The courses steered from noon to 9h. P. M., and the bearing of Porto Santo from the snip at that time, corrected for 14 point West variation; also the distances run, and the estimated distance of the ship from the land, being entered in a Traverse Table, will give the diff. of latitude 50'. 6, and the departure 47'. 8.

From hence the latitude of Porto Santo, by the ship's reckoning, is found to be 33° 5′ N, and the longitude, carried on by chronometer from the last lunar observation, 16° 29′ W.; differing 2 miles in latitude, and 10 miles in longitude, from its position, as laid down in Table LVI.

The ship's track during the preceding voyage is laid down on the Mercator's Chart, according to the latitude and longitude each day at noon,

326

ABSTRACT OF THE PRECEDING JOURNAL.

6° 27' W.

Longitude

by Lunar and True Bearings and Distances at Noon. Chronometer.

N. by W.

EXPLANATION AND USE

OF

THE TABLES.

TABLES I. AND II.

Difference of Latitude and Departure for Points and Degrees. THESE Tables are of very extensive use in Navigation, affording an easy and expeditious method of solving all problems in right-angled plane trigonometry, and consequently applicable to the various sailings, but particularly useful in working a traverse, whence they obtain the name of Traverse Tables. Table I. contains the difference of latitude and departure (in whole numbers and tenths), answering to distances not exceeding 300, and for courses to every quarter point of the compass. Table II. is of the same nature and extent; but for courses consisting of whole degrees. The courses are set down at the top of the pages when they do not exceed 4 points or 45 degrees, and at the bottom when they are greater than these quantities: the distances are regularly arranged in the columns marked Dist.; the first beginning at 1, and ending at 60; the second beginning at 61, and ending at 120, and so on to 300: corresponding to each of these distances, the difference of latitude and departure are set down in adjoining columns, marked Lat. and Dep.: but it must be carefully observed, that when the course is less than 4 points, or 45 degrees, these must be taken out as marked at the top, and when more, as noted at the bottom of the pages.

Now, the difference of latitude and departure, answering to any given course and distance, being found opposite the distance in that page of the table which contains the course; if, therefore, any two of the four parts, viz. the course, distance, difference of latitude, and departure, be given, and those two be found together in the tables, the other two parts will be found in their respective places on the same page. In like manner, the parts of any rightangled plane triangle may be found (provided two of them, exclusive of the right angle, be given), by taking out the hypothenuse as a Distance, the perpendicular in a Lat. column, the base in the Dep. column, and the angle opposite to it as a course. Hence, when these tables are applied in parallel or middle latitude sailing, the co. lat. or co. mid. lat. is taken as a course, the departure or meridional distance is found in the Dep. column, and the difference of longitude in the Dist. column: in Mercator's sailing, the meridional difference of latitude is taken out in the Lat. column, and difference of longitude in the Dep. column.

When any of the given parts (excepting the course, which is never to be multiplied or divided) exceed the limits of the table, any aliquot part, as a half, third, fourth, &c. is to be taken; and those found corresponding are to be doubled, trebled, &c., that is, multiplied by the same figure that the given number is divided by.