To find the proportion which a degree of lon gitude on any leffer parallel of latitude bears to a degree of longitude on the equator, or how many miles make a degree of longitude in any propofe parallel of latitude, take off any number of de grees, fuppofe 15, the fpace between two hot circles or meridians, from the affigned parallel. with a pair of compaffes, and apply that diftance to the equator, obferving how many degrees it makes there; after which ufe the following caly arithmetical operation: as the number of degrees on the equator, is to the number in the latitude given; fo is the number of miles (either geogra phical or English) in one degree of the equator to the number of miles equal to a degree in the afligned latitude. EXAMPLES. In the parallel of London, lat. 51 deg. if the fpace between two meridian lines drawn at the distance of 15 deg. of the equator, be taken with a pair of compaffes, and applied to the equator, it will be found to contain 9 deg. Then, as 159: 60: 37 geographical miles: or, as 15: 91 70 43 English miles. : Required the number of geographical and English miles in the parallels of latitude in which the following places are fituated: Cayenne, Trinidad, Martinico, Jamaica, Havannah, Cape St. Vincent, Cape Finisterre, Ratifbon, Edinburgh, Archangel, North Cape, and Spitzbergen. PROBLEM PROBLEM XLIII. To find the Antoci of any given Place". Bring the affigned place to the brafs meridian, and, having noticed its latitude, feek the fame number of degrees in the oppofite hemifphere, and that fituation will be the Antæci required. N. B. Places which are fituated under the equator have not any Antocci. EXAMPLES. What place has its inhabitants the Antoci to that part of the South Frozen ocean, which is fituated on the first meridian and in 51 deg. of South latitude ?-Anf. London. Find the Antoci to the following fituations:103° W. long. 20° S. lat-80° E. long. 14° S. lat. -72° W. long. 47° S. lat.-30° E. long. 60° S. lat. 41°E. long. 22° S. lat.-9° W. long. 38° S. lat. -760 W. long. 18°S. lat.-25° W. long. 15° S. lat. -156° W. long. 19° S. lat.-150° W. long. 17° N. lat.-173° W. long. 20° N. lat.-150° E. long. 34° N. lat.-165° E. long. 20° N. lat.-7° W. long. 16° N. lat.-18° E. long. 34° N. lat.. 80 W. long. 33 N. lat.-56° E. long. 21° N. lat. *See Art. 30. p. 26. G 2 PROBLEM PROBLEM XLIV. To find the Perioci of any propofed Place Obferve the latitude of the affigned place, and turn the globe half a revolution of 180 degrees; which may be performed with great correctness by remarking to what hour the index points when the given place is under the meridian, and revolving the fphere till the index points to the opposite hour; then will the place under the same degree of the meridian be the Perioci to the one propofed. This problem may be folved by an easy arithmetical operation. For as the Pericci muft be half the circumference of the globe, or 180° afunder, by fubtracting the longitude of the given place from this number of degrees, the longitude of the required place will be obtained on the oppofite fide of the first meridian; e. g. fuppofe the given place to be fituated in 40° E. longitude; thefe, deducted from 180° will leave 140, the W. longitude of the place fought; and the latitude is the Tame with that of the given place. N. B. If there were inhabitants exactly at the Poles, they would not have any Pericci. EXAMPLES. What place has its inhabitants the Perioci to a place fituated in 180 degrees of longitude and 51 degrees of North latitude ?-Anf. London. See Art. 30. p. 26. Find Find the Perioci to the following fituations: -176o E. long. 40° N. lat.-150 W. long. 60° N. lat.-166° E. long. 15° N. lat.-108° W. long. 19° N. lat.-100° W. long. 14° N. lat.104 E. long. 180 N. lat. 100° E. long. 33° S. lat.-124° W. long. 21° S. lat.-110° E. long. 55° S. lat.-30° W. long. 34° S. lat.-140° W. long. 22° N. lat.-64° W. long. 40° N. lat.150° W. long. 4c° N. lat. To find the Antipodes of any affigned Place *. Seek the Antoci of the given fituation, and the Perioci of this will be the Antipodes, or point of the globe diametrically oppofite, to the first place. Or in a more familiar way: bring the given place to the meridian and obferve its latitude; tum the globe half a revolution, or 180 degrees; then find in the oppofite hemifphere to that in which the given place is fituated a latitude equal to its own, and that is the antipodal fpot required. The Antipodes may moreover be obtained by bringing the propofed place to any part of the horizon, and. looking at the oppofite point of the horizon, where they will be found. By the laft folution of this problem it plainly appears, that a place and its Antipodes have the fame horizon; and alfo, by turning the globe either way, it will be found, that as the one place rifes above, the other defcends below the horizon; and confequently, that every appearance is exactly the reverfe in one place to that which it is in the other, as we have before obferved, Art. 29, Page 25. *See Art. 30. p. 26. N. B. N. B. This problem, like the last, may be folved by a familiar arithmetical operation, and for a fimilar reafon: the pupil has, therefore, only to fubtract the longitude of the affigned fituation from 180°, and the difference will be the longitude of the antipodes to that place, on the oppofite fide of the firft meridian: e. g. if the given place be fituated in 30° W. longitude, the one fought must have 150° E. longitude. Tracing the meridional line of this laft till a latitude equal to that of the given place be found, but on the oppofite fide of the equator, will give the exact antipodal fpot required*. EXAMPLES. What is the antipodal place to one fituated in 180° of long. and 51° of S. lat. ?—Ans. London. Find the antipodes to the following fituations: -30° W. long. 34° N. lat.-104° E. long. 18° S. lat.-150° W. long. 60° S. lat.-54° E. long. 49° S. lat.-91° W. long. 22° S. lat.-30° E. long. 60° S. lat. 10° E. long. 66° S. lat.-90° E. long. o lat.-150° E. long. 40° S. lat.-120° E. long. 52° N. lat.-160° W. long. 77° S. lat.24 E. long. 20° S. lat. The author has found it an improving exercise to his fcholars, to give them a map of the world drawn upon writing paper, and require them to infert with a pen the Pericci and Antipodes, to the principal places, by the method defcribed in this and the laft problem. It appears wholly unneceffary to give directions for placing the Antœci. PROBLEM |