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. XVI. The Description and Ʋse of the most Ʋseful Quadrant for the taking Alti∣tudes on Land or Sea, of the Sun or Stars, backwards or forwards, or any other Altitude of Hills, Trees, Steeples, or Castles, or any thing what∣ever.

THis Quadrant is made of well-seasoned and smooth dry Box Wood or Pear-tree. The Sides or Semidiameter of the Circle is about 19 or 20 Inches. C V and CH the Arch of the Quadrant is divided into 90 Degrees first, and each Degree into 6 Equal Parts, each Part being 10 Minutes, which is near enough for Sea or Land Observations, and numbred as you see from 10 to 90 deg. The two Sides next the Center, EF and GF, are divided each of them into 100 Equal Parts:

[illustration] geometrical diagram

That which is next the Horizon GFH, are called the Parts of Right Shadow: the other Side EFV, is the Parts of contrary Shadow. In the Center at C there is a Brass-Pin, and on it hang the Thred and Plummet; and on the Side there is a Sight made of Brass at E. There is also an Horizon-Vane, let in upon the Center C, with two Laggs that the Brass-Pin comes upon in the middle of the Slit; and a Shade-Vane and Sight-Vane, for Back-Observation. The Use of the Quadrant is,

EXAMPLE.

Admit I am ashore upon any Land or Island, and would know the Sun's Me∣ridian Altitude, and true Latitude of the Place. Take the Altitude thus; The String and Plummet being hanged on the Center C, turn the Brass-Pin to the Sun, and hold up the Center until the Shade of the Brass-Pin strikes on the Sight and Line of E, the Thred and Plummet playing easily by the Side: mark where it cuts the Arch of the Quadrant, as at F, that is the Sun's Altitude, and reckoned from H; and the Latitude is found by the same Rules as you have been given in the Use of the Fore-Staff. The best way to hold the Quadrant steady, is to skrew it with a Brass-Pin through at K, to a Staff set perpendicular, and then you may raise it by degrees, as the Sun rises.

PROPOSITION I. For Back-Observation at Sea.

Take the Handle of the Quadrant at H in your Hand, after the Vanes are set on, and fix the Shade-Vane; then hold your Quadrant as upright as you can; then bring your Sight-Vane to your Eye, and look through your Sight upon the Horizon-Vane. You must be sure to hold your Quadrant, so that the upper part of your Shad•• Vane, may be upon the upper part of the Slit on your Horizon-Vane, and look through the Slit for the Horizon: But if you cannot see the Horizon, but all Skie and no Water, you must draw your Sight-Vane a little lower down towards H; but if, on the contrary, you do see all Water and no Skie, then slide your Sight-Vane a little higher towards V, and then make Observation again; and then if the upper part of the Shade do lie upon the upper part of the Slit, and you see the Horizon at the same time, then it is well, and you must wait a little longer as your Judgment thinks fit, till the Sun is upon the Meridian, and so do as you did before; and if the Sun be to the Westward of the Meridian, and falling, you will see all Water and no Skie, the Work is done for that time and day. Then look what Degrees the Shade-Vane is put at, which in the Figure is at 70 deg. which note. Look also what Degrees and Minutes do stand against your Sight, which substract from the former Degrees by the Shade-Vane, and the Remainder is the Sun's Meridian Altitude. As in the Figure, The Sight-Vane is at 25 deg. 30 min. which taken out of 70 deg. the Remainder is 44 deg. 30 min. the Sun's Altitude, or the distance of the upper part of the Sun from the Horizon; from which if you substract 16 min. which is the Sun's Semidi∣ameter, the Remainder will be the Distance of the Sun's Center from the Horizon, or the true Meridian Altitude. And the way of working your Observation, is the very same as you have been given in the Use of the Fore-Staff.

PROP. II. Any Point being given, To find whether it be level with the Eye, or not.

Take the Quadrant and look through the Sight at E and Center-pin C, unto the Point given, or the Place you would know whether it be level, or not. If the Thred fall on CH the Horizontal Line, then is the Place level with the Eye: But if it should fall within, upon any of the Divisions, then it is higher; if without the Quadrant, then it is lower than the level of the Eye.

PROP. III. To find the Height of an House, Steeple, Tower, or Tree, from the Ground, at one Observation; and the length of the Ladder which will Scale it.

If you can approach the bottom or foot of the Thing whose Height you desire, the thing is easily performed by this Quadrant or Cross-Staff, holding up your Qua∣drant to the Place whose Height you would know, and looking through the Sight on the Side EC, going nearer or further from it, till the Thred cut 45 deg. or fall upon 100 Parts in the Quadrat: So shall the Height of the Thing above the level of your Eye, be equal to the Distance between the Place and your Eye.

If the Thred fall on 50 parts of a right Shadow, or 26 deg. ½ or Vanes on the Cross-Staff, set to the Number of Deg. the Height is but half the Distance.

If the Thred cut 25 Parts in the Quadrat, or 13 deg. 55 min. in the Arch of the Quadrant, it is but a quarter of the Distance: But if it fall on 75 Parts, or 36 deg. 53, it is three quarters of the Distance. The Rule is,

As 100, to the Parts on which the Thred falleth:

So is the Distance, to the Height required.

And on the contrary,

As the Parts cut by the Thred, are to 100:

So is the Height, to the Distance.

