1 10.0000000 As the Tangent of LI= 32 58 9.8119641 3. To find how London bears from Jerusalem, or the Angle at 1. I As the Sine of LI= 32 58 Co. Ar. 0.2642805 Is to the Sine of LPI= 37 24 9.7837878 So is the Sine of L P = 38 28 9.7938317 To the Sine of LIP = 44 or 9.8419000 Thus London bears from Jerusalem NW, and one 59' to the North. This Problem might be diversified and branched into several others, by having other Data ; but that if the Reader pleases he may make his own Exercise. PROBLEM VI. Given the Latitude of two Places ( one in North, the other in South Latitude, ) and their Distance from each other, to find their Difference of Longitude, and Position from one another. Practice, London Ij Cape Horn Practice. P Cape Horn (the farthest South A Point of America) Æ be 58° 00' South; and the Distance from London to Cape Hornbe 8890 English Miles; I demand the Dif S ference of Longitude ? Let L represent London, and C Cape Horn; through both these Places draw proper Circles, and there will be formed the Oblique Triangle PLC, or rather its Supplemental one COS, in which all the sides are given ; for OS = P L= 38° 28' the Co-Latitude of London ; CS= 32° oo', the Co-Latitude of Cape Horn ; and O C= 52° 06', the Complement of LC 8890 Miles = 127° 54' to a Semicircle ; to find the Difference of Longitude, or the Angle O SC, by Case 5, Of Oblique Triangles . Here OŠ - SC= A M = 6° 28'. Then the Sine of OS= 38° 28' Co. Ar. 0.2061683 the Sine of S C= 32° oo'Co. Ar. 0.2757903 Add the Sine of OCTAM = 29° 177 9.6894232 OC-AM the Sine of -AM = 22° 49' 9.5885896 2 2 The Sum = 19.7599714 thereof is the Sine of LOSC=490 20 = 9.8799857 The The Double of which is 98° 40' = 0 SC, whose Complement AS Q = 810 20', the Difference of Longitude fought. 2. To find how the said Cape bears from London, or the Angle at 0. o As the Sine of OC= 52 06 Co. Ar. 0.1028767 Is to the Sine of O SC = 98 40 9.9950126 So is the Sine of SC= 32 00 9.7242097 To the Sine of SOC = 41 35 9.8220990 Now the Angle at O is equal to the Angle at L, therefore Cape Horn bears S. W. by S. and almost to the W. of London. 3. Thus also the Angle at C will be found to be about 51 Degrees, by the Gunter ; so London bears from Cape Horn N E, and almost half to the E. These Problems being well understood, any thing further on this Head will be unnecessary, I shall now subjoin ( for the Reader's Curiosity, ) a Scheme of the Dimensions of all the chief Kingdoms of the World in length and breadth, the Metropolis of each, with its Distance and Bearing from the Metropolis of the whole World, viz. the City of London. Note, The Dimensions following are to be understood of English Statute-Miles. Kingdoms 450|Paris 518 Kingdoms Leng, Bread. Metropolis Dift. Bearing Europe. France 520 208 S. by E. Spain 620 480 Madrid 760 S. Germany 540 510 Vienna 860 E. by S. Poland 780 600 Cracow 700 E. Muscovy 1630 1500 Muscow 1530E. N. E. Sweden Stockholm 980N.E.by N. Denmark Copenhagen 700E. N. E. Norway Bergen 799/N. N. E. Italy 760 134 Rome 8441 S. E. Turkey 770 660 Constantinople 1640 E. by S. Asia. Tartary 3000 2250 Chambalu China 13801260 Peckin India 1680 1690 Agra 5290 E. by N. Persia 1440 1260 Tpaban 3200 E. by S. Turkey 2100 1740 Aleppo 2350 E. S. E. Africa. Egypt 650 310|Cairo 2154 S.E.by E Barbary 2300 380 Fez 12301S. S. W. Biledulgerid 2040 300 Dara 1590S. S.W. Zaara 12340 330 Zuenziga 20851S. S. E. Negroland 2280 600 Tombute 25701S. S. W. Guinea 1320 360 Arda 2919 S. by E. Nubia 840 570 Duncala |3475 S.E. by E. Ethiopia 3600 2180 Monomotapa 5421S. S. E. America. Mexico 2520 480 Mexico 5699 W.N.W. Florida 1000 600 Coca 4170W. N.W. Terra Canad. 1500 1920 Boston 3197W. N.W. Terra Firmali 260 480 St. Fee 152 12W. by S. Peru 1440 480 Lima 6463 W. S.W. Brasil 1600 1380 St. Salvador 4865 S. W. Chili 960 17297 S.W.by W. Paraguay 1560 1500 ljumption 15907 S.W. CHAP CH A P. IV. Spherical Trigonometry applied to Navi gation; shewing how to find the Differences of Latitude, and Longitude ; the Course and Distance failed, and the Departure from the first Meridian ; all in the Arches of a Great Circle of the Globe. G REAT Circle Sailing is of all others the most perfect and expeditious ; the Reafon is evident, because an Arch of a great Circle is the nearest Distance between any two Places on the Spherical Surface of the Earth, and consequently is the foonest failed. But because the Motion of a Ship is directed by the Wind, 'cwill be somewhat difficult to steer a Ship directly on a Circular Arch ; however 'tis possible to keep pretty near it, and the nearer the better. As this Method is most perfect and expeditious, so it is the truest and most natural of any ; yea could the Ship be all along conducted on the Arch of a Circle, it would then be perfectly true and natural. The Difference between Plain, Mercator's, and Middle Latitude Sailing, and this, is obvious in the Form of the Charts, and in the Solutions thereby ; the Charts there being all Rectilineal Plans, but in this the Chart is only a Stereographic Projection of VOL. II. the Rr |