PROBLEM XL. To find the Angle of Pofition between any two Places, i. e. an Angle formed at one affigned Place by the Meridian of that Place, and a great Circle paffing through that and another given Place. Rectify the globe for the latitude and zenith of one of the given places, over which fix the quadrant of altitude, and lay its edge to the other; the end of the quadrant will then fhew, by the mariner's compafs on the horizon, the angle of pofition. N. B. This operation is commonly, though very erroneously, fuppofed to give the bearing of one place from another, and is fo expreffed in fome treatises on the use of the globes. But to fhew in the clearest manner the palpable mistake of such writers, we have only to fix on two places which lie under the fame parallel of latitude, namely, Madrid and Pekin, lat. 40 deg. Now these must always bear directly Eaft and Weft from each other. But if Madrid be brought to the zenith, and the quadrant placed over it, and thence directed to the Eaft point of the horizon, it will not follow the courfe of the 40th parallel of latitude, and lead the eye to Pekin, but to much more Southern places, very far diftant from it, and which have a very different bearing, namely, the Ifle of Ceylon, &c. or if the quadrant be directed from Madrid to Pekin, this laft place will appear to bear N. E. from Madrid. Again, the angle of pofition between the meridian of Cape Clear, in Ireland, and St. St. Auguftin, in Florida, is about 82 deg. NorthWefterly; but the angle of pofition between St. Auguftin and Cape Clear, is only about 46 deg. North-Eafterly. Hence the beft writers defcribe the rhumb or courfe of bearing from one place to another in a different manner from the angle of pofition; hamely, they denominate this laft, That point of the compafs, toward which any perfon must conftantly fail or travel, in order to arrive at the diftant place given. But as many authors ftill continue to confound the terms, it may be useful in this place to establish a clear diftinction. The angle of pofition between any two places, which, as we have juft remarked, is obtained by the arch of a great circle (the quadrant being employed for the purpose), may be called their bearing in a geographical fenfe; and the bearing obtained in a rhumb line (as is the cafe with mariners) may be denominated their bearing in a nautical fenfe. EXAMPLES. What angle of pofition does a great circle paf fing through London and Jerufalem make with the meridian of London ? or what is the bearing of Jerufalem from London, in a geographical fenje? -Anf. 68 deg. South-Eafterly; or 22 deg. from Eaft toward the South; E. S. E. point of the compafs. What is the angle of position between London and the following places or what is their bearing from London in a geographical fenfe ?—Madrid, Rome, Conftantinople, Bombay, Calcutta, Canton, Pekin, the Madeira Lilands, the Cape Verd Islands, the Azores, the Caribbee Iflands, Jamaica, Newfoundland, Quebec, and Mexico? PROBLEM PROBLEM XLI. To find the Bearing of one Place from another in a nautical Senfe. The bearing of one fea-port from another, in a nautical fenfe, is determined by a kind of fpiral, called a rhumb line, paffing from one to the other, fo as to make equal angles with all the meridians through which it paffes; of course, if both places are fituated on the fame parallel of latitude, their bearing, as we have obferved in the N. B. to the 40th problem, is either Eaft or Weft from each other; if they are upon the fame meridian, they bear North and South from one another; if they lie upon a rhumb-line, their bearing is the fame with it; if they do not, notice to which rhumb-line the two places are nearest parallel, and that will fhew the bearing fought. EXAMPLES. The courfe from Cape St. Vincent in Portugal, to St. Salvador among the Bahama Iflands, is nearly W. by S. The courfe from Barbadoes to Cape Finisterre, N. E. by E. or thereabouts. The bearing of the Lizard point from the Island of Bermudas is nearly E. N. E. and that of Bermudas from the Lizard is W. S. W. both nearly upon the fame rhumb-line, but in contrary directions. N. B. The rhumb-lines were formerly delineated on fome confpicuous part of the watery furface of moft terreftrial globes, namely, in the Atlantic and Pacific oceans; but, to avoid confufion, fufion, they have lately, at least on Mr Bardin's globes, given place to the feveral tracks of eminent circumnavigators They are 32 in number, and coincide with the points of the world or of the horizon; and, hence mariners diftinguish the rhumbs by the fame names as the points of the compafs. To find the bearing of one place from another by a rhumb-line, the pupil has, therefore, only to find the correfponding point on the mariner's compafs on the horizon: e. g. The rhumbline which on Mr. Adams's globe paffes through Bermudas to the Lizard, is the fecond from the Eaft terwards the North; now by infpecting the compafs for its coinciding point, it will appear to be E. N. E. which fhews the bearing of the Lizard from Bermudas. The Fleur-de-lis + denotes the North rhumb; its oppofite is the South rhumb; and the equator reprefents the East and Weft rhumbs. See page 4. PROBLEM + This is an ornament inferted alfo in maps to denote the North, and it therefore regulates the fituation of all the other points. The North part of the mariner's compafs was marked by its immortal author with this beautiful flower, in compliment to France. This happened in confequence of the Neapolitan monarch being a. younger branch of the royal family then (1302) upon the throne of that kingdom. The fleur-de-lis not only formed a part of the arms of the kings of France, but was employed in the decorative embellishments of the crown itself. A late melancholy event renders a line of our great bard on this fubject strikingly appropriate : Cropp'd are the flower-de-luces in his arms. Flavio de Giovia, a native of Amalfi in Naples. See Arith. Quest, Art, Navigation. * See January 21, 1799, Chron, Tab. Edward PROBLEM XLII. To find how many Miles make a Degree of Longitude in any given Parallel of Latitude. It has been before obferved §, that the number of miles in a degree of longitude, varies according to the parallel of latitude, thefe laft becoming lefs and lefs the farther they recede from the equator towards either pole, and confequently each degree of thefe circles must be proportionably lefs alfo; for this reafon, an entire circle of 360 degrees in the vicinity of the poles will not make above 360 miles; and, in a ftill nearer approximation, not many furlongs or even feet. fo Edward the IIId. added the fleur-de-lis to the arms of England: Great Edward with the lilies on his brow GRAY. Since the union of the Britannic kingdoms, January 1, 1802, the fleur-de-lis has given place to the fhamrock, the badge of the Irish nation. Queen Anne granted to Sir Cloudefly Shovel for his arms, a cheveron between two fleurs-de-lis, and a crefcent + in bafe, to denote three victories that he had gained; two over the French, and one over the Turks. Miller fpecifies thirty-four fpecies of flower-de-luce, among which the Perfian is greatly esteemed for the fweetnefs and beauty of its variegated flowers, which are in perfection in February, or the beginning of March. · See October 22, 1707, Chron. Tab. + The Turkish fymbol, or rather that of the city of Byzantium, which bore this device from all antiquity; as appears from various medals. See Art. 24. p. 23. G To |