USE OF THE TABLE. 1. How many miles are the inhabitants of Quito, near the equator, and those of St. Petersburg, in lat. 60° N. carried round by the diurnal motion of the earth? In Quito 1°=60 miles. In St. Petersburg 1°=30 miles. )21600 G. ms. Ans. 25200 S. ms. 10800 G. ms. 1800 Ans. 12600 S. ms. 2. What is the distance from Charleston light-house, in long. 80° W. to Bermudas, in long. 64°W. and both in lat. 32 North. 80°-64-16° diff. long. 1° in lat. 32 is 51 miles. 16 X51 816 G. miles. In like manner may the distance be found between the following places. From C. May, lon. 75 W. to Fayal, lon. 29 W. both in 38 N. C. Finisterre 9 8 41 3 43 Rome If two places be in the same longitude, the difference of their latitudes is the distance between them. Required the distance between the city of Washington, in lat. 38 N., and Lima, in lat. 12 S., both in long. 77 W. 38+12=50X60-3000, the distance in G miles. How many miles is the Cape of Good Hope South and East of Philadelphia ? In the middle latitude 37°, a degree is 48 miles, then 60 48 5619: 4495 miles. Or, 98448=4485 G. ms. Ans. 4440 G. miles, S. and 4495 G. miles E. The square root of the sum of the squares of the difference of latitude and departure will give the distance between them. The ship Columbus was spoken in lat. 37° 57 N. and long. 67° 38′ W. bound to a port in lat. 42° 17′ N. and long. 72° 38' W. What is the distance to the port? Ans. 347. To find the bearing of one place from another by Arithmetic. RULE. To the distance, as found in the last case, add half the greater of the other two numbers, whether it be latitude or departure, and say,-As the sum is to the less number, so is 86 to the degrees, or angle required, if the difference of latitude be more than the departure. But if the departure be greater, the fourth number, found as above, must be taken from 90° for the answer. EXAMPLE. The city of A. is north and west of the town of B. The difference of latitude between them is 260 miles, the departure 230, and the distance 347 miles. Required the bearing of A. from B. Taking or of large numbers, will be sufficiently exact for geographi 347 130 477 23086 cal 86 1380 1840 purposes: 34 13 : thus, 954 3840 47)1978(420 Answering nearly to N. W.‡N 98 or N. W. b. N. & W 94 If the bearing of B. from A. was re quired, it would be 90-42=48°, or S.E. E. Suppose the difference of latitude between two places is 1970 miles; the difference of longitude, reduced to departure, is 955 miles, and the distance deduced thence 2139: Required the bearing? When the difference of latitude and departure are alike, or nearly so, the answer is 45°, and needs no calculation to find it; as in the example from Philadelphia to the Cape of Good Hope, which in that case is 45°, or S. E., as the Cape is South and East of that city. When there is little or no departure, the bearing is North or South; and when it is so with the latitude, the bearing is East or West. A TABLE OF ANGLES, which every Point and Quarter Point of the Compass makes with the Meridian. 3 3 42 11. N.E.....N.W... 4 45 00... S.E.. ... S.W. 50 37 .. 53 26. 4 1 47 49. 4 N.E.b.E.N.W.b.W. 5 5 64 41 5.... 56 15. S.E.b.E. S.W.b.W. 5. 59 04. 61 52 E.N.E...W.N.W. 6 .. 67 30. E.S.E... W.S.W. To reduce degrees of longitude into time. RULE. Multiply the degrees by 4 for minutes of time, and the minutes or miles of longitude by 4 for seconds, and divide the products by 60 for time. EXAMPLE. Required the time answering to 42° 43′ 45′′ of longitude. To reduce time into degrees of longitude. RULE. Multiply the hours by 15 for degrees, and divide the minutes and seconds respectively by 4. EXAMPLES. 1. Reduce 8 hrs. 37 ms. 38 sec. to degrees of longitude. 8x15=120° 0' 0" 37÷ 49 15 0 30 384 0 9 Ans. 129 24 30 2. What is the difference of longitude and time between Philadelphia, in longitude 75° 19′ W. and Alexandria in Egypt in 30° 16' East? Philadelphia 75° 19′ W. 105° X4-420' 0" 105° 35' hrs. 7 2 20 Hence, when it is noon at Philadelphia, it is 7 hrs. 2 ms. 20 sec. in the afternoon at Alexandria; and when it is noon at Alexandria, it is only 4 hrs. 57 ms. 40 sec. in the morning at Philadelphia-thus, 12 0 0 7 2 20 hrs. 4 57 40 NOTE. When the place required is east of the one given, the time requir ed will be as much later in the day, as the difference of longitude, reduced to time, gives hours and minutes ; and when west of the given place, it will be so much earlier. When it is 20 minutes past 2 o'clock in the afternoon at Marseilles, in longitude 5° 22′ E. what time is it at Boston light-house, in longitude 70° 58′ W. Ans, 9 hrs. 14 ms. 40 sec. in the morning. |