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2. A ship sails from latitude 15° 55′ S. on a S.E. § E. course till she finds herself in latitude 18° 49' S.: required the departure made ?
Hence the departure is 212
Natural Sines, Cosines, Tangents, and Cotangents.
This is a table of natural sines, cosines, tangents, and cotangents to every degree and minute of the quadrant. It will be found useful in finding the direct course from the beginning to the end of a traverse, and in many other computations of Navigation and Trigonometry in which it may be inconvenient to employ logarithms. Ample illustration of the advantage of this table is given in the Navigation and Nautical Astronomy which accompanies the present volume.
TABLES 4 AND 5.
Difference of Latitude and Departure, or Traverse Table for Points and for Degrees.
On account of the use of these Tables in working a traverse, they are frequently called Traverse Tables. The difference of latitude and departure due to any course and distance are found from one or other of these Tables by inspection. The course stands at the head of the page, or if more than 45°, at the foot-expressed in points and quarterpoints in Table 4, and in degrees in Table 5-and the difference of latitude and departure which the ship makes in running any distance on that course, from 1 mile to 300 miles is inserted in the body of the Table, and is found as in the examples following:
1. A ship sails N.W.
N. a distance of 78 miles: required the difference of latitude and departure by inspection ?
The given course is 3 points; and referring to Table 4, we find the page devoted to this course to be page 38, in
which, against 78 in a column headed Dist., stands 60.3 under the head Lat., and 495 under the head Dep. We conclude therefore that, for the given course and distance, the difference of latitude is 603 miles, and the departure 49.5 miles.
2. Suppose the course to be 5 points, and the distance. sailed 78 miles as before.
Then, as the course here exceeds four points, we look for it at the foot of the page (p. 34), and against 78 in the distance column, we find 688 in the adjacent departure column, and 368 in the difference of latitude column, so that the difference of latitude made is 36.8 miles, and the departure 68.8 miles.
3. Suppose the course to be 30°, and the distance sailed on that course 78 miles.
Then, turning to the page headed 30° in Table 5 (p. 70), we find against 78 in the Dist. column, the number 67.5 in the adjacent Lat. column, and 39 in the Dep. column: we conclude therefore that the difference of latitude made is 67.5 miles, and the corresponding departure 39 miles.
4. But if the course exceed 45°, if, for instance, it be 58°, it will be found at the bottom of the page (p. 72), and against the distance 78, there appears 661 for departure, and 413 for difference of latitude.
If the distance sailed on any course be greater than 300 miles, since the limits of the Table will then be exceeded, to render the Table still available we must take the half, or the third, or the fourth, &c., of the given distance, so that the part taken may be a distance within the limits of the Table: the diff. lat. and dep. corresponding to this aliquot part of the given distance, being each multiplied by 2, or by 3, or by 4, &c., according to the part taken, will give the
These Tables are employed not only in plane sailing, but also in parallel and mid-latitude sailings, as is sufficiently exemplified in the treatise on Navigation and Nautical Astronomy, to which the present collection is adapted. And in all computations of the parts of a right-angled triangle, provided the angles are expressed in degrees and minutes-seconds being disregarded, Table 5 may be used to save the trouble of arithmetical calculation.
Natural Cosines to Degrees, Minutes, and Seconds.
This Table is employed in the Author's method of clearing the lunar distance for the purpose of finding the longitude The several columns of cosines are headed by the degrees, the accompanying minutes being inserted in the first column on the left of the page: this is equally a column of the seconds, and is accordingly headed by the marks for minutes and seconds. As in the ordinary trigonometrical tables, the cosine of an arc or angle belonging to any number of degrees and minutes is found in the column of cosines, under the degrees, and in a horizontal line with the minutes found in the first column.
Suppose this cosine to have been extracted from the table; then, if there are seconds also in the arc or angle, we again refer to the same first column for these, and in the same horizontal line with them, and in the column headed 'parts for "" which immediately follows the column from which our cosine has been extracted, we shall find the correction for that cosine: this correction is always to be subtracted. The remainder will be the cosine of the given degrees, minutes, and seconds. But in taking out a cosine