[illustration] geometrical diagram

But when the Thred shall fall on the parts of the contrary Shadow, if it fall on 50 Parts, or 63 deg. 30 min. as it doth at C, the Height is double unto the Distance CD. If on 25, it is four times the Distance. If the Thred fall upon the contrary Shadow, this is the Rule,

As the Parts cut by the Thred, are unto 100:

So is the Distance, unto the Height.

On the contrary,

As 100, are unto the Parts cut by the Thred:

So is the Height, unto the Distance.

These are the Rules Mr. Gunter shews by the Quadrat, And what hath been said

of Height and Distance, the same may be understood of Height and Shadow; but here follows more useful Rules than these before-going.

PROP. IV. The Distance being given, To find the Altitude.

Suppose EFGD were a Tower, or Steeple, or Tree, or House, whose Altitude you would know, and you cannot come so neer as to measure between your Station of 45 deg. and the Base of the Thing, by reason of some Wall or Moat; yet by the Pro∣portion of the Line of Quadrature, you may help your self by going backwards.

Thus if you could not measure the Distance from B to D, then go backward from B to A, until the Thred cut the 26 deg. 30 min. of your Quadrant; and measure the Distance between B and A, as suppose it to be 32 Foot or Yards, equal to the Height DE 32; The whole Line DA being 64 Feet or Yards, which is double to the Height. By the Tables,

Suppose then the Angle made by the Thred on the Quadrant ADB, be equal to the Angle EAD 26: 30 min. and the Distance AD be 64 Yards, or 192 Foot, to find the Height DE, I say,

As the Radius 90 Degrees	100000
To the Tangent of the Angle EAD 26 deg. 30 min.	969773
So is AD 64 Yards	180618
To the Height required, DE 32 Yards	X, 50391

PROP. V. The Distance being given, To find the Distance from the Eye to the top of the Tower.

Let the Distance AD be 192 Feet, the Angle at the Eye A 26 deg. 30 min. and the Distance from the Eye or Hypotenusa AE is required.

As the Sine of the Angle AED 63 deg. 30 min.	995179
Is to the Radius 90 deg.	10
So is AD 192 Feet	1228330
To AE 214 5/10 Feet	233151

PROP. VI. Some part of the Distance being given, To find the Distance from the Eye or Hypotenuse.

Let the Part of the Distance given be AB 96 Feet, and it is required to find the Distance from the Eye or Hypothenuse EB, which is the Length or Hypothenuse to the Triangle DBE. First find the other Angles thus:

AE is 214 5/10 Feet	The Sum is 310 5/10	349206
AB is 96 5/10 Feet	The Difference 118 5/10	307371

The Angle at B is 153 deg. 30.	To Tang. ½ Sum of opposite Angle 76 deg. 45.	1062806
The Half-Tangent is 76 deg. 45.	1370177
1020971

	deg.	min.
The Half-Tang. difference is	58	20.
The Half-Tangent Sum	76	45
Sum	135	05
Taken out of	180	00
Whose Complement remains	44	55 Angle EBD.

Then to find the Length of BE,

As the Sine of the Angle ABE 135 deg. 5 min. or 44 deg. 55 min.	984885
To AE 214 5/10 Feet	333142
So is the Sine of the Angle EAB 26 deg. 30 min.	964952
To the Distance from the Eye BE 135 5/10 Feet or Hypotenuse	1298094
	313209

PROP. VII. Some part of the Distance being given, To find the Altitude.

Keep the Angle and Distance from the Eye found by the former Proposition.

As the Radius 90 deg.	10
Is to the Sine of the Angle EBD 44 deg. 55 min.	984885
So is EB 135 6/10	313225
To ED the Height required, 95 8/10 Feet	1298100

which is the same as before found, without sensible difference. By the same Rule you may find the nearest Observation in the Figure to the Tower.

PROP. VIII. To do the same thing by the Quadrant, and Scale of Equal Parts, another way.

Without Calculation, by your Quadrant or Scale of Equal Parts, you may be re∣solved of all the foresaid Propositions, by the help of a Line of Chords; you may lay it down and demonstrate it, as you see the Figure, by the same Scale of Equal Parts as you measured, the first Distance, will answer all the rest. This is so plain, it needs no other Precept.

Here is another way to find the Length of the Scaling-Ladder without Calculation, which in many Cases is the chief thing looked after; which cannot be so well done by the Quadrat, as by observing the Angles of the Quadrant; and this is the best way I know.

Let your Station be any where at random, or as neer as you can come to the Foot of the Tower or Wall, for the Ditch, or Moat, or Cannon shot: As suppose at B, and observe there the Angle of the Height of the Thing, which let be any Degrees what∣soever, as here is 45 deg. I say, If you go so far backwards from this Station of B, toward H, till you make the thing appear just at half the aforesaid Angle, which is here 22 deg. 30 min. the half of 45 deg. That then this Distance from B to H is the true Length of the Sloap-side BE, without farther trouble; and a Ladder of that Length will Scale the said Moat or Wall, allowing only the Height of your Eye from the Ground.

PROP. IX. Part of the Distance being given, To find the Remainder of the Distance.

