CASE II. Given the course and difference of latitude, to find the distance and departure.
Ex 1MPLE.-A ship from latitude 25° 30' .N. has sail ed S. S. E. E. until shc has arrived in latitude 21° 14' N. what distance has she sailed, and how many miles has shc departed Irom the meridian left ? 1. By Construction.—Draw the meridian line AB, (Plate CCCCIV. Fig. 5.) equal to 256 by either diago nal scale ; at the point A, representing the place sailed from, make with the meridian the angle BAC by the scale of rhumbs equal to the course 21 points ; and from the point 13 draw the parallel of latitude BC at right angles to AB. The line AC, applied to the diago nal scale used in measuring AB, will give the distance 298 miles, and BC, applied in like manner, will give the departure 153 miles.
s . By Inspection.—Having found thc course 24 points at the top of the table of difference of latitude and de parture, search in the difference of latitude column for 128, the half of the actual difference of latitude; oppo site to it the distance column will he found 149, and in departure column 76.6, each of which being doubled, we obtain 298 for the distance, and 153.2 for the depar ture.
4. By Gunter's Scale.—There being no logarithmic line of secants, the distance cannot be found in the scale hy the analogy used in computing it arithmetically ; but we have also cosine course to radius, as the difference of latitude to the distance, from which the distance may be found hy the scale of sines thus: Extend from the com plement of the course 5* points to 8 points on the scale of sine rhumbs, and that extent will reach from 256, the difference of latitude, to 298, the distance on the line of numbers. Again, from the radius or 45°, to 24 points on
the scale of tangent rhumbs, will reach from 256 to 153, the departure on the line of numbers.
1. By Construction.—Draw the meridian line AB, (Plate CCCCIV. Fig. 6,) and from A, the place sailed from, draw the line AD at right angles to AB, and equal to 185 ; through D draw DC parallel to AB, and inter secting thc line AC, previously drawn so as to make with AB an angle equal to the course. Then AC will be the distance, and AB the departure, the former of which will be found to measure 239 miles, and the latter 152 miles.
3. By Inspection.—Having found the course 41 points at the bottom of the traverse table, opposite the depar ture 185, or rather 184.7, which is the neatest to it, occurs 2'39 in the distance column, and 151.6. or the dif ference of latitude column, the designation of the latter being taken at the bottom, because the course was found there.
4. By Gunter's Scale—The extent from 4-1. to 8, on the line of sine thumbs, will reach from 185 .239. on the line of nutnbers ; also, the extent from 41 o 31- on the line of sine rhumbs will reach from 185 to 152 on the line of numbcrs.
The difference of latitude exceeding the latitude left, 2nd being of a different denomination, the ship has cross ed the equator, and arrived in south latitude.