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. I.

IN the former Books are contained such Pro∣blems Geometrically, as are most necessary for every professed ingenious Artist to un∣derstand and Practice; Now to the end the Practitioner may Elevate his Thoughts to the contemplation of those Glorious Bo∣dies, the Sun, Moon, and Stars; I shall here in this place give a brief Survey of the first Rudiments of Astronomy, for the help of young Practitioners and Mariners, for whom chiefly I take these pains; I shall give a brief and succinct Explanation of the se∣veral Circles of the Sphere, better than we could in the foregoing RHYTHMES to be understood, and then shew how to re∣solve the most usual and common Problems thereof; and after the Art of Dialling Geometrically and Instrumentally, and by Cal∣culation, as promised.

1. This is to be understood, that Astronomers do imagine 10 principal Points, and 10 Circles to be in the hollow inside of the first Moveable Sphere, which are commonly drawn upon any Globe or Sphere, besides divers other Circles which are not delineated, but only apprehended in the Fancy.

The Points are the two Poles of the World, the two Poles of the Zodiack, the two Equinoctial Points, the two Solstitial Points, and the Zenith and Nadir.

2. The Poles of the World are two Points, which are directly opposite to one another, about which the whole frame of Heaven moveth from the East into the West, whereof that which is seen on the North-side the Equinoctial, is called the Arctick-Pole.

3. And the other directly opposite to the former is called the Antrctick, or South-Pole, and can be seen only on the South-side of the Equator; a right Line imagined to be drawn from the one Pole to the other, is called the Axis or Axle-tree of the World.

4. All other Lines drawn through the Centre of the Sphere, and limited on each side of the surface of the Sphere, is a Diameter, but not an Axis, unless the Sphere move round about it.

5. The Poles of the Zodiack are two Points directly opposite to each other, distant from the North and South Pole 23 degr. 31 min. and are Diametrically opposite, on which the Heavens move, from the West into the East.

6. The Equinoctial Points are in the beginning of Aries and Libra, to which Points the Sun cometh the 11 of March, and 13 of September, and makes the Days and Nights of equal Length in all places in the World.

7. The Point of the Summer Solstice, is the beginning of Cancer, which the Sun cometh unto about the 12 of June, and longest day, to the Inhabitants on the North part of the World, and the shortest day to the Inhabitants of the South.

8. And the Point of the Winter Solstice, is the beginning of Capricorn, to which the Sun cometh the 11 of December, and maketh the shortest Days of the Year to the Inhabitants of the North Hemisphere, and the longest to the Inhabitants on the South-side the Equinoctial.

9. The Vertical Point, or Zenith, is the Point directly over-head, and is the Centre or Pole of the Horizon, 90 degr. every way from the Horizon.

10. The Nadir is the opposite Point under our Feet.

Circles of the Sphere.

The Ten Circles are as followeth; The Equinoctial, or likewise called the Equator, which is the chief Circle in the Sphere, dividing the Heavens in the middle between the two Poles; the two Points of Aries and Libra, cut this Circle in opposite Points, and make the Days and Nights of equal length over all the World.

2. The Meridian is a great Circle passing through the Poles of the World, and the Zenith of the Place; the Sun when he comes to this Meridian, it is Noon; the number of Meridians is as many as can be imagined Vertical Points from the West to the East, whereof the Cosmographers have described, 180.

3. The Horizon is distinguished by the names of Rational, or Sensible; the first is a great Circle every where Equidistant from the Zenith, and divides the superior or upper Hemisphere, from the lower, and by chance are distinguished by the names of Right, Oblique, and Parallel-Horizon.

A Right-Horizon have the Inhabitants under the Equator, who have the Horizon passing through the Poles of the World, and cuts the Equator at Right-Angles.

An Oblique-Horizon is such an one as cuts the Equinoctial Oblique, or aslope, or hath any degr. of Latitude from the Equator.

A Parallel-Horizon is one that hath the Poles for the Zenith and Nadir, and the Equinoctial for the Horizon.

The Sensible-Horizon is a Circle that divideth the part of the Heavens, which we see, from the part we see not, called a Finitor.

4. The Zodiack is a great Circle, that divides the Equator into two equal parts; the Points of Intersection are Aries and Libra, the one half declining toward the North, the other to the South 23 degr. 31 min. his ordinary breadth is 12 degrees; but later Writers make it 14 or 16 degrees by reason of the Wandring of Mars and Venus.

In the middle thereof is a Line called the Ecliptick, from which the Latitude of the Planets are numbred both Northward and Southward; the Circumference of this Circle containeth 360 degr. which is divided into 12 equal Parts called Signs, every one representing some living Creature, either in Shape or Property, as you read in the De∣nominations; and also every Sign containeth 30 degr. and every degree containeth 60 min. and every min. 60 seconds, and every second 60 thirds.

The Names and Characters of the 12 Signs.

♈	♉	♊	♋	♌	♍
Aries.	Taurus.	Gemini.	Cancer.	Leo.	Virgo.
♎	♏	♐	♑	♒	♓
Libra.	Scorpio.	Sagitarius.	Capricornus.	Aquarius.	Pisces.

5. The Six uppermost are the Northern, and Six undermost the Southern Signs.

Of the Colures.

