The bearing and distance being found, as already shewn; under the same course with 118 as difference of latitude, is found departure or difference of longitude 254. The difference in these results is owing to the odd minutes in the course being rejected. EXAMPLE OF A TRAVERSE. Suppose a ship to sail from latitude 43° 25' N. on the following courses, viz. SWbS. 63 miles, SSWW. 45 miles, SbE. 54 miles, and SW6W. 74 miles. Required the latitude arrived at, and the difference of longitude made good. Solution by Middle Latitude Sailing. The difference of latitude and difference of longitude, corresponding to each course and distance, are found to be as in the following table. Courses Therefore the latitude arrived at is 40° 19' N. and the difference of longitude made good is 143.80'=2° 23' 48" westward. Solution by Mercator's Sailing. The difference of latitude and difference of longitude, corresponding to each course and distance, are found to be as in the following table. 13'92 142'98 NOTE. Note. The book belonging to a ship, in which are entered the courses, distances, winds, &c. from which the daily computation of the ship's place at sea is made, is called the Log Book ; the account or register itself, the logs and the computations from the log, the dead reckoning, or account. Since this reckoning is liable to many errors, arising in the measures of distance, determinations of course, effects of tides and currents, and the estimation of lee-way, &c. it is very important to procure corrections frequently, by making astronomical observations suitable for determining the latitude and longitude. Meridian altitudes of the sun, or, when an observation of this kind cannot be obtained, two other altitudes of the same luminary with the intermediate time, for the latitude ; and distances of the moon from the sun and certain fixed stars, for the longitude, may be considered as observations best adapted to the general practice of mariners, END OF NAVIGATION. CONIC SECTIONS are the figures, made by the mutual intersection of a cone and a plane. 2. According to the different positions of the cutting plane, there arise five different figures or sections ; namely, á triangle, a circle, an ellipse, a parabola, and a hyperbola : only the three last of which are peculiarly called conic sections. 3. If the cutting plane pass through the vertex of the cone, and any part of the base, the section will evidently be a triangle; as VAB. |