Let part of the Distance given be AB 96 Feet, and the Remainder of the Distance cannot be measured, by reason of danger of Shot, or Moat of Water, or some other Impediments; Therefore by the 7 Rule I found the Angle at B to be 44 deg. 55 min. So that the Angle BED 45 deg. 05 min. is the Complement thereof: Which known, I say,

As the Radius	10
To the Sine of the Angle BED 45 deg. 5 min.	985011
So is the Distance from the Eye BE 135 6/10 Feet	313225
To the Remainder of the Distance BD 96 Foot	298236

PROP. X. By the Height of the Sun, and the Length of the Shadow, To find the Height of any Tree, Tower, or Steeple.

This Conclusion may be tried by a little Quadrant or Pocket-Instrument, by which you may take the Sun's Altitude to a Degree, ½ or ¼, which is near enough for these Conclusions.

[illustration] geometrical diagram

Suppose DE to be a Turret, Tree, or Steeple, whose Height is required to be found by the Shadow it makes on Level Ground, the Rule is thus, viz. Let the Height of the Sun be 37 deg. 00 min. and the Length of the Shadow 40 Foot, the Rule is,

As the Radius 90 deg.	10
To the Length of the Shadow 40 Foot	160206
So is the Tangent of the Sun's Height 37 deg.	987711
To the Height of the Thing desired	147917

which is found to be 30-14 Parts, which shews the Height to be a little above 30 Foot.

Here is another way to do the same without the help of a Quadrant and Sun's Altitude, viz. Set up a Staff of any Length, suppose 3 Feet in Length, as CB, and

the Shadow which it makes from B to A is 4 Feet; Because the Shadow of the Tower from the Base thereof to B is 40 Feet, I say,

As the Shadow of the Staff, is to the Height of the Staff:

So is the Shadow of the Steeple, to the Height of the Steeple.

The Operation may be performed by Natural Numbers, or by Logarithms, thus, viz.

As 4 Feet, to 3 Feet: So 40 Feet, to 30 Feet.

〈 math 〉〈 math 〉

As the Shadow of the Staff 4 Feet AB, Log.	4.0,60206
To the Length of the Staff 3 Feet BC	3.0, 47712
So is the Shadow of the Steeple 40 Feet DB	40, 1, 60206
	2, 47918
To the Height of the Tower 30 Feet DE	1, 47712

A Constant Kalendar; OR AN ALMANACK For Three Hundred Years. But more exactly serving for Nineteen Years, BEING THE CIRCLE of the MOON, OR THE GOLDEN NUMBER. With New Exact TABLES OF THE Suns Declination, Rectified by the best Hypothesis, until the LEAP-YEARS 1695. BY Capt. SAMUEL STURMY.

London, Printed Anno Domini 1668.

AN ALMANACK For XXXII. Years. According to the English and Foreign Accounts.

Anno Dom.	Prime.	••pact	Sund. Letter	Shrove Sunday.	Easter Sunday.	White Sunday.	Diff.
1664	12	12	CB	Feb. 21	10	May 29	1
1665	13	23	A	5	March 26	14	0
1666	14	04	G	25	April 15	June 03	0
1667	15	15	F	17	7	May 26	1
1668	16	26	ED	2	March 22	10	0
1669	17	7	C	21	April 11	30	0
1670	18	18	B	13	3	22	1
1671	19	29	A	March 05	23	June 11	5
1672	01	11	GF	Feb. 18	7	May 26	0
1673	2	22	E	9	March 30	18	1
1674	3	3	D	March 1	April 19	June 07	5
1675	4	14	C	Feb. 14	4	May 23	0
1676	5	25	BA	6	March 26	14	0
1677	6	6	G	25	April 15	June 03	1
1678	7	17	F	10	March 31	May 19	0
1679	8	28	E	March 2	April 20	June 08	5
1680	9	9	DC	Feb. 22	11	May 30	0
1681	10	20	B	13	3	22
1682	11	1	A	26	16	June 04
1683	12	12	G	18	8	May 27
1684	13	23	FE	10	March 30	18
1685	14	04	D	March 1	April 19	June 07
1686	15	15	C	Feb. 14	4	May 23
1687	16	26	B	6	March 27	15
1688	17	7	AG	26	April 15	June 03
1689	18	18	F	10	March 31	May 15
1690	19	20	E	March 2	April 20	June 08
1691	1	11	D	Feb. 22	April 12	May 31
1692	2	22	CB	7	March 27	May 15
1693	3	3	A	Feb. 26	April 16	June 4
1694	4	14	G	18	8	May 27
1695	5	25	F	Feb. 3	March 24	12

The Ʋse of the Alma∣nack for 32 Years.

THis Table shew∣eth first the Date of the Years; secondly, the Prime, or Golden Num∣ber; thirdly, the Epact; fourthly, the Dominical Letter for these Years; and then in their Or∣der the Chief Movable Feasts (viz.) Shrove-Sunday, Easter-day, and Whitsunday, upon which all the rest depend. The Foreign Account is com∣monly ten days before us; but their Mova∣ble Feasts fall sometimes at the same time with ours, sometimes 1, 2, 3, 4, or 5 Weeks before ours, as you see in the last Column of the Ta∣ble.

Of the Terms.

THere are four times of the Year ap∣pointed for the Deter∣mining of Causes; these are called Terms. Two of these Terms (viz.) Hillary Term, and Michaelmas Term, are at a constant time of the Year: but Easter Term and Trinity Term are sooner or later, as those Feasts happen. Each of these Terms hath several Returns, and each Return hath four Days belonging to it. The first is the Day of Return or Essoin, for the Defendant in a Personal Action, or the Tenant in a Real Action. The second is the Day of Exception, for the Plaintiff or Defendant to lay an Exception. The third is the Day whereon the Sheriff must re∣turn the Writ. The fourth is the Day of Appearance in the Court. These four Days follow each other in order, except a Sunday or Holyday take up any of them, and then the Day following serves for both Occasions.

