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. XIII. How to use the Cross-Staff.

SEt the end of the Cross-Staff to the outside of the Eye, so that the end of the Staff come to stand right with the Center of the Motion of the Sights. Then move the Cross so long off from you or towards you, holding it right up and down, and winking with your other Eye, till that the upper end come upon the middle or Center of the Sun or Star, and the lower end right with the Horizon, the Cross then shall shew upon the side of the Staff belonging thereunto, the Degrees of the Altitude of the Sun or Star. Note, The Staff is marked with two Lines of Numbers, with 90 Degrees next the Eye, and diminishing from 90 to 80 and 70, 60 towards the outmost end: The Complement-Sine beginneth towards the Eye-end, and encreaseth contrarywise towards the outmost end, as from 10, to 20, 30. The first Number sheweth you the Altitude, the second Number is the Sun's distance from the Zenith.

The Sun or Stars being high elevated from the Horizon, the Cross cometh nearer the Eye than when they are but a little elevated, and do stand neer the Horizon; thereby the eye mak••th (seeing now to the lower, and then again to the upper end of the Cross) greater

motion in looking up and down, than when the Sun or Star doth stand low. And inso∣much the Center of the Sight, by such looking up and down together with the end of the Staff, a Man seeth then smaller Angles then if it did remain stedfast, in regard where∣of the Cross cometh nearer to the Eye than it should, and there is found too much Altitude. This being found by many, besides my self, by experience, they were there∣fore wont to cut off a piece of the end of their Staff, or set the Crosses a Degree and ½ or two Degrees nearer the Eye; but it is not the right means for to amend the afore∣said Errors. The best means of all in my opinion is this; That upon each several Height which men will observe, they do try with two Crosses set upon the like De∣grees, how the Staff must be set, that they may see the end of the same two Crosses right one with the other.

[illustration] geometrical diagram

Having found that, and then taking off one of the Crosses, and setting the Staff again, in the same manner as before, all Errours will be so prevented, which by the lifting up or casting down of the Eye, might any manner of way happen.

EXAMPLE.

I desire to observe the Sun or any Star in the South: I make my Estimation, as neer as I can, how high that shall stand, or take the Height of them a little before they shall come to the South, which I take to be 50 Degrees. I set therefore the two

Crosses each upon their 50 Degrees, and the end of the Staff in the hollow of the Eye-bone, on the outside of the Eye, and bow the Head forward or backward, or over the one side or the other, till I see the utmost end of both the Crosses right one with the other, according as is shewn by these Lines AB and CD, as is apparent enough by the foregoing Figure; That the Sight-beams over the ends of the Crosses shall then agree with the Lines which might be drawn over the end of the Crosses, to the Point or Center at the end of the Staff, which doth agree with the Center of the Quadrant, or the beginning of the Equal Points upon which the Staff is marked. Keeping in memory such standing of the Staff, I take off the one Cross, and set the Staff again in the aforesaid manner to the Eye, and observe without any errour of the Eye.

In taking the Height of the Sun with the Cross-Staff, Men do use red or blew Glasses, for the saving and preserving the Eyes; yet it is notwithstanding a great let, and very troublesom for the Sight, especially if it be high: therefore the Quadrant and Back-Staff is much better, as will be shewed in the next Chapter.

Thus I have shewed you how to take an Observation by the Fore-Staff. The next thing that followeth in course will be to shew you how to work your Observation; which to do, take notice of these following Rules.

To Work your Observation.

IF the Sun hath North Declination, and be on the Meridian to the Southwards of you, then you must substract the Sun's Declination from your Meridian Altitude, and that Remainder is the Height of the Aequinoctial, or the Complement of the La∣titude North. But if the Sun hath South Declination, you must add the Sun's De∣clination to your Meridian Altitude, and the Sum is the Height of the Aequator, or the Complement of the Latitude North. If the Sun hath North Declination, and be on the Meridian to the Northwards, then add the Sun's Declination to his Meridian Al∣titude, and the Sum is the Height of the Aequator, or the Complement of the Latitude South, if the said Sum doth not exceed 90 deg. but if it doth exceed 90 deg. you must substract 90 deg. from the said Sum, and the Remainder is your Latitude North.

If the Sun hath South Declination, and be to the Northwards at Noon, you must then substract the Sun's Declination from his Meridian Altitude, and the Remainder is the Complement of your Latitude South. When the Sun hath no Declination, then the Meridian-Altitude is the Complement of the Latitude. If the Sun be in the Ze∣nith, and if at the same time the Sun hath no Declination, then you are under the Aequinoctial.

But if the Sun hath North Declination, and in the Zenith, then look how many Degrees and Minutes the Declination is, and that is the Latitude you be in North.

But if your Declination be South, then you are in South Latitude. If you observe the Sun or Star upon the Meridian beneath the Pole, then add your Meridian Alti∣tude to the Complement of the Sun or Stars Declination, and the Sum is the Height of the Pole.

Rules for Observation in North Latitude.

SUppose I am at Sea, and I observe the Sun's Meridian Altitude to be 39 deg. 32 min. and the same time the Sun's Declination is 15 deg. 20 min. North; I de∣mand the Latitude I am in.

	deg.	min.
The Meridian Altitude	39	32
The Declination North, subst.	15	20
The Complement of the Lat.	24	12
	90	00
The Latitude I am in	65	48 North.

