and 1947, over 48° and against the Distance 291; this multiplied by 4 gives the Distance 1164 Miles. Hence the Courfe is S. 48° W. and Distance 1164 Miles. BY MERCATOR. ift. Look for the Meridian Difference of Latitude and Differer.ce of Long. until they are found ftanding in their refpective Courfes, (as if they were Latitude and Departure,) and the Course will be found among the Degrees or Points in the Latitude Columns ; belonging to this, find the Proper Difference of Latitude, oppofite to which ftands the Dift. in its Column. TO Now of the Meridian Difference of Latitude, and the of the Difference of Longitude are 170,7 and 119,2, the nearest Numbers in the Tables are 107,7 and 119,6 ftanding together over 48°, which is the Course; over 48° in the Latitude Column, I look for the of the Prop. Difference of Latitude, which is 77,7, the nearest is 77,6, against this ftands 116 in the Distance Column, this multiplied by 10 gives 1160 the Dittance nearly as before. The Difference of Latitude and Departure given, to find the Course, Dif tance, and Difference of Longitude, by Middle Latitude and Mercator's Sailing. A Ship from the Latitude of 37° 00' N. and Longitude 48° 20′ W. fails between the North and Eait, until she be in Latitude 51° 15′ N. and finds that she has made 564 Miles of Departure, what was her direct Course, Distance run, and Longitude in? Draw the Meridian A P, make it equal to 855 the Difference of Latitude; on P erect the Perpendicular PN, and make it=564 the Departure; join D and N, then will the Angle PDN be the Course N. 33° 25′ W. and D N the Distance 1025 Miles. A, the Distance of the Departure 564, draw E F parallel to D P; with the Chord of 60° defcribe the Arch T S, and upon it fet off the Comp. of the Middle Latitude 45° 53' from S to T, through T draw DO, to cut E F in O, then will OD be the Difference of Lon. 785,6 Miles, by Middle Latitude Sailing. = Again, produce DP to A, and make D A 1200 the Merid. Difference of Latitude; draw A B parallel to P N, and produce D N until it cuts A B in B; then will A B be 791,7 Miles, the Diff. of Long. by Mercator's Sailing. By CALCULATION. As the Diff. of Lat. 855 2.93197 As Radius 90° 10.00000 900 10.00000 Is to the Diff. of Lat. 855 2.93197 So is the Departure 564 2.75128 So is Sec. Cou. 33°25 10.07848 12.75128 To the Tan, of Cou. 33° 25' 9.81931 To the Distance To find the Difference of Longitude. By Mid. Lat. Sailing. 13.61045 10.00000 1025 3.01045 By Mercator's Sailing. As Co-Si. Course 33° 25′ 9.92152 Her direct Course is N. 33° 25′ E. or N. E by N. nearly, and Distance 1025 Miles. By GUNTER. ift. Extend from 855 to 564 on the Line of Numbers, that Extent will reach from Radius or 45°, to 33° 25′ the Course, on the Line of Tangents.' 2dly. Extend from Radius or 90°, to the Course 33° 25′ on the Line of Sines, that Extent will reach from the Departure 564, to the Distance 1025, on the Line of Numbers.' 3dly. Extend from Radius or 90°, to the Complement of Middle Latitude 55° 53' on the Line of Sines, that Extent will reach from the Departure 564, to 785 Miles, the Difference of Longitude by Middle Latitude Sailing.' 4thly. Extend from the Sine of the Courfe 33° 25' to the CoSine of the Course 56° 35' on the Line of Sines, that Extent will reach from the Meridional Diff. of Lat. 1200 to 792 Miles the Diff. of Long. by Mercator.' 'Or, the Extent from the Diff. of Lat. 855, to the Departure 564, will reach from the Meridional Diff. of Lat. 1200, to 792, on the Line of Numbers.' By INSPECTION. With the Difference of Latitude and Departure, find the Course and Distance as in Cafe VI. in Plane Sailing. Take the Comp. of Middle Latitude as a Courfe, and the Departure in its Column, the correfponding Distance will be the Difference of Longitude; by Middle Latitude Sailing. And Having found the Courfe, inftead of the Proper Difference of Latitude, find the Meridional Difference of Latitude in the Latitude Column belonging to the Courfe; the correfponding Departure will be the Difference of Longitude, by Mercator's Sailing. Now taking of the Diff. of Lat. of the Departure viz. 85.5 and 56.4, the nearest Numbers ftanding together in the Tables to thefe are, 85.5 and 55.5, under 