interval For the sine of the change in the object's bearing, is to the distance run by the ship in the interval, as the sine of the angle included between the ship's course and the bearing of the object at the first observation, is to its distance at the second observation.

But whether the distance of the place from which the departure is taken, is estimated or computed, the opposite point to that on which it bears is considered as the first course, and its distance as the first distance sailed from the place; and the other courses and distances made during the day, being determined by the compass and the log, they are severally written in chalk, on a painted black board, called the log board, of which the general form will be found below; and afterwards copied into a book, similarly ruled, called the log book. The courses are either corrected for leeway before they are put down on the log board, or the leeway is marked in the proper column opposite the course to which it belongs. The setting and drift of currents, and the estimated effect of the swell of the sea, are also inserted in the column of remarks; and this column, besides, must contain an account of every occurrence deemed of importance.

Then the several courses in the log book being corrected, as in the preceding problems, for leeway and variation, and the distances on each course summed up and entered in a traverse table, care being taken to introduce the effect of currents and the swell of the sea, when any exist, as separate courses and distances, the latitude and longitude arrived at are determined by the methods which have already been explained, under the different heads of Practical Navigation; but in general the whole of the computations may be performed with sufficient exactness by inspection.

The computation of the ship's place from the reckoning is always made at noon, and the operation is called working a day's work. An abstract of the result is inserted in the log book, containing the true course and distance which the ship on the whole has made during the day; the difference of latitude and departure; the latitude and longitude as deduced from the reckoning, with those also which are obtained from observations; and the bearing and distance of the port, or of the nearest land that lies in the ship's way.

When the variation of the compass is given in degrees, it will be found convenient first to correct the courses in the traverse table for leeway only, and, with these courses and distances, to find the difference of latitude and departure, and thence the compass course and the distance made during the day. This resulting course being then corrected for variation, with it and the distance already found, the true difference of latitude and departure may be readily obtained; and the calculation for the difference of longitude may then be made in the usual manner.

In hard blowing weather, with a contrary wind and a high sea, it is impossible to gain any advantage by sailing, and the object is then to avoid, as much as possible, being driven back. To effect this

object, it is usual to ly-to under no more sail than is necessary to prevent the violent rolling which the ship would otherwise acquire. The tiller being put over to leeward brings the ship's head round towards the wind, which then having little power on her sails, she loses her way through the water, and the directive power of the rudder consequently ceases; her head falls off from the wind, the sail which she has set fills again, and gives her fresh way through the water, which acting on the rudder brings her head about to the wind, and she thus comes up and falls off alternately. In such cases the middle point between those on which she comes up and falls off is taken as her apparent course, and the leeway and variation being allowed from that point, the result is entered as a course in the traverse table, with the estimated drift of the ship through the water as a distance.

But notwithstanding all the care that can be taken in keeping a sea reckoning, the place of the ship as deduced from it must always be considered as only approximately determined. It is often extremely difficult to arrive at any considerable certainty respecting the precise course and distance which a ship has actually made. Different rates of sailing between the times of heaving the log, want of care in steering, and sometimes also the great difficulty in steering steadily; sudden squalls, incorrect allowances for leeway and variation, and many other circumstances, conspire to render the ship's place, as deduced from the common reckoning, very uncertain. No opportunity ought therefore to be lost to determine her place by celestial observations; and the sea reckoning should be chiefly considered as a means of estimating her situation nearly in the interval between such observations.

The log is dated according to the civil reckoning of time, and the place of the ship therefore, computed at noon, is for the middle of the civil day; the courses and distances in the afternoon or P. M. of the preceding day, being connected with those made in the morning, or A. M. of the current day, in computing the change of her place from the last noon.

When the place of the ship has been determined by observation, her place by the reckoning ought to be disregarded, and the future reckoning should be carried forward from her place found by observation, till other observations give a new point of reference. But some mariners keep a separate account of the ship's place, by the reckoning and by observation, during the whole voyage; which, as they conceive, enables them to judge of the total effect of currents and other generally operating causes of error on the reckoning.

The following days works, with the explanatory remarks on the method of working them, will be sufficient to enable the student to understand clearly the method of proceeding in any case.

A more extended journal might have been given, but the author has found it more advantageous, in teaching this branch of naviga

tion, to propose to the student, after he has acquired a knowledge of the method of working a day's work, to undertake the fancied charge of the navigation of a ship on a proposed voyage; the teacher giving the winds, and the student, under his direction, finding what in the given circumstances will be the most advantageous courses to steer. Then such distances, leeway, &c. being given, as the teacher, with a due regard to the wind, &c. judges proper, the student proceeds to make the proper corrections on the different courses, and to determine, as in actual sea practice, the situation of the ship.

When observations are obtained for the latitude only, and the latitude by observation differs from that by account, some persons apply a conjectural correction to the difference of longitude for the error in the reckoning, which the observed latitude indicates. Such corrections however ought never to be applied, unless the real cause of the mistake should be discovered; but the longitude as well as the latitude should be carried forward by the reckoning from the last observation, till another can be obtained.

The occurrences of the afternoon or P. M. are written on the lower half of each page, and those of the forenoon or A. M. on the upper half of the following page. Each page therefore shews what has been done during the civil day, and the result of the day's work in the middle of the page between A. M. and P. M. shews the situation, &c. of the ship at noon.

Extract from a Journal of a Voyage from St. Michael's towards England.