or place, is to be noted down on the log-board. This is called taking a departure.

As the distance inferred from estimation is very susceptible of error, particularly in hazy weather, or when that distance is considerable, it will be advisable to make use of the following method in taking a departure ; viz., Let the bearing of some well-known place be observed, and, when the ship has run a convenient distance, on a direct course, let the bearing of the same well-known place be again observed; then there will be a triangle formed, in which there is one side given: that is, the distance sailed between the times of observation, and all the angles, to find the distance between the ship and the place observed. This may be done by Problem I., Oblique Sailing, page 256; or it may be very readily determined by means of a good chart. In like manner may a departure be taken from a light-house at night.

In making out the first day's work after leaving the land, especial care must be taken, in setting down the bearing and distance of the departure in a traverse table, to make use of the opposite point of the compass to that bearing; and, also, to make due allowance for the variation. Thus, if the object from which the departure was taken bore N. E. b. E., and the variation of the compass be 2 points westerly, then the true course for the traverse Table is S. W. b. S.; abreast of which, in the proper column, is to be placed the estimated or computed distance.

The course steered, is indicated by the compass; the distance sailed, in a given time, is determined by the log-line and the half-minute or quarter-minute glass. In Her Majesty's Royal Navy, the log is hove once in every hour; and so it is on board ships belonging to the East India Company.

The several courses and distances sailed during the interval of 24 hours, or from noon to noon, together with all the remarks and occurrences that are worthy of notice, are generally marked down with chalk on a board, painted black, called the log-board. This board is usually divided into six columns: the first column on the left hand. contains the hours from noon to noon, viz., from noon to midnight, and then from midnight to noon; the second and third columns contain the knots and fathoms sailed every hour; the fourth contains the courses steered; the fifth the winds; and in the sixth the various remarks are written,-such as, the state of the weather, the sails set or taken in, the observations for ascertaining the ship's place, the variation of the compass, and whatever else may be deemed necessary. The log-board is transcribed every day at noon (under the direction of the Master), into the log-book, which is divided into columns exactly in

the same manner.

The form of the log-book which is now made use of in the Royal Navy, will be shown presently.

The courses steered must be corrected for the variation of the compass, and also for lee-way, if any. If the variation be westerly, it must be allowed to the left hand of the course steered; but if easterly, to the right hand thereof, in order to obtain the true course.-See Problem VI., page 577.

The lee-way is to be allowed to the right hand of the course steered, if the larboard tacks be on board; but to the left hand, if the starboard tacks be on board.

The variation of the compass should be determined twice a day (every morning and evening), if possible. The method of doing this is shown in the several problems contained between pages 565 and 577.

With respect to the lee-way, its nature or effect may be thus explained :

When a ship is close-hauled, and the wind blowing fresh, that part of the wind which acts upon the hull and rigging, together with a considerable part of the force which is exerted on the sails, tends to drive her immediately from the direction of the wind, or, as it is termed, to lee-ward. But since the bow of a ship exposes less surface to the water than her side, the resistance will be less in the first case than in the second; the velocity, therefore, in the direction of her head, will, in most cases, be greater than in the direction of her side; and the ship's real course will be between those two directions. Hence the angle contained between the line of the ship's apparent course and the line she actually describes through the water, is termed the angle of lee-way, or, simply, the lee-way.

The angle of lee-way that a ship makes may be very readily determined in the following manner; viz., Draw a semi-circle on the taffrail, with its diameter at right angles to the ship's keel, and its circumference divided into points and quarter-points; then let the angle be observed which is contained between the semidiameter pointing right aft, or parallel to the keel, and that which points in the direction of the wake, and it will be the lee-way required. Or, after heaving the log, if the line (before it is drawn in) be applied to the centre of the semi-circle, the points and quarter-points contained between its direction and the fore and aft radius of the semi-circle will be the lee-way, as before.

Many writers on navigation have given rules for ascertaining the quantity of lee-way which a ship makes, independent of observation. These are as follow; viz.,

1. When a ship is close-hauled, has all her sails set, the water smooth,

with a light breeze of wind, she is then supposed to make little or no lee-way.

2. Allow one point when the top-gallant-sails are handed. 3. Allow two points when under close-reefed top-sails.

4. Allow two points and a half when one top-sail is handed.

5. Allow three points and a half when both or the three top-sails are handed.

6. Allow four points when the fore-sail or fore-course is handed. 7. Allow five points when under the main-sail or main-course only. 8. Allow six points when under a balanced mizen.

9. Allow seven points when under bare poles.

As these rules depend entirely upon the quantity of sail set, without any regard to the model of the ship, or to the nature of the way in which she may be trimmed for sailing, it is evident that they are far from being general, and that they are, in reality, little more than mere probable conjectures. But since the accuracy of a ship's reckoning depends, in some measure, upon the truth of the lee-way, it ought to be deduced, at all times, from actual observation, as above directed; and then its value should be carefully noted down, in a separate column, on the log-board; so that all concerned may be thereby enabled to correct the courses steered, in making out their days' works at noon.

