EXAMPLES.-A ship from latitude 48° 50' N. has sailed N. E. by E.1 E. 436 miles.—Required the lati tude come to, and the departure.
1. By Construction.—Draw the line AD, (Fig. 4. Plate CCCCIV.) of indefinite length, to represent the meridian, and at the point A, which denotes the place sailed from, make with AD, by means of the scale of rhumbs, an angle of 5-1 points, in a direction upwards, and towards the right hand. From some convenient scale of equal parts, such as the larger diagonal scale, take off 436 with the compasses, and putting one foot on A, extend the other to C, and C will be the ship's place. Lastly, from C let fall a perpendicular on AD, and AB will be the difference of latitude, and BC the departure. These lines being successively applied to the same scale from which the distance was measured, will give the dif ference of latitude 206 miles, and the departure 385 miles.
2. By Calculation.
Table I. entitled the Traverse Table, or t'ne table of difference of latitude and departure, is constructed by this case, and is commonly computed for every degree of the quadrant in which the course may be expressed. We have not judged it necessary, however, in this work, to give a table for more than quarter points, that being sufficiently precise for ordinary purposes. Neither have we extended the distance beyond 240 miles, as it is easy, by taking. somc portion of the distance, to make that extent suit the solution of every case. The table
of difference of latitude and departure being previously constructed, the difference of latitude and departure cor responding to any particular course and distance, may be found by inspection in the following manner.
3. By Inspection.—Search in Table, I. for the course of 51 points, which in the present example is found at the bottom of the table; and opposite half the distance 218, there is found in the difference of latitude column 102.3, and in the departure column 192.3. These num bers, therefore, being both doubled because the distance was halved, we obtain 204.6 miles for the difference of latitude, and 384.6 miles for the departure. The desig nation of the columns is taken at the top or bottom, ac cording as the course is found at the top or bottom.
4. By Gunter's Scale.—The extent from the radius, or 8 points, to the complement of the course 21 points on the scale of sine rhumbs, will be found to reach from 436 on the line of numbers, to 2()6 ; and the extent from 8 points to 51 points on the scale of sine thumbs, will be found, in like mAnner, to reach from 436 on the line of numbers to 334 on the same scale.
'Ike ship having been in north latitude, and made 2041 miles, or 3° 24y of northing, the difference of latitude is added to the latitude left, to obtain the latitude come to.