৮ The above rule is on a supposition that the earth revolves on its axis, from west to east, in 24 hours; but it has been already observed, (Chap. VII. Art. 6,) that the earth makes one complete revolution on its axis in 23 hours, 56 minutes, 4.1 seconds; hence, where greater accuracy is required, we must multiply the number of geographical miles by 15.041 for the answer. EXAMPLES. 1. At what rate per hour are the inhabitants of Pekin carried from west to east by the revolution of the earth on its axis ? Answer. The latitude of Pekin is 400, in which parallel a degree of longitude is equal to 46 geographical, or 53 American miles. (See Ex. 1. Prob. XVII.) Now, 46 multiplied by 15, produces 690, and 53 multiplied by 15 produces 795; hence, the inhabitants of Pekin are carried 690 geographical, or 795 American miles per hour. By the table. In latitude 400 a degree of longitude is equalto 45.96 geographical miles, and 52.94 American miles. Now, 45.96 multiplied by 15, produces 689.4; and 52.94 multiplied by 15 will give 794.1: Hence, the inhabitants in this parallel are carried 689.4 geographical, or 794.1 American miles per hour, by the earth's revolution on its axis; which result is more correct than the former. And, if we multiply 45.96 by 15.041, and also 52.94 by 15.041, the answer will be found still more correctly. 2. At what rate per hour are the inhabitants of the following places carried, from west to east, by the revolution of the earth on its axis: Truxillo, a town in Peru; Sofala, a town in Africa, and capital of a country of the same name; Lahore, a city of Asia, and the capital of a province of the same name, several times the capital of Hindoostan and the residence of the great Moguls; Kiev, a city in European Russia, situated on the right bank of the Dnieper; and Christiana, the most beautiful city in Norway, situated in a bay or gulf, about 25 miles from the sea. PROBLEM XIX. The hour of the day at any particular place being given, to find what hour it is in any other place. RULE. Bring the place at which the time is given to the brass meridian, and set the index of the hour circle to the given hour at that place: then, turn the globe till that place for which the time is required be brought to the meridian, and the index will show the hour at that place. If the place where the hour is sought lie to the east of that wherein the time is given, turn the globe westward; but if it lie to the west, the globe must be turned eastward. Or, bring the given place to the meridian, and set the index of the hour circle to 12; turn the globe (as before) till the other place comes to the meridian, and the hours passed over by the index will. be the difference of time between the two places. If the place where the hour is sought, lie to the east of that wherein the hour is given, the difference of time must be added to the given time; but if to the west, subtract the difference of time: Thus, a place 15 degrees to the eastward of another, has the sun on its meridian an hour earlier than the latter place; therefore, when it is 12 o'clock in the former place it is but 11 o'clock in the latter; and 12 o'clock in the latter place corresponds to 1 o'clock in the former, &c. Or, without the hour circle, find the difference of longitude between the two places, (by Prob. VI.) and convert it into time by allowing 15 degrees to an hour, or 4 minutes of time to one degree. The difference of longitude in time, will be the difference of time between the two places, with which proceed as in the last rule. To convert degrees, minutes, and seconds into time, at the sate of 360 degrees for 24 hours, and the contrary, Say as 3600: 24h. or as 150: 1h.:: any number of degrees, &c.: the time required. The converse of this rule will give the degrees. Hence, degrees of longitude may be converted into time by multiplying by 4, observing that minutes or miles of longitude multiplied by 4, produce seconds of time, and degrees of longitude, when multiplied by 4, correspond to minutes of time: and, on the contrary, minutes of time divided by 4, will give degrees of longitude: if there be a remainder after dividing by 4, multiply it by 60, and divide the product by 4, or, which amounts to the same thing, multiply the remainder by 15, the quotient in the former case, or the product in the latter, will be minutes of a degree, or miles of longitude. EXAMPLES. 1. When it is 9 o'clock in the morning at NewYork, what hour is it at Dieppe, a sea-port of France, in the English Channel? By the first method. Bring New-York to the meridian, and set the index of the hour circle to 9 o'clock; then, by turning the globe westward till Dieppe comes to the meridian, the index will point to 2 o'clock nearly, which is the hour at that place; hence, as Dieppe lies to the east of NewYork, when it is nine in the morning at the latter place, it is two in the afternoon at the former. By the second method. Bring New-York to the meridian and set the index to 12 o'clock, then, by turning the globe, as before, till Dieppe be brought to the meridian, the hours passed over by the index will be five, which is the difference of time between both places. And, because Dieppe lies to the east of New-York, this difference of time must be added to the given time; that is, 5 hours added to 9 hours will give 14 hours; consequently, it is 2 hours past noon, or 2 o'clock in the afternoon at Dieppe. By the third method. The difference of longitude between both places is found (by Prob. VI.) to be 75° 5. Now 75 degrees, divided by 15, will produce 5, and 5' multiplied by 4 will give 20; hence, the difference of time corresponding to the difference of longitude, is equal to 5 hours, 20 seconds, with which proceed as in the last method, and you will find the time at Dieppe to be 2 hours and 20 seconds past 12 o'clock, when it is nine in the morning at New-York, which is nearly the same as before. 2. What o'clock is it at Bencoolen, a sea-port on the south-west coast of Sumatra, when it is six o'clock in the afternoon at Cashmere, a city of Asia, and capital of a province of the same name, famous for its manufacture of delicate and unrivalled shawls? Answer. 7 hours, 54 minutes, 12 seconds in the after noon. 3. When it is six o'clock in the morning at Columbia, the seat of government of South Carolina, what o'clock is it at Palos, a sea-port in Spain, from which port Christopher Columbus sailed, on his first voyage for the discovery of the New World, in the year 1492? 4. When it is noon at Palos, what o'clock is it in the Guanahani, or San Salvadore, one of the Bahama Islands, and the first land discovered by Columbus, on Friday October the 12th of the same year that he sailed from Palos ? 5. When it is noon at Washington city, what o'clock is it at the following places: St. John, in New-Brunswick; the Azores, or Western Islands; Madeira; Oporto, a city and sea-port in Portugal; Waterford, a city and sea-port in Ireland; Portsmouth in England; Palermo, a large and beautiful city of Sicily, and capital of the island; Corinth, a town in the Morea, near the isthmus of the same name, and anciently one of the most flourishing : cities of Greece; Medina, a city of Arabia, celebrated as containing the tomb of Mahomet; Bassora, a city of Asia in the government of Bagdad; and Nankin, a large city of China, not equalled perhaps by any in the world for the extent of ground enclosed within its walls? PROBLEM XX. The hour of the day at any particular place being given, to find all places on the globe where it is then noon, or any other given hour. RULE. Bring the given place to the brazen meridian, and set the index to the given hour in that place; turn the globe till the index points to the other proposed hour, and all the places that are then under the meridian, are those required. If the hour at the given place be earlier than that at those places sought, the globe must be turned westward, but if later, turn it eastward. Or, bring the given place to the brazen meridian, and set the index of the hour circle to 12; then, as the difference of time between the given and required places is always known by the problem, if the hour at the required places be earlier than the hour at the given place, turn the globe eastward till the index has passed over as many hours as are equal to the given difference of time; but if the hour at the required places be later than the hour at the given place, turn the globe westward, till the index has passed over as many hours as are equal to the given difference of time; and, in each case, all the places required will be found under the brazen meridian. Or, without the hour circle, convert the difference of time between the given place and the required places into the corresponding degrees of longitude, as in the last problem; then, the difference of longitude in degrees being thus determined, if the hour at the required places be earlier than the hour at the given place, the places sought lie so many degrees to the westward of the given place |