The Beginning and End of Hillary Term and Michaelmas Term, with all their Returns, you shall find in this following Kalendar, which are constant if no Sunday hinder them.

Easter Term begins Wednesday Fortnight or 17 Days after Easter, and ends the Munday after Holy-Thursday, or the Munday before VVhitsunday: It hath these five Returns.

• Quind. Pasc. A Fornight after Easter.
• Tres. Pasc. Three Weeks after Easter.
• Mens. Pasc. A Month after Easter.
• Quinq. Pasc. Five Weeks after Easter.
• Crast. Ascen. The Day after Holy-Thursday.

Trinity Term begins the Friday after Trinity-Sunday, which is next Sunday to Whit-sunday, and hath these four Returns.

• Crast. Trin. The Munday after Trinity-Sunday.
• Oct. Trin. A Week after Trinity-Sunday.
• Quind. Trin. A Fortnight after Trinity-Sunday.
• Tres. Trin. Three Weeks after Trinity-Sunday.

The Exchequer opens four Days before Trinity-Term; but eight Days before the other Terms.

Lo! here a Trade surpasseth all the rest; No Change annoys the Lawyer's Interest. His Tongue buyes Lands, builds Houses, without Toil; The Pen's his Plough, the Parchment is his Soil; Him Storms disturb not, nor Militia Bands. The Tree roots best, that in the Weather stands.

How to Rectifie the Tables of the Sun's Declination at any Time by Prostaphaereses.

Prostaphaereses of the Suns Declination.

Day Month.	Jan.	Feb.	Mar.	Apr.	May.	June.	July.	Aug.	Sept.	Octob.	Nov.	Dec.
Sec.	Sec.	Sec.	Sec.	Sec.	Sec.	Sec.	Sec.	Sec.	Sec.	Sec.	Sec.
1	17	36	42	40	28	8	15	33	42	41	30	9
2	18	37	43	39	28	7	15	34	43	42	29	8
3	19	37	43	40	27	6	16	35	43	42	29	7
4	20	38	44	40	27	5	17	35	43	42	28	6
5	20	37	44	39	26	4	18	34	43	41	28	5
6	21	37	43	39	25	4	19	35	43	41	28	4
7	21	38	43	38	25	3	19	35	44	41	27	3
8	22	39	43	38	24	2	19	35	43	40	26	2
9	24	38	44	38	23	2	20	36	44	40	25	1
10	24	39	45	37	23	1	21	36	43	40	24	1
11	25	39	44	37	22	0	21	37	43	40	24	0
12	25	40	44	37	22	1	22	38	43	39	23	0
13	26	41	43	37	21	1	22	38	43	39	22	1
14	26	40	44	37	20	2	23	38	44	38	21	2
15	27	41	44	35	20	3	23	38	43	38	21	3
16	28	42	43	35	19	4	24	39	44	37	20	4
17	28	41	42	35	19	4	25	39	43	38	20	5
18	29	41	43	35	18	5	26	39	43	37	19	6
19	30	41	43	34	17	6	26	39	43	37	18	7
20	31	42	42	34	17	7	27	40	43	36	17	8
21	31	42	43	33	16	8	27	40	43	36	16	9
22	32	42	43	33	15	8	28	41	44	35	16	10
23	32	43	43	32	14	9	29	40	43	35	15	11
24	32	43	42	32	14	10	29	41	42	34	14	12
25	33	44	42	31	12	11	30	41	43	34	13	12
26	33	44	41	3••	12	12	30	41	42	33	13	13
27	34	43	41	30	11	13	30	41	42	34	12	14
28	35	43	41	29	9	14	31	41	43	32	11	16
29	35	43	41	29	9	14	31	41	43	32	11	16
30	35		41	29	9	14	32	42	42	32	10	16
31	36		41		8		33			31		17

The Ʋse of the Table.

* 1.1IN this Kalendar, Printed for the Year 1665, 66, 67, and 1668. the Sun's Declination to be trusted sufficient; but for any Year after 1668. the Rule is thus.

For Example. I would know the Sun's Declination for the Year 1689. you must always substract 1668. from the Year gi∣ven, which is here 1689. the Remainder is 21 Years; which being divided by 4, the Quotient is 5 Leap-Years, and 1 remains, which sheweth it is the first Year.

Now I desire to rectifie the Table for the first day of April, which in the Kalendar you have 8 deg. 36 min. and in this Table you have 40 Seconds;* 1.2 which multiplied by 5 Leap-years, give 200 Seconds, that is 3 m. 20 sec. to be added to 8 deg. 36 min. So have you 8 deg. 39 min. for the Sun's Decli∣nation in 1689.

A Table of the Sun's Declination.

