When the course is given in points, the log. sine, log. cosine, &c., may be found in Table XXV., otherwise in Table XXVII. In all cases, where the complement of course, or cosine, &c., is used, the degrees or points put down are the course itself, but the logarithms belonging to the complement or cosine, &c., of that course are taken. A Table of the Angles which every Point of the Compass makes with the Meridian. In the following Table, the Rules for solving the various Cases of Plane Sailing are collected. PLANE SAILING. Diff. of latitude. Radius distance: cos. course: difference of latitude. Departure. Distance. Distance. Course. Course. Diff. of lat tude. Course. Radius distance: sine course: departure. Cosine course: diff. of latitude :: radius: distance. Sine course departure: radius: distance. Distance: radius: departure; sine course. Diff. of latitude radius: departure tang. course. CASE I. Course and distance sailed given, to find the difference of latitude and departure from the meridian. A ship from the latitude of 49° 57' N., sails S. W. by W. 244 miles; required the latitude she is in, and her departure from the meridian sailed from. BY PROJECTION. Draw the line CA, to represent the meridian of the place C, from whence the ship sailed. With the chord of 60° in your compasses, and one foot in C, as a centre, describe the compass W. S. E. Take 5 points in your compasses from the line of rhumbs on the plane scale, and set it off on the arc, from S. towards W., for the course; through this point and C draw the line CB, and make it equal to the distance 244; draw BA parallel to the east and west line EW, to cut the meridian in A. Then will CA be the difference of latitude 135.6, and AB the departure 202.9. W Distance 244 Coursespts Departure B BY LOGARITHMS. Diff. Lat Extend from radius or 8 points* to 5 points on the line marked SR; that extent will reach from the distance 244, to the departure 202.9, on the line of numbers. 2dly. Extend from radius or 8 points to 3 points, the complement of the course, on the line SR; that extent will reach from the distance 244, to the difference of latitude 135.6, on the line of numbers. Thus may all the operations be performed in the several cases of Navigation. By this case are calculated the tables of latitude and departure (Tables I. and II.) for every degree, point, and quarter point of the mariner's compass, to the distance of 300 miles. By the inspection of these tables, a day's work may be calculated in a much more expeditious manner than by logarithms or by Gunter's scale. In consequence of this facility, the method by inspection is generally used at sea in preference to every other method. BY INSPECTION. Find the given course at the top or bottom of the tables, either among the points or degrees, and in that page, against the distance taken in its column, will stand the difference of latitude and departure in their columns.t It must be observed, that, in using these tables, the names Dist. Lat. Dep. must be found at the top if the course is found there, but if the course is found at the bottom, those names must be found at the bottom. Thus the course S. W. by W. or 5 points, is found at the bottom of the table of difference of latitude and departure for points; and against 244 in the distance column stands 135.6 for the difference of latitude, or 202.9 for the departure. * When the course is given in points, make use of the lines marked sine rhumbs, and tangent rhumbs, on the upper side of the scale; when in degrees, make use of the lines marked sine and tangent. When the distance is too great to be found in the tables, you must divide it by 2, 3, 4, or any convenient number; the numbers corresponding to the quotient being multiplied by the divisor will give |