Now, let us suppose that we have sailed from A to B: we shall then know AB' equal proper diff. lat. = 745 miles; AC' meridional diff. of lat. = 1042; and C'C= the difference of longitude equal to 1295 miles. It is required to find the course B'AB, and the distance AB. For the Distance. 6.982132 As cos A 51° 11' 0.202850 10.000000: AB' 745 3.112270: radius 2.872156 10.000000 3.075006 : tang. A 51° 11' E. 10.094402: AB 1189 2. A ship sails from latitude 37° N. longitude 22° 56′ W., on the course N. 33° 19' E.: till she arrives at 51° 18′ N.: required the distance sailed, and the longitude arrived at. Ans. Dis. 1027 miles; long. 9° 45′ W. MERCATOR'S CHART. 24. MERCATOR'S CHART is a Map constructed for the use of Navigators. In this chart all the meridians are represented by straight lines drawn parallel to each other, and the parallels of latitude are also represented by parallel straight lines drawn at right-angles to the meridians. The chart may be thus constructed. Draw on the lower part of the paper a horizontal line to represent the parallel of latitude which is to bound the southern portion of the to the extent of the map to be made, lay off, on this line, any number of equal distances, and through the points draw a series of parallels to represent the meridians. Then draw a line on the side of the map, and for the second parallel of latitude, find from the table of meridional parts the meridional difference of latitude corresponding to the degrees between the first and second parallel, and lay off this distance for the interval between the two parallels. Then find the meridional difference between the second and third, and lay it off in the same way for the third parallel, and so on, for the fourth, fifth, &c. A place whose latitude and longitude are known, may be laid down in the same manner; for it will always be determined by the intersection of the meridian and parallel of latitude. If the chart is constructed on a small scale, the divisions on the graduated lines, may be degrees instead of minutes; and the meridians and parallels may be drawn only for every fifth or tenth degree. We have already seen (Art. 23), that the meridional difference of latitude bears a constant ratio to the difference of longitude, so long as the course remains unchanged: and hence we see that on Mercator's chart, every rhumb will be represented by a straight line. LINE OF MERIDIONAL PARTS ON GUNTER'S SCALE. 25. This scale corresponds exactly with the table of meridional parts, excepting, that in the table, the circle is divided to minutes, while the scale is divided only to degrees. A scale of equal parts is placed directly beneath the scale of meridional parts; if the former corresponds to divisions of longitude, the latter will represent those of latitude. Hence, a chart may be constructed from those scales, by using the scale of equal parts for the lines of longitude, REMARK. In the following table, in the nine right hand columns of each page, where the first or leading figures change from 9's to O's, points or dots are introduced in stead of the O's, to catch the eye, and to indicate that from thence the two figures of the Logarithm to be taken from 7248 7536 7825 8113 8401 8699 289 126 1272 1558 287 285 150 176091 6381 6670 6959 151 8977 9264 9552 9839 413 699 985 152 181844 2129 2415 2700 2985 3270 3555 3839 4123 4407 4691 49755259 5542 5825 6108 6391 6674 6956 7239 283 7521 7803 8084 8366 8647 8928 9209 9490 9771 051 155190332 0612 0892 1171 1451 1730 2010 2289 2567 153 154 156 3959 4237 281 2846 279 4514 4792 5069 5346 5623 278 3125 3403 3681 157 5899 6176 6453 6729 7005 7281 7556 158 8657 8932 9206 159 201397 1670 1943 7832 8107 8382 276 9481 9755 •29 •303 577 ⚫850 1124 274 2761 3033 3305 3577 3848 272 |