JANUARY XXXI.
South Declination.					Leap-ye.		First.		Second.		Third.		South Declination.
				1664		1665		1666		1667
				1668		1669		1670		1671
				1672		1673		1674		1675
				1676		1677		1678		1679
				1680		1681		1682		1683
				1684		1685		1686		1687
				1688		1689		1690		1691
				1692		1693		1694		1695
Day Mo.	Da. Week	☽ Epact Hour.	☉ Ris. & Setting.	Deg. Min.	Differ.	Deg. Min.	Differ.	Deg. Min.	Differ.	Deg. Min.	Differ.
1	A	29	Circumcis.	21 50		21 43		21 45		21 47
2	B	28	4 1 8	21 40	10	21 33	10	21 35	10	21 38	9
3	C	26 12	4 2 8	21 30	10	21 22	11	21 25	10	21 28	10
4	D	25 08	4 3 8	21 20	10	21 11	11	21 14	11	21 17	11
5	E	23 21	4 4 8	21 09	11	21 00	11	21 03	11	21 6	11
6	F	✶	Twelf day.	20 57	12	20 48	12	20 51	12	20 54	12
7	G	22 10	4 7 8	20 45	12	20 36	12	20 39	12	20 42	12
8	A	21	4 8 8	20 33	12	20 24	12	20 27	12	20 30	12
9	B	20 06	☉ in ♒	20 21	12	20 11	13	20 14	13	20 17	13
10	C	18 18	4 11 8	20 8	12	19 58	13	20 1	13	20 4	13
11	D	✶	4 12 8	19 55	13	19 44	14	19 49	14	19 51	13
12	E	17 15	4 14 8	19 41	14	19 30	14	19 33	14	19 37	14
13	F	16	Hilary.	19 27	14	19 16	14	19 19	14	19 23	14
14	G	15 03	4 11 8	19 12	15	19 01	15	19 04	15	19 8	15
15	A	✶	4 18 8	18 57	15	18 46	15	18 50	14	18 54	14
16	B	14 0	4 20 8	18 42	15	18 31	15	18 35	15	18 39	15
17	C	12 12	4 21 8	18 27	15	18 15	16	18 19	16	18 23	16
18	D	✶	4 23 8	18 11	16	17 59	16	18 3	16	18 7	16
19	E	11 1	☉ to ♒	17 55	16	17 42	17	17 47	16	17 51	16
20	F	9 0	Oct. Hilar.	17 38	17	17 26	16	17 30	17	17 34	17
21	G	7 10	Except.	17 22	16	17 9	17	17 13	17	17 17	17
22	A	✶	Ret. Brev.	17 5	17	16 51	18	16 56	17	17 00	17
23	B	6 6	Term beg.	16 47	18	16 34	17	16 38	18	16 42	18
24	C	4 18	4 33 8	16 30	17	16 16	18	16 20	18	16 25	17
25	D	✶	Conv. Paul	16 12	18	15 58	18	16 2	18	16 7	18
26	E	3 7	4 37 8	15 54	18	15 40	18	15 44	18	15 49	18
27	F	2 0	Qu. Hilar.	15 35	19	15 21	19	15 25	19	15 30	19
28	G	1 3	Except.	15 16	19	15 2	19	15 7	18	15 11	19
29	A	✶	Ret. Brev.	14 57	19	14 43	19	15 48	19	14 52	19
30	B	29 16	Appear.	14 38	19	14 22	21	14 28	20	14 33	19
31	C	28 12	4 46 8	14 18	20	14 4	28	14 8	20	14 13	20

A Table of the Sun's Declination.

FEBRUARY XXVIII.
South Declination.					Leap-ye.		First.		Second.		Third.		South Declination.
				1664		1665		1666		1667
				1668		1669		1670		1671
				1672		1673		1674		1675
				1676		1677		1678		1679
				1680		1681		1682		1683
				1684		1685		1686		1687
				1688		1689		1690		1691
				1692		1693		1694		1695
Da. Mo.	D. Week.	☽ Epact. Hour.	☉ Ris. & Setting.	Deg. Min.	Differ.	Deg. Min.	Differ.	Deg. Min.	Differ.	Deg. Min.	Differ.
1	D	27	4 18 8	13 59		13 44		13 48		13 53
2	E	26 1	Purif. Mar.	13 39	20	13 24	20	13 28	20	13 33	20
3	F	25	Crast. Pur.	13 10	20	13 3	21	13 8	20	13 13	20
4	G	23 10	Except.	12 58	22	12 43	20	12 48	20	12 52	2••
5	A	22 22	Ret. Brev.	12 38	20	12 22	21	12 27	21	12 32	20
6	B	21	Appear.	12 17	21	12 1	21	12 6	21	12 11	21
7	C	20 18	4 59 8	11 56	21	11 40	21	11 45	21	11 50	21
8	D	19	☉ in ♓	11 35	21	11 19	21	11 24	21	11 29	21
9	E	18 8	Oct. Pur.	11 14	21	10 57	22	11 2	22	11 8	21
10	F	18 18	Except.	10 52	22	10 36	21	10 40	22	10 47	21
11	G	17 3	Ret. Brev.	10 30	22	10 14	22	10 19	21	10 24	23
12	A	15 16	Term ends.	10 8	22	9 52	22	9 57	22	10 2	22
13	B	✶	5 11 7	9 46	22	9 30	22	9 35	22	9 40	22
14	C	14 12	Valentine.	9 24	22	9 7	23	9 13	22	9 18	22
15	D	13	5 14 7	9 2	22	8 45	23	8 50	23	8 55	23
16	E	12 1	5 16 7	8 39	23	8 22	22	8 27	23	8 33	22
17	F	11 14	5 18 7	8 17	22	8 0	23	8 5	22	8 11	22
18	G	9 10	☉ 10 ♓	7 54	23	7 37	23	7 42	23	7 44	22
19	A	8	5 22 7	7 31	23	7 14	23	7 20	22	7 26	20
20	B	7 0	5 24 7	7 8	23	6 51	23	6 57	23	7 3	25
21	C	6 19	5 26 7	6 45	23	6 28	24	6 34	23	6 39	24
22	D	5	5 28 7	6 22	23	6 4	23	6 10	24	6 16	23
23	E	4 7	5 30 7	5 59	23	5 41	23	5 47	23	5 53	23
24	F	3 20	Matthew.	5 36	23	5 18	23	5 24	23	5 30	23
25	G	2	5 34 7	5 12	24	4 55	24	5 0	24	5 5	25
26	A	1 16	5 36 7	4 49	23	4 31	23	4 37	23	4 43	22
27	B	✶	5 38 7	4 25	24	4 8	24	4 13	24	4 19	24
28	C	29 5	☉ 20 ♓	4 2	23	3 44		3 50	23	3 56	23
				3 39	23

