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.

IV. Propositions assistent to the finding of the Variation of the Compass.

THE Propositions that will be serviceable herein are the 3. 7. 8. 9. 10. 11. and 14. but more especially the Third and the Eleventh: and those I shall here illustrate by Exam∣ple, though all the rest (as occasion may fall out) will be also usefull thereunto. By the Third Proposition you may find the Amplitude of the Sun's Rising and Setting.—By the Eleventh you may find the Azimuth at any time of the day.— By either of which the Variation of the Compass may be found, and also which way it varieth.

I. To find the Variation by the Amplitude.

BY the Third Proposition you found the Sun's Amplitude at his rising or setting to be 33 degr. 20 min. from the true East or West Points of the Horizon towards the North. Having thus before-hand found the Amplitude, in the Morning I set my Compass to the Sun at his Rising; and if I find that the Sun by my Compass do rise 33 d. 20 m. from the West-point thereof towards the North, then may I be ascertain'd that my Compass hath no Variation, but that the Fly or Wires do point directly North and South.—But finding before-hand the Amplitude to be 33 d. 20 m. and I should find the Sun to rise but 28 degr. from the East-point of my Compass, then substracting 28 degr. from 33 degr. 20 min. the difference is 5 degr. 20 min. and so much doth my Compass varie from the true East-point, and con∣sequently all the other Points of the Compass as much.

Now to find which way the Compass varieth, you must ob∣serve whether your Amplitude, found by your Calculation, be to the Right or Left-hand of the Sun's rising or setting. And

if it be on the Right-hand, you may conclude the Variation to be Easterly; but if on the Left-hand, Westerly.

As for Example; Finding by the Amplitude that the Sun should rise 33 d. 20 min. from the East Northerly, when I come to set my Compass to the Sun at his rising, I find that the Sun riseth but 28 degr. from the East Northerly; wherefore the Am∣plitude found is on the Left-hand, and so I conclude the Varia∣tion to be 5 d. 20 min. Westerly.

II. To find the Variation by the Azimuth.

SUppose the Sun's Azimuth found by the Eleventh Propositi∣on to be 107 degr. 30 min. from the North, and when I set the Compass, I find the Magneticall Azimuth to be 102, the dif∣ference between the true and the Magneticall Azimuth being 5 d. 30 m. which is the Variation.

Now to know whether this Variation be towards the East or towards the West: seeing by the Azimuth found the Sun should have been 107 d. 30 min. from the North, which is 17 degr. 30 min. from the East; but setting of the Sun with my Compass, I find that it was from the East to the Southward onely 12 degr. so that the Degree upon which the Sun should have been was more towards the Right-hand then the Degree on which it was; therefore I conclude the Variation to be 5 degr. 30 min. Easterly.