those parts into quarters; on B, as a centre, transfer the divisions of the arc to the chord BE, which, marked with the corresponding figures, will be a line of rhumbs.

4. To construct the Line of Sines.*

Through each of the divisions of the arc AD draw tight lines parallel to the radius AC; and CD will be divided into a line of sines, which are to be numbered from C to D for the right sines; and from D to C for the versed sines. The versed sines may be continued to 180 degrees, by laying the divisions of the radius CD from C to E.

5. To construct the Line of Tangents.

A rule on C, and the several divisions of the arc AD, will intersect the line DG, which will become a line of tangents, and is to be figured from D to G with 10, 20, 30, 40, &c.

6. To construct the Line of Secants.

The distances from the centre C to the divisions on the line of tangents, being transferred to the line CF from the

centre

For Definitions of Sines, Tangents and Secants, see PLANE TRIGONOMETRY; and for that of Rhumbs, see NAVIGATION.

centre C, will give the divisions of the line of secants; which must be numbered from A toward F with 10, 20, 30, lo

7. To construct the Line of Semitangents, or the Tangents of half the Arcs.

A rule on E, and the several divisions of the arc-A D, will intersect the radius C A, in the divisions of the semi or half tangents; mark these with the corresponding figures of the arc A D.

The semitangents on the plane scales are generally continued as far as the length of the rule, on which they are laid, will admit; the divisions beyond 90° are found by dividing the are AE like the arc AD, then laying a rule by E and these divisions of the arc AE, the divisions of the semitangents above 90 degrees will be obtained on the line CA continued.

8. To construct the Line of Longitude.

Divide AH into 60 equal parts; through each of these divisions parallels to the radius AC, will intersect the arc AE in as many points; from E, as a centre, the divisions of the arc EA, being transferred to the chord EA, will give the divisions of the line of longitude.

The points thus found on the quadrantal arc, taken from A to E, belong to the sines of the equally increas ing sexagenary parts of the radius; and those arcs, reck

FFf

oned

oned from E, belong to the cosines of those sexagenar parts.

9. Ta construct the Line of Latitudes.

A rule on A, and the several divisions of the sines on CD, will intersect the arc BD, in as many points; on B, as a centre, transfer the intersections of the arc BD, to the right line BD; number the divisions from B to D with, 10, 20, 30, &c. to 90; and BD will be a line of latitudes.

10. To construct the Line of Hours.

Bisect the quadrantal arcs BD, BE, in a, b; divide the quadrantal arc a b into 6 equal parts, which gives 15 degrees for each hour; and each of these into 4 others, which will give the quarters. A rule on C, and the several divisions of the arc ab, will intersect the line MN in the hour, &c. points, which are to be marked as in the figure.

11. To construct the Line of Inclination of Meridians,

Bisect the arc EA in c; divide the quadrantal arc be in to 90 equal parts; lay a rule on C and the several divisions of the arc bc, and the intersections of the line HM will be the divisions of a line of inclination of meridians,

END OF VOLUME FIRST.