A Table of the Sun's Declination.

MARCH XXXI.
South Declination.					Leap-ye.		First.		Second.		Third.		South Declination.
				1664		1665		1666		1667
				1668		1669		1670		1671
				1672		1673		1674		1675
				1676		1677		1678		1679
				1680		1681		1682		1683
				1684		1685		1686		1687
				1688		1689		1690		1691
				1692		1693		1694		1695
Day Mo.	Da. Week	☽ Epact Hour.	☉ Ris. & Setting.	Deg. Min.	Differ.	Deg. Min.	Differ.	Deg. Min.	Differ.	Deg. Min.	Differ.
1	D	28 1	David.	3 15		3 20		3 26		3 32
2	E	26 14	5 44 7	2 51	24	2 57	23	3 3	23	3 9	23
3	F	✶	5 46 7	2 28	23	2 33	24	2 29	24	2 45	24
4	G	25 10	5 48 7	2 4	24	2 9	24	2 16	13	2 21	24
5	A	24	5 50 7	1 40	24	1 46	23	1 52	24	1 58	23
6	B	23 0	5 52 7	1 16	24	1 22	24	1 28	24	1 34	24
7	C	21 11	5 54 7	0 53	23	0 59	23	1 5	23	1 11	23
8	D	21	5 56 7	0 29	24	0 35	24	0 41	24	0 46	24
9	E	20 7	5 58 7	0 5	24	0 11	24	0 17	24	0 23	23
-	10	F	18 20	☉ in ♈	Nor. 18	24	Nor. 13	24	North 6	11	North 1	22	Aequinoctial.
North Declination.	11	G	✶	6 2 6	0 42	24	0 37	23	0 30	24	0 25	24	North Declination.
12	A	17 16	6 4 6	1 6	23	0 00	24	0 54	24	0 49	24
13	B	16	6 6 6	1 29	24	1 24	23	1 18	24	1 12	23
14	C	15 5	6 8 6	1 53	23	1 47	24	1 42	24	1 36	24
15	D	14 1	6 10 6	2 16	24	2 11	24	2 5	23	2 00	32
16	E	12 14	6 12 6	2 40	24	2 35	23	2 29	24	2 23	23
17	F	✶	6 14 6	3 4	23	2 58	23	2 52	23	2 46	23
18	G	11 2	6 18 6	3 27	23	3 21	24	3 15	23	3 10	24
19	A	10	6 16 6	3 50	24	3 45	23	3 39	24	3 33	23
20	B	9 0	☉ 10 ♈	4 14	23	4 8	23	4 2	23	3 56	23
21	C	7 11	6 22 6	4 37	23	4 31	23	4 25	23	4 19	23
22	D	✶	6 24 6	5 00	1	4 54	23	4 49	24	4 43	24
23	E	6 7	6 26 6	5 23	23	5 17	23	5 12	23	5 6	23
24	F	4 20	6 28 6	5 46	23	5 40	23	5 35	23	5 29	23
25	G	✶	An. Mar.	6 9	23	6 3	22	5 57	22	5 52	23
26	A	3 8	6 32 6	6 31	22	6 25	22	6 20	23	6 15	23
27	B	2	6 34 6	6 54	23	6 48	23	6 42	22	6 37	22
28	C	1 7	6 36 6	7 16	22	7 11	22	7 5	23	7 0	23
29	D	29 17	6 38 6	7 38	22	7 33	22	7 28	23	7 22	22
30	E	28 14	☉ 20 ♈	8 1	23	7 55	22	7 50	22	7 45	23
31	F	27	6 42 6	8 23	22	8 17	22	8 12	22	8 7	22

A Table of the Sun's Declination.

