will be the distance the ship will make good.

SOUNDINGS.

In the open sea, the tides require about six hours and a quarter to rise from low to high water, and an equal interval to fall from high to low water. If the rise or fall was an uniform quantity throughout, by simply taking a proportionate part of the rise or fall due to the time of tide, we should at once obtain the quantity required to reduce the soundings to the low water of that day. But the water does not rise