Nine geometricall exercises, for young sea-men and others that are studious in mathematicall practices: containing IX particular treatises, whose contents follow in the next pages. All which exercises are geometrically performed, by a line of chords and equal parts, by waies not usually known or practised. Unto which the analogies or proportions are added, whereby they may be applied to the chiliads of logarithms, and canons of artificiall sines and tangents. By William Leybourn, philomath.

PROBL. IX. The Difference of Longitude, and Distance of two Places, with the Latitude of one of the Places, being given, to find the Rhumb that leads from one to the other.

The Analogie or Proportion.

As the proper Distance upon the Rhumb is to the Difference of Longitude;

So is the Radius to the Sine of the Rhumb from the Meridian.

Thus, if one of the Places lay in the Latitude of 50 degr. and the other in a greater Latitude, but unknown; the Dif∣ference of Longitude between them 5 ½ degr. and their pro∣per Distance upon the Rhumb 6 degr. the Inclination of the Rhumb to the Meridian which leadeth from one Place to the other will be found to be 33 degr. 45 min. that is the N. E. by N. Point.

Ʋpon the Chart.

LET the Meridians A B and D C be drawn through A and C, and through A a Parallel of Latitude A D. Then open the Compasses (having respect to the Latitudes) from K to L, the quantity of 6 degr. in the Meridian; and setting one foot of that Extent in A, with the other foot cross the Meridian C D in C, and draw the right Line A C for the Rhumb. Lastly, by your Chord or Quadrant find the quantity of the Angle B A C, 33 degr. 45 min. and that is the Rhumb required N. E. by N.

But if you were to find this Rhumb by the Plain Sea-Chart, it would be found almost the E. N. E. Point within 1 degr. 30 min. differing from truth very near 3 whole Points to the Eastward.