APRIL XXX.
North Declination.					Leap-ye.		First.		Second.		Third.		North Declination.
				1664		1665		1666		1667
				1668		1669		1670		1671
				1672		1673		1674		1675
				1676		1677		1678		1679
				1680		1681		1682		1683
				1684		1685		1686		1687
				1688		1689		1690		1691
				1692		1693		1694		1695
Da. Mo.	D. Week.	☽ Epact. Hour.	☉ Ris. & Setting.	Deg. Min.	Differ.	Deg. Min.	Differ.	Deg. Min.	Differ.	Deg. Min.	Differ.
1	G	26 2	6 44 6	8 45		8 39		8 34		8 29
2	A	25 22	6 46 6	9 7	22	9 1	22	8 56	22	8 51	22
3	B	24 0	6 48 6	9 29	22	9 23	22	9 18	22	9 13	22
4	C	23 11	6 50 6	9 50	21	9 44	21	9 39	21	9 34	21
5	D	✶	6 52 6	10 11	21	10 6	22	10 1	22	9 56	22
6	E	22 0	6 54 6	10 32	21	10 27	21	10 22	21	10 17	21
7	F	20 20	6 56 6	10 53	21	10 48	21	10 43	21	10 38	21
8	G	19	6 57 6	11 14	21	11 9	21	11 4	21	10 59	21
9	A	18 9	6 59 6	11 35	21	11 30	20	11 25	21	11 20	21
10	B	✶	☉ in ♉	11 55	20	11 50	20	11 46	21	11 40	20
11	C	17 5	7 2 5	12 15	20	12 10	20	12 6	20	12 1	21
12	D	15 6	7 4 5	12 35	20	12 30	20	12 26	20	12 21	20
13	E	14 14	7 6 5	12 55	20	12 50	20	12 46	20	12 41	20
14	F	13	7 8 5	13 25	20	13 10	19	13 6	20	13 1	20
15	G	12 2	7 10 5	13 34	19	13 29	19	13 25	19	13 20	19
16	A	11 15	7 11 5	13 53	19	13 48	19	13 44	19	13 40	20
17	B	10	7 13 5	14 12	19	14 7	19	14 3	19	13 59	19
18	C	9 11	7 15 5	14 31	19	14 26	19	14 22	19	14 18	19
19	D	8	7 17 5	14 50	19	14 45	18	14 41	19	14 36	18
20	E	7 0	☉ 10 ♉	15 8	18	15 3	18	14 59	18	14 55	19
21	F	6 20	7 29 5	15 26	18	15 21	18	15 17	18	15 13	18
22	G	5	7 22 5	15 44	17	15 39	17	15 35	18	15 31	18
23	A	4 9	George.	16 1	17	15 56	18	15 53	18	15 48	17
24	B	3 21	7 25 5	16 18	17	16 14	17	16 10	17	16 6	18
25	C	2	Mark.	16 35	17	16 31	16	16 27	17	16 23	17
26	D	1 18	7 49 5	16 52	17	16 47	18	16 44	17	16 40	17
27	E	✶	7 31 5	17 59	16	17 5	16	17 1	17	16 57	17
28	F	29 6	7 32 5	17 25	16	17 21	16	17 17	16	17 13	16
29	G	28 2	7 34 5	17 41	15	17 37	16	17 33	16	17 29	16
30	A	27	☉ 20 ♉	17 56	15	17 52	15	17 49	16	17 44	15

A Table of the Sun's Declination.

MAY XXXI.
North Declination.					Leap-ye.		First.		Second.		Third.		North Declination.
				1664		1665		1666		1667
				1668		1669		1670		1671
				1672		1673		1674		1675
				1676		1677		1678		1679
				1680		1681		1682		1683
				1684		1685		1686		1687
				1688		1689		1690		1691
				1692		1693		1694		1695
Day Mo.	Da. Week	☽ Epact. Hour.	☉ Ris. & Setting.	Deg. Min.	Differ.	Deg. Min.	Differ.	Deg. Min.	Differ.	Deg. Min.	Differ.
1	B	✶	Ph. & Ja.	18 11		18 8		18 4		18 00
2	C	25 11	7 39 5	18 26	15	18 23	15	18 19	15	18 15	15
3	D	24	7 40 5	18 41	15	18 37	14	18 34	15	18 30	15
4	E	23	7 42 5	18 55	14	18 52	15	18 48	14	18 45	15
5	F	22 13	7 44 5	19 9	14	19 6	14	19 2	14	18 59	14
6	G	21	7 45 5	19 25	14	19 19	13	19 16	14	19 13	14
7	A	20 9	7 46 5	19 36	14	19 33	14	19 30	14	19 27	14
8	B	18 21	7 47 5	19 49	13	19 46	13	19 43	13	19 40	13
9	C	✶	7 49 5	20 2	13	19 59	13	19 56	12	19 53	13
10	D	17 18	☉ in ♊	20 14	12	20 11	12	20 8	12	20 5	12
11	E	16	7 50 5	20 26	12	20 24	13	20 20	12	20 18	13
12	F	15 6	7 53 5	20 38	12	20 36	12	20 32	12	20 30	12
13	G	14 2	7 54 5	20 49	11	20 47	11	20 43	12	20 41	11
14	A	12 15	7 55 5	21 00	11	20 57	12	20 55	11	20 52	11
15	B	✶	7 56 5	21 11	10	21 9	10	21 6	10	21 3	11
16	C	11 4	7 57 5	21 21	10	21 19	10	21 16	10	21 14	11
17	D	10	7 58 5	21 31	9	21 29	9	21 26	10	21 24	10
18	E	9 0	7 59 5	21 40	10	21 38	9	21 36	9	21 34	10
19	F	7 13	8 0 4	21 50	9	21 47	9	21 45	9	21 43	9
20	G	✶	8 1 4	21 59	8	21 56	9	21 54	8	21 52	9
21	A	6 9	☉ 10 ♊	22 7	8	22 5	8	22 2	9	12 1	9
22	B	4 1	8 3 4	22 15	7	22 13	8	22 11	9	22 9	8
23	C	✶	8 4 4	22 22	7	22 21	7	22 19	7	22 17	8
24	D	3 10	8 5 4	22 29	7	22 28	7	22 24	7	22 31	7
25	E	2	8 6 4	22 36	7	22 35	6	22 33	7	22 38	7
26	F	1 6	8 7 4	22 43	6	22 41	6	22 40	6	22 45	7
27	G	29 19	8 8 4	22 49	6	22 47	6	22 46	6	22 51	6
28	A	28 15	8 8 4	22 55	5	22 53	5	22 52	5	22 56	5
29	B	27	8 9 4	23 00	5	22 58	5	22 57	5	23 1	5
30	C	26 4	8 10 4	23 5	4	23 3	5	23 2	5	23 6	5
31	D	✶	8 10 4	23 9	4	23 8	5	23 7	5

