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.

Observe these Rules for North Latitude.

ADmit we were in a Ship at Sea the fifth of May, Anno 1694. and by Observation I find the upper side of the Sun to be distant from the Zenith 37 deg. 36 min. the Sun being upon the Meridian, I require the Latitude the Ship is in.

	deg.	min.
The Sun's Distance from the Zenith	37	36 his upper Edge.
The Sun's Semidiameter, add	00	16
The Center of the Sun from the Zenith	37	52
North Declination	19	02
The Latitude required, the Ship is in	56	54

Suppose a Ship at Sea the 29th of July, Anno 1682. and I find the Complement of the Sun's Meridian Altitude by observation to be 32 deg. 54 min. The Latitude of that Place the Ship is in, is required.

	deg.	min.
The Complement of the Altitude is	32	54
The Sun's Semidiameter add to it	00	16
The Distance of the Sun's Center from Zenith	33	10
North Declination, add	16	07
The Latitude the Ship is in	49	17

Suppose a Ship were at Sea the 13th of Sept. 1683. and I find the Complement of the Sun's Meridian Altitude, or Distance from the Zenith, 45 deg. 42 min. I demand what Latitude the Ship is in.

	deg.	min.
The Complement of the Altitude is	45	42
The Sun's Semidiameter add to it	00	16
The Distance of the Center of the Sun	45	58
The Declination South, substract	00	07
The Latitude the Ship is in	45	51

Admit a Ship were at Sea the fourth of December, Anno 1690. and the Comple∣ment of the Sun's Meridian Altitude that day were 49 deg. The Latitude the Ship is in, is required.

	deg.	min.
The Complement of the Meridian Altitude	49	07
The Sun's Semidiameter—Add	00	16
The Center of the Sun distant from the Zenith	49	23
The Sun's Declination South, substract	23	30
The Latitude the Ship is in North	25	53

Suppose I were in a Ship at Sea the 23d of May, Anno 1695. and I am also in Longitude to the East of the Meridian of London 135 deg. and I find the Comple∣ment of the Meridian Altitude by Observation to be 13 deg. 12 min. The Latitude is required.

	deg.	min.
Declination in the Meridian of London	22	17
The Proportional Minutes, substract	00	03
The Sun's Declination in the Meridian given	22	14
The Complement of the Sun's Altitude	13	12
The Sun's Semidiameter, added	00	16
The True Zenith Distance of the Sun	13	28
The True Latitude the Ship is in North	08	46

That is, by reason the Sun is to the Northward of my Zenith, and the Declination more than the true Distance from the Zenith or Complement of the Meridian Altitude; therefore substract 13 deg. 28 min. from 22 deg. 20 min. and the Remainder is the true Latitude 8 deg. 52 min. North.

EXAMPLE.

Let the Complement of the Sun's Altitude be ZS, the Altitude 76 deg. 32 min. in the North BS, the Declination North ES 22 deg. 14 min. if you add the Altitude SB 76 deg. 32 min. to the Declination SE 22 deg. 14 min. the Sum is BE 98 deg. 46 min. the Distance of the Aequinoctial from the Horizon in the North BZ 90 deg. being substracted from it, remaineth for ZE, the Distance of the Aequinoctial from the Zenith towards the South, 8 deg. 46 min. just BP the Latitude of the Place, and Altitude of the Pole above the Horizon.

	d.	m.
BS	76	32
SE	22	14
BE	98	46
	90	00
B	08	46

[illustration] geometrical diagram

Let the Complement of the Sun's Altitude be ZS 13 deg. 28 min. the North Decli∣nation ES 22 deg. 14 min. being more than the Distance of the Sun from the Zenith, substract ZS 13 deg. 28 min. the Complement of the Altitude from SE the Declinati∣on, there remaineth 8 deg. 46 min. the Distance of the Aequinoctial from the Zenith ZE or Latitude of the Place BP, as before. I have been the more large on this, by reason I would have Learners perfect in it, it being most useful Questions.

When that you Sail far Northward or Southward, that the Sun goeth not down, as they find that Sail about the North Cape, and to Spitsberghen, or Greenland; and that you would observe the Altitude by the Sun, also when he is in the North at the lowest,

First, There must be added to the Altitude of the Sun taken above the Horizon, the Complement of the Sun's Declination; that is, the Distance betwixt the Sun and the Pole, that Number sheweth the Altitude of the Pole.

Secondly, Or else the observed Altitude must be substracted from the Declination, that which remaineth is the depression or depth of the Aequinoctial under the Hori∣zon in the North, just to the Altitude of the same in the South, the Complement thereof is the Altitude or Height of the Pole.

Thirdly, If you take the Complement of the Sun's Altitude, and substract from it the Complement of the S••n's Declination, there remaineth the Distance of the Pole from the Zenith, or the Altitude of the Aequinoctial in the South; the Complement thereof is the Altitude or Height of the Pole.

Fourthly, Or else if you add the Declination to the Complement of the Altitude, and you substract 90 Degrees out of that Number, there remaineth the Depth of the Aequinoctial in the North under the Horizon; that being substracted out of 90, there remaineth the Altitude of the Pole.