Page:Philosophical Transactions - Volume 002.djvu/35

 For finding whereof, every Expert Mariner is instructed, or may be so, from his Sea-Books, and so it needs not here to be set down. Nor how by the help of these, the Azimuth required may, to Degrees, if not nearer, be found out upon a good Globe or Planisphere, (whereof there is a design to have one, that is, the Analemma, contrived into a form of Instrument for the use of the publick, and that ere long; which will with great facility perform all that the Globe can do, with much more exactness and conveniency) that being sufficiently known.

But to do it accurately, you must constitute a Spherical Oblique-angled Triangle, of the three Complements, of the Suns Declination, its Altitude, and of the Height of the pole; the measures of all the Sides whereof are known; One from the Zenith to the Pole; another from the Pole to the Point of the Suns Altitude; and the third, from that point to the Zenith, Now by those you are to find out the Angle at the Zeinth, which being found, substract it from 180, and the remainder is the Suns true Azimuth, or Distance from the Meridian of the Place.

This Angle is to be found divers wayes, as by the Tables of Sines, Logarithmes, &c. the manners of doing whereof, are set down and demonstrated by John Newton in his Institutio Mathematica, Case 11. and in other Books of Trigonometry.

And the true Azimuth of the Sun being thus found, and the Magnetical Azimuth of it, according to your Needle, observed, substract the lesser Number from the greater, and the Remainder is the Variation of the Needle. If the Magnetical Azimuth be less than the other, then the Variation is towards the same side of the Meridian, where the Sun is; if greater, on the other.

To observe the Suns Azimuth by the Needle, and the Needles Variation to Degrees, any Needle, long enough to afford upon a Card under it, a Circle divided into Degrees, put in a Square Box, after the ordinary manner of Clinatories, will serve turn; by placing the Box so, as the Sun may shine upon any two opposite sides of it, at the same times that the Suns Height, &c. are taken: For then the Needles Distance from the Diameter of the Circle on the Card, that is parallel to those sides, is the Magnetical Azimuth required. The