In very strong gales, with a contrary wind and a high sea, it is not prudent to attempt working to windward: in such cases, the grand object is, to avoid, as much as possible, losing ground, or being driven back. With this intention, it is customary to lay the ship to, under no more sail than may be barely sufficient to check that violent rolling which she would otherwise acquire, to the endangering of her masts, yards, and rigging. When a ship is brought to, the helm is kept about three parts alee, which brings her head gradually round to the wind. The force of this element having then very little power on the sails, the ship consequently loses her way through the water, which ceasing to act upon the rudder, her head falls off from the wind; the sail which she has set fills, and gives her fresh way through the water, which, acting on the rudder, brings her head again gradually round to the wind; and thus she obtains a kind of vibratory motion, coming up to the wind and falling off from it alternately.

Ships lie-to under different sails, according to circumstances; and one vessel will lie-to considerably better under some particular sail than another. But, in general, a close-reefed main-top-sail is, perhaps, the most eligible sail to lie-to under; because of its being nearly over the centre of motion, and, also, because of its elevated position, which renders it far less susceptible of being becalmed in the trough of the sea than either the courses or storm-stay-sails.

When a ship is lying-to, observe the points of the compass upon which she comes up and falls off, and take the middle point for her apparent course to which let the variation and the lee-way be applied, and the true course will be obtained. Thus, suppose a ship lying-to under a close-reefed main-top-sail, with her larboard tacks on board, comes up S. S. W., and falls off to S. W. b. W.; then, allowing the variation to be 14 point west, and the lee-way to be 24 points, the course made good is S. W. W.: for the middle point between S. S. W. and S. W. b. W. is S. W. S.; to which, 1 point westerly variation being allowed to the left, and 24 points lee-way to the right, makes the true course S. W. W.

The setting and drift of currents, with the heave and drift of the sea, should be set down as courses and distances upon the log-board: these are to be corrected for variation only.

The computation made from the several corrected courses, and their corresponding distances, is called a day's work; and the ship's place, deduced therefrom, is called her place by account, or dead reckoning.

If the course and distance made by a ship could be correctly ascertained, by means of the compass and the log, nothing more would be necessary in determining her true place at sea; for the absolute course and distance being known, the latitude and longitude could be readily computed, by Problem VI., page 695. But, in consequence of the irregularities to which the heaving of the log is subject, particularly during the night, with many unforeseen and unavoidable causes, such as sudden squalls, imperfect compasses, unequal care in the helmsman, inaccurate allowances for variation and lee-way, &c. &c., the latitude and longitude of the ship, as inferred from dead reckoning, will very seldom agree with the truth, or with those immediately deduced from celestial observation. In consequence of this discrepancy, several writers on navigation have proposed to apply a conjectural correction to the departure or meridian distance, in order to find the true longitude. Thus, if the course be near the meridian, the error is wholly attributed to the distance, and the departure is to be increased or diminished accordingly; if it be near a parallel, that is, near the east or west point of the compass, the course only is supposed to be erroneous; and if the course be towards the middle of the quadrant, viz., near four points, the assumption is that both course and distance are wrong. These corrections, being computed and applied according to the rules given by different authors, will generally place the ship upon different sides of her meridian by account: hence, since the corrections arising from these rules are evidently founded upon a vague kind of guess-work, they ought to be absolutely rejected.

When the latitude by account differs from that by observation, the

log-line and half-minute glass should be carefully examined, and, if found erroneous, the distance sailed, as indicated thereby, should be corrected accordingly, by the Problems given for that purpose, between pages 272 and 276. If the corrected distance, thus found, with the course, does not produce a coincidence in the latitudes by account and observation, the mariner should then consider whether the variation has been properly determined and allowed upon the courses steered by compass; if not, these courses are to be again corrected; but no other alteration whatever should be made in them. If the latitudes by account and observation be still found to disagree, the navigator should next consider whether the ship's place has been affected by a current or by the heave of the sea, and allow for their course and drift to the best of his judgment. By carefully applying these corrections, a new difference of latitude and departure, and a new course and distance, will be obtained; which will, in general, produce an approximation in the latitudes: beyond this, no alteration whatever should be made in the departure with the view of finding the longitude by account.

However, since there are many mariners who, from long-established practice, are not willing to depart from the common system of correcting the dead reckoning by the rules laid down for that purpose in certain Epitomes of Navigation; and since these rules are exceedingly complicated, and admit of a variety of cases, the following General· Rule is given for the use and guidance of such persons, which reduces those various cases into one very concise method, and thus does away with the necessity of consulting several complex rules before the desired correction can be obtained.

A General Rule for Correcting the Dead Reckoning.

Augment the distance sailed by two-thirds of the difference between the latitude by account and that by observation, when the observed latitude is before or ahead of that by account; but diminish the distance sailed in the same proportion, when the observed latitude is astern or behind that by account. Then,

Enter the general Traverse Table with this corrected distance and the difference of latitude by observation, and find the corresponding departure. Now, with the departure, thus found, in a latitude column, and the middle latitude as a course, find the corresponding distance, and it will be the corrected difference of longitude.

Example 1.

Suppose a ship, from a place in latitude 47:49 N. and longitude 9:29′ W., sailed S. 43: W. 160 miles, and then finds her latitude by