The mariners magazine, or, Sturmy's mathematical and practical arts containing the description and use of the scale of scales, it being a mathematical ruler, that resolves most mathematical conclusions, and likewise the making and use of the crostaff, quadrant, and the quadrat, nocturnals, and other most useful instruments for all artists and navigators : the art of navigation, resolved geometrically, instrumentally, and by calculation, and by that late excellent invention of logarithms, in the three principal kinds of sailing : with new tables of the longitude and latitude of the most eminent places ... : together with a discourse of the practick part of navigation ..., a new way of surveying land ..., the art of gauging all sorts of vessels ..., the art of dialling by a gnomical scale ... : whereunto is annexed, an abridgment of the penalties and forfeitures, by acts of parliaments appointed, relating to the customs and navigation : also a compendium of fortification, both geometrically and instrumentally / by Capt. Samuel Sturmy.

CHAP. II. Theorems premised.

FOr the better understanding of the Reasons of Dials, these Theorems would be known.

I. That every Plane whereupon any Dial is drawn, is part of the Plane of a Great Circle of the Heaven, which Circle is an Horizon to some Country or other; That the Center of the Dial, representeth the Center of the Earth and World; and the Gnomon which casteth the Shade, representeth the Axis, and ought to point directly to the two Poles.

II. That these Dial Planes are not Mathematically in the very Planes of Great Cir∣cles; for then they should have their Centers in the Center of the Earth, from which they are removed almost 4000 miles; and yet we may say they lye in the Planes of Circles parallel to the first Horizon, because the Semidiameter of the Earth beareth so small proportion to the Suns Distance, that the whole Earth may be taken for one Point or Center, without any perceivable Error.

III. That as all Great Circles of the Sphere, so every Dial Plane hath his Axis, which is a straight Line passing through the Center of the Plane, and making Right An∣gles with it; and at the end of the Axis be the two Poles of the Plane, whereof that above our Horizon is called the Pole Zenich, and the other the Pole Nadir of the Dial.

IV. That every Plane hath two Faces or Sides: and look what respect or situation the North Pole of the World hath to the one side, the same hath the South Pole to the other; and these two Sides will receive 24 Hours always: so that what one Side wanteth, the other Side shall have; and the one is described in all things as the other.

V. That as Horizons, so Dial Planes are with respect to the Aequator divided into first, Parallel or Aequinoctial; secondly, Right; thirdly, Oblique Planes.

VI. A Parallel or Polar Plane maketh no Angles with the Aequator, but lies in the Plane of it, or parallel to it; that is, hath the Gnomon erected on the Plane at Right Angles, as the Axis of the World is upon the Plane of the Aequator: be∣cause the Axis and Poles of the Dial are here all one with the Axis and Poles of the World, and the Hour-lines here meet all at the Center, making equal Angles, and dividing the Dial Circle into 24 equal parts, as the Meridians do the Aequator, in whose Plane the Dial lies.

VII. A Right Horizon or Dial Plane cutteth the Aequator at Right Angles, and so cutteth through the Poles of the World, that it hath the Gnomon parallel to the Plane, and so the Hour-lines parallel one to another; because their Planes, though infinitely extended, will never cut the Axis of the World: yet have those Dials a Center, though not for the meeting of the Hour-lines, viz. through which the Axis of the Dial Circle passeth, cutting the Plane at Right Angles, and cutting also (neer enough for the projecting of a Dial) the Circle of the World.

VIII. An Oblique Horizon or Dial Plane cutteth the Aequator at Oblique Angles; that is, hath for their Gnomon the side of a Triangle, whose Angles vary according to the more or less Obliquity of the said Horizon: and the Gnomon shall always make an Angle with the Plane, of so many Degrees as the Axis of the World maketh with the Plane, or as either of the Poles of the World is elevated above the Plane.

IX. Every Oblique Horizon is divided by the Meridians or Hour-circles of the Sphere into 24 unequal parts; which parts are always lesser, as they are neerer to the Meridian of that Horizon or Plane; and greater, as they are farther off: and on both sides of the Meridian of the Plane, the Hour-circles which are equally distant in time, are also equally distant in space. Whence it is, that the divisions of one Quadrant of your Dial Plane being known, the divisions of the whole Circle are likewise known.

X. The Hour-lines in an Oblique Dial, are the Sections of the Planes of the Hour-circles of the Sphere, with the Dial Plane: and because the Planes of Great Circles do always cut one another in Halves by Diameters, which are straight Lines pas∣sing

[illustration] geometrical diagram

through the common Center; therefore Lines drawn from the Center of the Dial, to the Intersections of the Hour-circles with the Great Circles of the Plane, shall be those very Sections, and the very Hour-lines of the Dial.

XI. Every Dial Plane being an Horizon to some place in the Earth (as was said Theo∣rem I.) hath his proper Meridian, which is the Meridian cutting through the Poles of the Plane, and making Right Angles with the Plane. If the Poles of the Dial Plane lie in the Meridian of the Place, then is the Meridian of the Plane all one with the Meridian of the Place, and the Gnomon or Style shall stand erected upon the Noon-line, or Line of 12 a Clock, as in all direct Dials. But if the Plane decline, then shall the Substyle Line, or Line which the Gnomon standeth upon, which is the Meridian of the Plane, vary from the Line which is the Meri∣dian of the Place; and this Variation shall be East, if the Declination be West of the Plane: And contrarily, because the Visual Lines, by which the Sphere is pro∣jected on Dial Planes, do, like the Beams of a Burning-glass, intersect or cross one another in a certain Point of the Gnomon (to be assigned at pleasure, and cal∣led Nodus) and so do all place and depaint themselves on the Dial Plane, beyond the Nodus, the contrary way.

XII. Dials are most aptly denominated from that part of the Sphere where their Poles lie, though some Authors have chosen to denominate them from the Circles in which their Planes lie; as the Dial Plane which lieth in the Aequinoctial, or Parallel to it, is called by many an Aequinoctial Plane; but I concur with those who would ra∣ther call it a Polar Plane, because the Poles thereof are in the Poles of the World.