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.

V. To find the Day and Hour of the Change or New Moon, and thereby the Full and Quarters.

FIrst you must find the Moon's Epact for the present Year you are in: This Num∣ber is found out in the First Book, Page 12. and also in the Table before at the beginning of the Kalendar. The Change also may be found out by the Golden Num∣ber; yet that would stand so scattering and without form, that it is much hand∣somer and readier to find out by this Epact, which runs for the most part in a Constant Order, only here and there skipping a Day or a Number, which is marked with this ✶.

Having found out the Epact for this present Year, turn to the Month you desire, and there find out the said Number of the Epact in the third Column of the Months, and mark what Day of the Month it stands against; for that is the Day of the Change or New Moon. Likewise if you have respect unto the Dominical Letter, which is by it, you shall see what Day of the Week it is.

Now here in this Column there are two Rows of Figures; The first shews the Epact-Number, and the next the Time of the Day reckoned by the Hours from Noon, which are plain to understand till you come to 12 Hours after Noon, which is Midnight; but then the Numbers above 12, you must reckon to the Morning of the next Day.

So that these Hours after Noon,
13,	14,	15,	16,	17,	18,	19,	20,	21,	22,	23,	24,
are all one with these,
1,	2,	3,	4,	5,	6,	7,	8,	9,	10,	11,	12,
the next Day in the Morning.

Thus in the Year 1666. the Epact being 4, and the Dominical Letter G, you shall find this Epact-Number 4 against the 21 of July being Saturday; and the Figure o standing by it, shews that the New Moon is just at Noon.

Again, You shall find the Epact-Number against the 16th of November, being Friday; and the Figure of 2 standing by it, shews that it is about 2 Hours after Noon the Moon changeth. Now this is the true time of the New Moon, according to the Moon's mean Motion; which though it may differ half a day from the true Change, yet it seldom differs so much, and is better for the following Conclusion than the true time.

Having first found out the time of the New Moon, you may from thence reckon the Age of the Moon, and find the Quarters and Full Moon.

Thus the Moon's Age is	Days	Hours	Min.
At the First Quarter	7	09	11
At the Full Moon	14	18	22
At the Last Quarter	22	03	33
An Whole Moon	29	12	44

Or else observe the Dominical Letter that is against ••••e Epact, or Day of the New Moon; and where you find that Letter again, that is the First Quarter; for the Full Moon take two Weeks and one Day, which will fall upon the Letter next to it; for the Last Quarter take one Week more, which will fall upon the Letter of the Full Moon.

Thus if the New Moon fall upon A, the First Quarter falls upon the next A, and the Full Moon on the next B a week after, and the Last Quarter on the next B. And thus you have this brief Kalendar or Constant Almanack for many Years; only for the more exactness in the Hour of the Moon's Change and Age, it is restrained to 19 Years: For though the Change of the Moon (for the most part) hapneth again upon the same Days, for several Revolutions of the Prime or Golden Number XIX; yet not upon the same Hour of the Day, but alters every Revolution 7 Hours, 27 Minutes, 30 Seconds, proceeding forward for the most part; but the Leap-years coming in with a Day more than ordinary, keeps this Motion so much backward, that in 300 Years it neither gains nor loseth a Day, only differeth in the Hour of the Day; yet for the more exactness, it will be better to renew this every 19 Years. All these things this brief Kalendar shews plainly, with little or no trouble more than in an yearly Almanack. I shall now proceed to some other Conclusions. I have been very large already, in the First Book, of Things concerning the Use of the Moon in other Conclusions; to which I refer you for any thing of the Tides, or the Southing of the Moon, or the Rising or Setting of the Moon, or what else is necessary in Navigation.

I thought to have entred my Figure of the Sea-Compass, for the Surveying of Land, which was promised in the Argument; As likewise the Gunner's Scale and Gauging Rod: But I refer you to the several Books in the following Treatise, where the Figure and the Use of it, is together for your satisfaction.