33° against Distance 102, and 85.4 and 57.6, under 34° against Distance 103, now 33° added to 34° is 67, half is 33° 30' the Courfe; and 102 added to 103 gives 205, half is 102.5, which multiplied by 10, gives 1025 the Distance. To find the Difference of Longitude. Over the Complement of Middle Latitude 46°, find of the Departure, viz. 141 in its Column, and againft it ftands 196 in the Dif tance Column, this multiplied by 4, gives 784 Miles, the Diff. of Longitude, by Middle Latitude Sailing. Again, the Courfe being 33° 25' or nearly 33°, look for of the Meridional Diff. of Lat. 120 in the Latitude Columns, under 33° and 34, the nearcft Numbers to thefe are c.9 and 120.2, the Departures correfponding are 77.9 and 81.1, their Sum is 159, half is 79.5, which, multiplied by 10, gives 795 the Diff. of Lon. by Mercator's Sailing, nearly as before. From what has been faid, it is eafy to perceive that all the Cafes (fave the firft) in Middle Latitude and Mercator's Sailing, are projected and worked in the fame Manner as in Plane Sailing, and to obtain the Difference of Longitude by Middle Latitude Sailing, the Complement of the Middle Latitude is taken as the Courfe in Plane Sailing, and with this Courfe and the Departure, the Distance is found, which, will be the Difference of Longitude by Middle Latitude Sailing. And having the Course, take the Meridional Difference of Latitude, as if it was the Proper Difference of Latitude, the correfponding Departure will be the Difference of Longitude by Mercator's Sailing. The Courfe and Distance given, to find the Difference of Latitude, and Difference of Longitude. A Ship from Cape Clear, in Latitude 51° 15′ N. and Longitude 9° 50' W. fails S. W. by S. until he has run 1022 Miles, what Latitude and Longitude is de in? Now 849.8, or 850 divided by 60, gives 14° 10'S. and being fubtracted from the Latitude of Cape Clear, leaves 37° 5' the Latitude in; Hence the Middle Latitude is found to be 44° 15', and Meridional Difference of Latitude 1194. Whence, To find the Difference of Long. by To find the Diff. of Long. by MerMid. Lat. Sailing. cator's Sailing. As Co-fi. Mid. Lat. 44° 10′ 9.85571 2.75420 90o 10.00000 12.75420 As the Co-fi. Courfe 3 Pts. 9.91985 13.82174 9.91985 To the Diff. of Lon. 791.6 2.89849 To the Diff. of Lon. 797.8 3.90189 Sum The Courfe and Difference of Latitude given, to find the Distance and Difference of Longitude. and Longitude 22° 56′ W. fails N. 22° 20′ E. then by Obfervation is found to be in the Required the Diftance run, and Longitude Diff. 14 15 855 Miles Merid. Parts 1)88 1544.7 Mid. Lat. 3593 2393 1200 Merid. Diff. of Lat. Ey Mid. Lat. Sailing, To find the Difference of Longitude. By Mercator's Sailing. 3.07918 These four Cafes are all that can well happen at Sea, but as fome young Men are inattentive and frequently looking in the Book to fee if their Calculation is the fame as that set down. The Teacher perhaps finds it neceffary to let fuch work the following Questions by Way of Exercise. Quest. ft. Required the Bearing and Distance of Hang. Cliff in Shetland, in Latitude 60° 9' N. and Long. 90° 58′ W. and the North Cape of Lapland, in Lat. 71° 10' N. Long. 26° 3′ E. Anf. {N. N. 44° 48' E. Dift. 931.5 Miles, by Mercator's Sailing. N. 45° 19' E. Dift. 940 Miles, by Middle Lat. Sailing. Quest. 2d. A Ship in Lat. 37° c' N. and Longitude 48° 20/ W. fails between the N. and E. until fhe is in the Latitude of 51° 18′ N, and finds fhe has made 564 Miles of Dep. Required her direct Course, and Diftance run, and Longitude in? Anf. N. 33° 19' E. Dift. 1027 Miles, Lon. in 35° 14′ W. by N. 33° 19′ E. Dift. 1027 Miles. Lon. in 35° 08′, by Mer- Quest. 3d. A Ship from the Lat, of 50° 30' N. fails S. S. W. 150 Leagues, what Lat. is fhe in, and how much has fhe differed her Longitude? Lat. in 43° 34' N. Diff. of Long. 253.3 Miles, by Mercator's Sailing. Anf. Lat. in 43° 34'N. Diff. of Long. 252.6 Miles, by Middle Latitude Sailing, Queft. 4th. A Ship from Latitude 20° 40' N. fails N. E. by E. until the be in the Latitude of 27° 16' N. Required her Dift. run, and Difference of Longitude ? Anf. Dift. run 712.8 Miles, Diff. of Long. 648.1 Miles, by Dift. run 712.8 Miles, Diff, of Long. 648.6 Miles, by |