run out in 30 seconds. A quantity of the line called the stray line, is allowed to run out before the glass is turned, that the log may be without the reach of the ship's wake. When the glass is run out, the knots, and parts of a knot between the ship and the mark at the end of the stray line, indicate the distance which the ship has run from the log in the interval of time measured by the sand glass; hence her hourly rate of sailing is known. The time which the sand glass takes in running out, and the length of the knots of the log line, should frequently be examined ; for the time by the sand glass is materially affected by the state of the atmosphere, and the log line is liable to contract from the action of the water, and it may happen that the whole line, or different parts of it may accidentally be stretched. If either the glass or the line, or both, be found erroneous, the error must be ascertained, and the true distance may then be found by a simple formula, which may be thus investigated. Let k = the true length of a knot, and m = the measured length of one; t = the seconds in the same part of an hour that k is of a mile, s = the seconds run by the glass, and d= the distance as determined by these erroneous instruments. d m i d m erroneous; a general expression for the true k ks distance when the log line and the glass are both erroneous. If s = t, or if the log line only is erroneous, the general expres d m sion becomes as before, and if m = k, or the glass only is k td erroneous, the expression is If t = 30 seconds, and k = 50 t d m 30 d m 3 d m feet, we have the true distance when 50 S both the log line and the glass are erroneous. If m = 50 feet, or if the glass only is erroneous, this expression is 30 d ; and if s = 30, or if the glass only is erroneous, the expression . ks 5 s dm is 50 If t, k, and s were given to find a corresponding value of m, we s k have t:s::k:m = 3 PRACTICAL APPLICATION OF THE PRINCIPLES OF NAVIGATION. To find the difference of latitude or the difference of longitude between any two places whose latitudes and longitudes are given. Rule. When the given latitudes are of the same denomination, subtract the less from the greater ; but when they are of different denominations add them together; and the suin or the remainder will be the difference of latitırde. The difference of longitude is found in the same manner, observing however that the difference of longitude signifies the less arc of the equator intercepted between two meridians; and that therefore when the longitudes are of different denominations, and their sum exceeds 180°, that sum must be subtracted from 360° to find the difference of longitude. EXAMPLES Required the difference of latitude and difference of longitude between the Lizard Point and the Peak of Pico ? Lizard Point lat 49° 58' N Pico lat 38 28 N diff lat 11 30 = 690 miles. Lizard Point long 5°11'W Pico long.. 28 33 W diff long 23 22 = 1402 miles. Required the difference of latitude and difference of longitude between Halifax and the Cape of Good Hope ? Halifax lat .... 44°44' N Cape of Good Hope lat . 34 29 S diff lat 79 13 = 4753 miles. Halifax long 65° 36' W Cape of Good Hope long .... 18 23 E diff long 83 59 = 5039 miles. Required the difference of latitude and difference of longitude between Cape Horn and South Cape, Van Diemen's land ? Cape Horn lat. 55° 58' S South Cape lat 43 37 S diff lat 12 21 = 741 miles. Cape Horn long 67°21' W South Cape long 46 49 E 214 10 360 0 EXAMPLES FOR EXERCISE. Required the difference of latitude and difference of longitude between the following places ? 1. Between Cape Amber, in Madagascar, and Bombay? Answer, diff lat 1856, and diff long 1411 miles. 2. Between Dondre Head, in Ceylon, and Socotra ? Answer, diff lat 395, and diff long 1593 miles. 3. Between Savannah and Cape Clear ? Answer, diff lat 1164, and diff long 4287 miles. 4. Between Cape Padaran and Cayenne? Answer, diff lat 670, and diff long 3895 miles. 