places. Rule. Bring one of these places to that half of the brass meridian which is numbered from the equator towards the poles, and mark the degree above it; then bring the other place to the meridian, and the number of degrees between it and the above mark will be the difference of latitude. Or, find the latitudes of both the places (by Prob. I.) Then, if the latitudes be both north or both south, subtract the less latitude from the greater, and the remainder will be the difference of latitude: but, if the latitudes be one north and the other south, add them together, and their sum will be the difference of latitude. Examples. 1. What is the difference of latitude between Philadelphia and Petersburg? Answer. 20 degrees. 2. What is the difference of latitude between Madrid and Buenos Ayres? Answer. 75 degrees. 3. Required the difference of latitude between the following places? Delhi and Cape Comorin Alexandria and the Cape of St. Salvador and Surinam Trinidad I. and Trincomalé 4. What two places on the globe have the greatest difference of latitude? PROBLEM VIII. To find the difference of Longitude between any two places. Rule. Bring one of the given places to the brass meridian, and mark its longitude on the equator; then bring the other places to the brass meridian, and the number of degrees between its longitude and the above mark, counted on the equator, the nearest way round the globe, will show the difference of longitude. Or, find the longitudes of both the places (by Prob. III.) then, if the longitudes be both east or both west, subtract the less longitude from the greater, and the remainder will be the difference of longitude; but, if the longitudes be one east and the other west, add them together, and their sum will be the difference of longitude. When this sum exceeds 180 degrees, take it from 360, and the remainder will be the difference of longitude. Examples. 1. What is the difference of longitude between Barbadoes and Cape Verd? Answer. 41° 48' 2. What is the difference of longitude between Buenos Ayres and the Cape of Good Hope? Answer. 76° 50'. 3. What is the difference of longitude between Botany Bay and O'why'ee? Answer. 52° 45', or 523°. Pelew I. and Ispahan Vesuvius Mount Etna and Teneriffe Boston in Amer. and Berlin North Cape and Gibralter 5. What is the greatest difference of longitude comprehended between two places? PROBLEM IX. To find the distance between any two places. Rule. The shortest distance between any two places on the earth, is an arc of a great circle contained between the two places. Therefore, lay the graduated edge of the quadrant of altitude over the two places, so that the division marked O may be one of the places, the degrees on the quadrant comprehended between the two places will give their distance; and if these degrees be multiplied by 60, the product will give the distance in geographical miles; or multiply the degrees by 691, and the product will give the distance in English miles. Or, take the distance between the two places with a pair of compasses, and apply that distance to the equator, which will show how many degrees it contains. If the distance between the two places should exceed the length of the quadrant, stretch a piece of thread over the two places, and mark their distance; the extent of thread between these marks, applied to the equator, from the meridian of London, will show the number of degrees between the two places. Examples. 1. What is the nearest distance between the Lizard and the island of Bermudas? 2. What is the nearest distance between the island of Bermudas and St. Helena ? 4. What is the direct distance between London and Jamaica, in geographical and in English miles? 5. What is the extent of Europe in English miles from Cape Matapan in the Morea, to the North Cape in Lapland? 6. What is the extent of Africa from Cape Verd to Cape Guardafui ? 7. What is the extent of South America from Cape Blanco in the West to Cape St. Roque in the east? 8. Suppose the track of a ship to Madras be from the Lizard to St. Anthony, one of the Cape Verd Islands, thence to St. Helena, thence to the Cape of Good Hope, thence to the east of the Mauritius, thence a little to the south-east of Ceylon, and thence to Madras; how many English miles is the Land's End from Madras? Simple as the preceding problem may appear in theory, on a superficial view, yet, when applied to practice, the difficulties which occur are almost insuperable. In sailing across the trackless ocean, or travelling through extensive and unknown countries, our only guide is the compass, and except two places be situated directly north and south of each other, or upon the equator, though we may travel or sail from one place to the other by the compass, yet we cannot take the shortest route, as measured by the quadrant of altitude. To illustrate these observations by examples; first, Let two places he situated in latitude 50° north, and differing in longitude 48° 50′, which will nearly correspond with the Land's End and the eastern coast of Newfoundland. The arc of nearest distance being that of a great circle, truly calculated by spherical trigonometry, is 30° 49′ 6′′, equal to 18491 geographical miles, or 21413 English miles; but, if a ship steer from the Land's End directly westward in the latitude of 50° north, till her difference of longitude be 48° 50′, her true distance sailed will be 18832 geographical miles, or 21813 English miles, making a circuitous course of 343 geographical miles, or 403 English miles. Those who are acquainted with spherical trigonometry and the principles of navi. gation, particularly great circle sailing, know that it is impossible to conduct a ship exactly on the arc of a great circle, except, as before observed, on the equator or a meridian: for, in this example, she must be steered through all the different angles, from N. 70° 49′ 50′′ W. to 90 degrees, and continue sailing from thence through all the same varieties of angles, till she arrives at the intended place, where the angle will become 70° 49′ 30′′, the same as at first. ΤΟ Secondly. Suppose it were required to find the shortest distance between the Lizard, lat. 49° 57′ N. long. 5° 21′ W. and the island of Bermudas, lat. 32° 35′ N. long. 63° 32′ W. The arc of a great circle contained between the two places, will be found, by spherical trigonometry to be 45° 44', being 2744 geographical miles, or $178 English miles. See the method of calculating such problems in Keith's Trigonometry, second edition, page 278. Now, for a ship to run this shortest track, she must sail from the Lizard S. 89° 29′ W. and gradually lessen her course so as to arrive at Bermudas on the rhumb bearing S. 49° 47′ W. but this, though true in theory, is impracticable: the course and distance must therefore be calculated by Mercator's sailing. The direct course by the compass will be found to be S. 68° 9' W., and the distance upon that course 2800 geographical miles, or 3243 English miles; making a circuitous course of 56 geographical miles, or 65 English miles. Hence, to find the distance between any two places whose latitudes and longitudes are known, in order to travel or sail from any place to the other, on a direct course by the mariner's compass, the following methods must be used. 1. If the places be situated on the same meridian, their difference of latitude will be the nearest distance between them in degrees, and the places will be exactly north and south of each other. 2. If the places be situated on the equator, their difference of longitude will be the nearest distance in degrees, and the places will be exactly east and west of each other. 3. If the places differ both in latitudes and longitudes, the distance between them and the point of the compass on which a person must sail or travel, from the one place to the other, must be found by Mercator's Sailing, as in navigation. 4. If the places be situated in the same latitude, they will be directly east and west of each other; and their difference of longitude, multiplied by the number of miles which make a degree in the given latitude, according to the following table, will give the distance. |