6. These are two great Circles, or two Meridians passing through the Poles of the World, crossing one the other at right Angles, and dividing the Equinoctial and the Zodiack into four equal parts, making thereby the four Seasons of the Year.

7. The Solstitial Colure is as before, a great Circle drawn through the Poles of the World, the Poles of the Zodiack, and the Solstitial Points of Cancer and Capricorn, shewing the beginning of Summer and Winter.

8. The Equinoctial Colure, is a Circle passing by the Poles of the World through both the Equinoctial Points of Aries and Libra, shewing the beginning of the Spring and Autumn, when Days and Nights are equal.

9. The T••opick of Cancer is a lesser Circle of the Sphere, equally distant from the Equinoctial to the Northward 23 degr. 31 min. 30 seconds, wherein when the Sun is, he is entring Cancer, and making his greatest Northern Declination.

10. The Tropick of Capricorn is also a lesser Circle, equally distant from the Equi∣noctial Southward 23 deg. 31 min. 30 seconds, to which when the Sun cometh, which is the 10th of December, maketh his greatest Southern Declination.

11. Of the two Pole Circles.

These are two lesser Circles, distant so much from the Poles of the World, as the Tropick of Cancer and Capricornus is from the Equinoctial 23 degr. 30 min. which are the Pole Points of the Zodiack, which moving round the Poles of the World, describe by their motion the said two Circles; that about the North-Pole is the Arctick Circle, and that about the South the Antarctick Circle.

12. The first Six are called great Circles, and the other Four lesser Circles; by the Centre of a Circle is meant a Point or Prick in the middle of a Circle, from whence all Lines drawn to the Circumference are equal, and are known by the names of Radius.

13. That is said to be a great Circle, which hath the same Centre as the Sphere, and Divides it into two equal halfs, called Hemispheres; and that is a lesser Circle, which hath a different Centre from the Centre of the Sphere, and Divides the Sphere into two unequal Portions or Segments.

14. Of other Circles imagined but not described in a material Sphere or Globe.

Such are the Azimuths, Almicanters, Parallels of Latitude and Declination.

Azimuth or Vertical Circles pass through the Zenith, and Intersect the Horizon with right Angles; wherein the distance of the Sun or Stars from any part of the Meri∣dian are accounted, which are called Azimuth, and the East and West is called the Prime Vertical Azimuth.

15. The Sun or any Star having Elevation or Depression above or below the Horizon, are then properly said to have Azimuths; but if they be in the Horizon, either rising or setting, the Arch of the Horizon between the Centre of the Sun or Star, and the true Points of East and West, is called Amplitude.

16. Circles of Altitude called Almicanters, are Circles Parallel to the Horizon, and Intersect the Vertical Circles with right Angles, which are greatest in the Horizon, and meet together in the zenith of the place, in which Circles the Altitude of the Sun, Moon, or Stars above the Horizon are accounted, which is the Arch of an Azimuth, contained betwixt the Almicanters, which passeth through the Centre of the Sun, Moon, or Stars, and the Horizon.

17. Parallels of Declinations are lesser Circles, all Parallel to the Equinoctial, and may be imagined to pass through every degree and part of the Meridian, and are de¦scribed upon the Poles of the World; in like manner, the Declination of the Sun or-Star is measured by the Arch of the Meridian between the Sun and Star, and the Equi∣noctial.

18. Parallels of Latitude in the Heavens, are lesser Circles described upon the Poles of the zodiack or Ecliptick, and serve to define the Latitude of a Star, which is the Arch of a Circle contained betwixt the Centre of any Star or Planet, and the Ecliptick Line, making right Angles therewith and counted toward the North or South Poles of the Ecliptick, the Sun never passeth from under the Ecliptick-Line, is said there∣fore to have no Latitude.

19. Longitude of the Sun or Stars is measured by the Arch of the Ecliptick, com∣prehended between the Point of Aries, and a supposed great Circle passing from the Poles of the Ecliptick and the Sun or Stars Centre, and accounted according to the order and succession of the Signs.

20. Longitude on the Earth, is an Arch of the Equinoctial contained between any assigned Meridian where it begins, and the Meridian of any other place, but accounted Eastward from the first place, as the Right-Ascention; but in my Tables it is counted East and West from the Meridian of the Lands-end terminating at 180 degrees.

21. Right-Ascention is an Arch of the Equinoctial accounted from the beginning of Aries, which cometh to the Meridian with the Sun, Moon, or Stars, or any portion of the Ecliptick; and by it there are Tables made for the Sun, Moon, and Stars to know the time of their coming to the Meridian, as by the help of the hour of the Star, the true time of the Night.

22. Oblique Ascention, is an Arch of the Equinoctial between the beginning of Aries and that part of the Equinoctial, that riseth with the Centre of the Sun or Star, and any portion of the Ecliptick in any Oblique-Sphere.

23. Ascentional-difference is the Arch of Difference between the Right-Ascention, and the Oblique-Ascention, and thereby is measured the time of the Sun or Stars before, and after Six.

24. Elevation of the Pole is the Height thereof above the Horizon, which is equal to the distance between the zenith, and the Equinoctial, whose Complement is equal to the distance of the zenith from the North or South Pole, or the Elevation of the Equator above the Horizon; these Circles I have inserted, to the end they may be perfectly known; for without them, the Reader cannot well understand the following Problems of the Sphere that are depending thereon.