To find the Antæci, Periæci, and Antipodes of any place. Rule. Place the two poles of the globe in the horizon, and bring the given place to the eastern part of the horizon; then, if the given place be in north latitude, observe how many degrees it is to the northward of the east point of the horizon; the same number of degrees to the southward of the east point will shew the Antœci; an equal number of degrees, counted from the west point of the horizon towards the north, will shew the Pericci; and the same number of degrees, counted towards the south of the west, will point out the Antipodes. If the place be in south latitude the same rule will serve by reading south for north, and the contrary. OR THUS: For the Antaci. Bring the given place to the brass meridian and observe its latitude, then in the opposite hemisphere, under the same degree of latitude, you will find the Antœci. For the Periæci. Bring the given place to the brass meridian, and set the index of the hour circle to 12, turn the globe half round, or till the index points to the other 12, then under the same degree of latitude with the given place you will find the Pericci. For the Antipodes. Bring the given place to the brass meridian, and set the index of the hour circle to 12, turn the globe half round, or till the index points to the other 12, then under the same degree of latitude with the given place, but in the opposite hemisphere, you will find the Antipodes. Examples. 1. Required the Anteci, Periæci, and Antipodes of the island of Bermudas? Answer. A place in Paraguay, a little N. W. of Buenos Ayres, is the Antaci; the Pericci is a place in China N. W. of Nankin; and the S W part of New Holland is the Antipodes 2. Required the Anteci, Periæci, and Antipodes, of the Cape of Good Hope? 3. Captain Cook, in one of his voyages, was in 50 degrees south latitude and 180 degrees of longitude ; in what part of Europe were his antipodes ? 4. Required the Anteci of the Falkland Islands? 5. Required the Pericci to the Philippine Islands? 6. What inhabitants of the earth are Antipodes to Buenos Ayres? PROBLEM KVIL To find at what rate per hour the inhabitants of any given place are carried, from west to east, by the revolution of the earth on its axis. Rule. Find how many miles make a degree of longitude in the latitude of the given place (by Problem XIII.) which multiply by 15 for the answer.* Or, Look for the latitude of the given place in the table, Problem IX, against which you will find the number of miles contained in one degree; multiply these miles by 15, and reject two figures from the right hand of the product; the result will be the answer. Examples. 1. At what rate per hour are thinhabitants of Madrid carried from west to east by he revolution of the earth on its axis. Answer. The latitude of Madrid is about 40° N. where degree of longitude measures 46 geographical, or 53 English miles (see Example 1. Prob XII) Now, 46 multiplied by 15 proces 690, and 53 multiplied by 15 produces 795; hence, the inhabitants of Madrid are carried 690 geographical, or 795 English miles per hour. By the Table. Against the latitude 40 you will find 45.96 g p * The reason of this rule is obvious, for, if m be the number of miles contained in a degree, we have 24 hours: 360o × m. : :1 hour to the answer; but, 24 is contained 15 times in 360; therefore, 1 hour: 15 x m. : : 1 hour to the answer: that is, on a supposition that the earth turns on its axis from west to east in 24 hours; but we have before observed that it turns on its axis in 23 hours 56 min. 4 sec., which will make a small difference not worth notice. graphical miles, and 52.85 English miles: Hence, 45.96 × 15 – 689.40 and 52.85 × 15 = 792.75, by rejecting the two right hand figures from each product, the result will be 689 geographical miles, and 792 English miles, agreeing nearly with the above. 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? A particular place and the hour of the day at that place being given, to find what hour it is at 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 12;* turn the globe 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 time is given, count the difference of time forward from the given hour; if it lie to the west, reckon the difference of time backward. OR, WITHOUT THE HOUR CIRCLE. Find the difference of longitude between the two places (by Problem VIII.) and turn it into time by allowing 15 degrees to an hour, or four 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 above. Degrees of longitude may be turned into time by multiplying by 4; observing that minutes or miles of longitude, when multiplied by 4, produce seconds of time, and degrees of longitude when multiplied by 4, produce minutes of time. The index may be set to any hour, but 12 is the most convenient to count from, and it is immaterial which 12 on the hour circle the index is set to. It has been remarked in the note page 6, that some globes have two rows of figures on the hour circle, others but one; this dif ference frequently occasions confusion; and the manner in which authors in general direct a learner to solve those problems wherein the hour circle is used, serves only to increase that confusion. this, and in all the succeeding problems, great care has been taken to render the rules general for any hour circle whatsoever. In Examples. 1. When it is ten o'clock in the morning at London, what hour is it at Petersburg? Answer. The difference of time is two hours; and, as Petersburg is eastward of London, this difference must be counted forward, so that it is twelve o'clock at noon at Petersburg. Or, The difference of longitude between Petersburg and London is 30° 25', which multiplied by 4 produces 2 hours 1 min. 40 sec. the difference of time shewn by the clocks of London and Petersburg; hence, as Petersburg lies to the east of London, when it is ten o'clock in the morning at London, it is one minute and forty seconds past twelve at Petersburg. 2. When it is two o'clock in the afternoon at Alexandria in Egypt, what hour is it at Philadelphia? Answer. The difference of time is seven hours; and because Philadelphia lies to the west of Alexandria, this difference must be reckoned backward, so that it is seven o'clock in the morning at Philadelphia. OR, The longitude of Alexandria is Difference of longitude 30° 16' E. 75 19 W. 105 35 4 Difference of longitude in time 7h. 2 m. 20 sec., the clocks at Philadelphia are slower than those at Alexandria; hence, when it is two o'clock in the afternoon at Alexandria, it is 57 m. 40 sec past six in the morning at Philadelphia. 3. When it is noon at London, what hour is it at Calcutta? 4. When it is ten o'clock in the morning at London, what hour is it at Washington ? 5. When it is 9 o'clock in the morning at Jamiaca, what o'clock is it at Madras? 6. My watch was well regulated at London, and when I arrived at Madras, which was after a five month's voyage, it was four hours and fifty minutes slower than the clocks there. Had it gained or lost during the voyage? And how much? PROBLEM XIX. A particular place and the hour of the day 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 brass 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 gobe 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 brass meridian. OR, WITHOUT THE HOUR CIRCLE. Reduce the difference of time between the given place and the required places into minutes; these minutes, 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, the quotient will be minutes or miles of longitude. The difference of longitude between the given place and the required places being thus determined, if the hour at the required places be earlier than the hour at the given place, the required places lie as many degrees to the westward of the given place as are equal to the difference of longitude; if the hour at the required places be later than the hour at the given place, the required places lie as many degrees to the eastward of the given place as are equal to the difference of longitude. Examples. 1. When it is noon at London, at what places is it past eight o'clock in the morning. Answer. The diff rence of time between London, the given place, and the required places, is 34 hours, and the time at the requ red places is earlier than that at London; therefore, the required places lie 34 hours westward of London; consequently, by bringing to London the brass meridian, setting the index to 12, and turning B b |