Suppose I were in a Ship at Sea the 18th of April, Anno 1667. and by Observati∣on I find the Sun's Meridian Altitude to be 62 deg. 15 min. The Latitude is required.

	deg.	min.
The Meridian Altitude	62	15
The Declination North, subst.	14	18
The Complement of the Latitude	47	57
	90	00
The Latitude I am in, required	42	03

Admit you were in a Ship at Sea the 5th of November, Anno 1679. and I find the Sun's Meridian Altitude to be 24 deg. 56 min. The Latitude is required I am in.

	deg.	min.
The Meridian Altitude	24	56
The Declination South, add	18	37
The Complement of the Latitude	43	33
	90	00
The Latitude I am in	46	27

Suppose a Ship at Sea the 28th of May, Anno 1666. and I find the Sun's Me∣ridian Altitude by Observation 56 deg. 45 min. The Latitude is required I am in.

	deg.	min.
The Meridian Altitude	56	45
The Declination North, Subst.	22	46
The Complement of the Latitude	33	59
	90	00
The Latitude required I am in	56	01

Admit a Ship at Sea the 11th of June 1668. and find the Sun's Meridian Al∣titude by Observation 79 deg. 30 min. North, It is required the Latitude I am in.

	deg.	min.
The Meridian Altitude	79	30
The Declination North	23	31 add.
	103	01
	90	00
The Latitude I am in	13	01 required.

Suppose I were at Sea the 14th of May 1693. and the Meridian Altitude of the Sun was 69 deg. 07 min. North, I demand the Latitude the Ship is in at that time.

	deg.	min.
The Meridian Altitude	69	07
The Declination North	20	53 add.
	90	00
	90	00
The Ship is under	00	00 the Aequinoctial.

Rules for Observation in South Latitude.

SUppose I at Sea in a Ship the second of June, Anno 1666. and I find the Sun's Meridian Altitude by Observation to be 64 deg. 45 min. The Latitude the Ship is in, is required.

	deg.	min.
The Meridian Altitude North	64	45
The Declination North, add	23	15
The Complement of the Latitude	88	00
	90	00
The Latitude the Ship is in-	02	00 South.

Suppose a Ship at Sea the 28th of December, Anno 1695. and in Longitude 169 deg. East, and I find the Meridian Altitude by Observation to be 59 deg. 52 min. The Latitude the Ship is in, is required. The Declination in the Meridian of Bristol for the 28th of December, is 22 deg. 25 min. and the daily difference of Declination is at this time 8 min. Therefore if you look in the Table of Proportion following, you will find the Proportional Minutes to be about 4, which you must add to the Declination of the Meridian of Bristol, and the Sum will be the true Declination for the Longitude 169 deg. East, which is 22 deg. 29 min.

	deg.	min.
The Meridian Altitude North	59	52
The Declination South, substr.	22	29
The Complement of the Latitude	37	23
	90	00
The Latitude the Ship is in, which was	52	37 required.

Suppose I were at Sea in a Ship the 29th of June, 1679. and I find the Sun's Me∣ridian Altitude to be 62 deg. 30 min. North, The Latitude is required.

	deg.	min.
The Meridian Altitude North	62	23
The Declination North, add	22	26
The Complement of the Latitude	84	49
	90	00
The Latitude the Ship is in	05	11 South.

Admit I am in a Ship at Sea the 20th of January 1667. the Sun's Declination 20 deg. 4 min. and the Sun's Meridian-Altitude 79 deg. 36 min. South, I require the Latitude the Ship is in.

Answer, 9 deg. 30 min. South.

Admit a Ship were at Sea, the Sun's Declination 13 deg. 53 min. South, and the Sun's Meridian Altitude 80 deg. 43 min. South, The Latitude is required.

	deg.	min.
The Declination South	13	53
The Meridian Altitude	80	43 add.
	94	36 the Sum.
Substr.	90	00
The Latitude the Ship is in	04	36 South.

If you observe the upper part of the Sun, you must substract 16 min. But to the contrary, if you observe the lower part of the Sun, you must add 16 min. for the Sun's Diameter, and the Sum will be the true Altitude of the Sun's Center.

Rules for Observing the Stars.

SUppose I am at Sea, and observe the Brightest of the 7 Stars upon the Meridi∣an, and find his Meridian Altitude to be 47 deg. 20 min. and the Latitude were required.

	deg.	min.
The Declination of this Star is	23	03 North.
The Meridian Altitude	47	20
Substract the North Declination	23	03
The Complement of the Latitude	24	17
	90	00
The Latitude I am in	65	43

Admit I were at Sea, and observe Hydra's Heart on the Meridian, his Altitude is 36 deg. 15 min. and his Declination is 7 deg. 15 min. South, The Latitude of the Place is demanded.

	deg.	min.
The Meridian Altitude is	36	15
The Declination is South	07	15 add.
The Height of the Aequinoctial above	43	30 the Horizon.
	90	00
The Latitude the Ship is in	46	30 required.

This you see is plain, and needs no further Precept but what is already said.