5. Between Algiers and Genoa ? Answer, diff lat 456, and diff long 353 miles. To find the latitude and longitude at which a ship has arrived, when those of the place which she left, and the difference of latitude and longitude which she has made, are given. Rule. If the latitude left and the difference of latitude are of the same denomination, add them together; but if they are of different denominations, take their difference; and the sum or the remainder will be the latitude arrived at, and of the same denomination with the greater. Remark. As no place can be farther distant from the equator than the poles, the latitude cannot exceed 90°. The longitude in is found in the same manner as the latitude; but as the longitude is reckoned both east and west, if when the longitude left and the difference of longitude are of different denominations, their sum should exceed 180°, the difference between the sum and 360° will be the longitude arrived at, and of a contrary denomination to the longitude left. EXAMPLES. If a ship sail from Cape Finisterre towards the southwest till her diff of lat is 140, and her diff of long 118 miles, required her latitude and longitude in ? Cape Finisterre lat 42° 54' N Long... 9° 16' W diff lat 140 2 20 S diff long 118 = 1 58 W lat in 40 34 N long in 11 14 w If a ship sail from lat 50° 18' S long 178° 21' E towards the SE till her diff lat is 638 and her diff long 400 miles, required her latitude and longitude in ? Lat left..... 50° 18' S Long...... 178°21'E 6 40 E 185 01 360 0 long in 174 59 W M EXAMPLES FOR EXERCISE. In the following examples the latitude and longitude arrived at are required. Answer. Long left. Long in. 0 0 238 N 141 W 3 58 N 2 21 W 5. 64 2 N 3 13 W 304 S 158 E 58 58 N 0 35 W 6. 39 37 S 28 17 E 112 s 300 E 41 29 S 33 17 E To know in what quarter of the horizon the course between any two places lies ? Rule. If the place bound to has greater north latitude, or less south latitude than the place to be sailed from, the course will be northerly; otherwise it will be southerly. And if the place bound to has greater east longitude, or less west longitude than the place to be sailed from, the course will be easterly; otherwise it will be westerly. These directions combined will indicate the quarter in which the course lies. EXAMPLE In what quarter of the horizon will the course lie from lat 28° N long 16° W to lat 35° N long 2° W ? Here the place bound to has greater north lat than the place to be sailed from, the course therefore is northerly. And as the place bound to has less west long than the place to be sailed from, the course is also easterly. The course is therefore between the north and east, or in the northeast quarter of the horizon. In what quarter of the compass will the course lie in sailing from the first to the second of each of the following places ? 1. From Aberdeen to Rotterdam ? Answer, in the SE quarter. 2. From Ushant to Cape Ortegal? Answer, in the S W quarter. 3. From the Lizard to Halifax? Answer, in the SW quarter. 4. From the Cape of Good Hope to Van Diemen's Land ? Answer, in the S E quarter. 5. From Cape Horn to St. Helena ? Answer, in the N E quarter. 6. From Lisbon to Cape Farewell ? Answer, in the NW quarter. 7. From the Cape of Good Hope to Rio Janeiro ? Answer, in the NW quarter. To correct the distance given by the log and half minute glass, when the line, the glass, or both are erroneous. GENERAL RULE. Multiply the given distance by three times the measured length of a knot, and divide the product by five times the secunds which the glass takes in running out, and the quotient will in EXAMPLES. A ship runs 126 miles, but it is found on examination that the length of the knots on the log line, is 52 feet, and that the glass runs out in 27 seconds, required the true distance? 126 3 x 52 = 156 1756 630 126 19656 = 145.6, true distance. 27 X 5 = 135 EXAMPLES FOR EXERCISE. 87 In the following examples the true distance is required. Dist. by Length of Seconds by log knots. glass. Answer. Miles. Feet, Seconds. True distance. 48 96 53 224 300 144 184 152 50 105 28 When the true course and the variation of the compass are given, to find the compass course. Rule. If the variation is west, allow it to the right, but if east, allow it to the left of the true course, and the point thus determined will be the required compass course. EXAMPLE. If the true course from the Lizard to St. Mary's is S WW, and the variation of the compass at the Lizard is 2 W, what is the compass course ? Answer, 2 points allowed to the right if S WW gives WS, the required compass course. EXAMPLES FOR EXERCISE. In the following examples the compass courses are required |