A Table of the Sun's Declination.

JUNE XXX.
North Declination.					Leap-ye.		First.		Second.		Third.		North Declination.
				1664		1665		1666		1667
				1668		1669		1670		1671
				1672		1673		1674		1675
				1676		1677		1678		1679
				1680		1681		1682		1683
				1684		1685		1686		1687
				1688		1689		1690		1691
				1692		1693		1694		1695
Da. Mo.	D. Week.	☽ Epact. Hour.	☉ Ris. & Setting.	Deg. Min.	Differ.	Deg. Min.	Differ.	Deg. Min.	Differ.	Deg. Min.	Differ.
1	E	25 0	☉ 20 ♊	23 13		23 12		23 11		23 10
2	F	23 13	8 11 4	23 17	4	23 16	4	23 15	4	23 14	4
3	G	✶	8 11 4	23 20	3	23 19	3	23 19	4	23 18	4
4	A	22 1	8 12 4	23 23	2	23 22	3	23 22	3	23 21	3
5	B	20 21	8 12 4	23 25	2	23 25	3	23 24	2	23 24	3
6	C	19	8 12 4	23 27	2	23 27	2	23 26	2	23 26	2
7	D	18 10	8 13 4	23 29	1	23 28	1	23 28	2	23 28	2
8	E	✶	8 13 4	23 30	1	23 29	1	23 29	1	23 29	1
9	F	17 6	Days at a stand.	23 31	0	23 30	1	23 30	1	23 30	1
10	G	15 19	23 31	0	23 31	1	23 31	1	23 31	1
11	A	14 15	☉ in ♋	23 31	1	23 31	0	23 31	0	23 31	0
12	B	13	Days shorten.	23 30	1	23 31	0	23 31	0	23 31	0
13	C	12 4	23 29	0	23 30	0	23 30	1	23 30	1
14	D	11 16	8 13 4	23 29	2	23 29	1	23 29	1	23 29	1
15	E	10	8 13 4	23 27	2	23 27	2	23 28	1	23 28	1
16	F	9 13	8 12 4	23 25	3	23 25	2	23 26	2	23 26	2
17	G	8	8 12 4	23 22	3	23 23	2	23 23	3	23 24	2
18	A	7 1	8 12 4	23 19	3	23 20	3	23 20	3	23 21	3
19	B	6 21	8 11 4	23 16	4	23 17	4	23 17	3	23 19	2
20	C	5	8 11 4	23 12	4	23 13	4	23 13	4	23 15	4
21	D	4 10	8 11 4	23 8	5	23 9	5	23 9	4	23 11	4
22	E	✶	☉ 10 ♋	23 3	5	23 4	4	23 5	4	23 6	5
23	F	3 0	8 10 4	22 58	5	23 0	5	23 1	4	23 2	4
24	G	1 19	John Bapt.	22 53	6	22 55	6	22 56	5	22 57	5
25	A	✶	8 8 4	22 47	6	22 49	4	22 51	5	22 51	6
26	B	29 6	8 8 4	22 41	7	22 43	7	22 45	6	22 45	6
27	C	28 4	8 7 4	22 34	7	22 36	7	22 38	7	22 39	6
28	D	26 17	8 6 4	22 27	7	22 24	7	22 31	7	22 33	6
29	E	✶	Peter Ap.	22 20	7	22 22	8	22 34	7	22 26	7
30	F	25 13	8 4 4	22 12	8	22 14	8	22 16	8	22 18	8

A Table of the Sun's Declination.

JULY XXXI.
North Declination.					Leap-ye.		First.		Second.		Third.		North Declination.
				1664		1665		1666		1667
				1668		1669		1670		1671
				1672		1673		1674		1675
				1676		1677		1678		1679
				1680		1681		1682		1683
				1684		1685		1686		1687
				1688		1689		1690		1691
				1692		1693		1694		1695
Day Mo.	Da. Week	☽ Epact Hour.	☉ Ris. & Setting.	Deg. Min.	Differ.	Deg. Min.	Differ.	Deg. Min.	Differ.	Deg. Min.	Differ.
1	G	24	8 3 4	22 4		22 6		22 8		22 10
2	A	23 1	☉ 20 ♋	21 56	8	21 58	8	22 00	8	22 2	8
3	B	22 14	8 2 4	21 47	9	21 49	9	21 51	9	21 54	9
4	C	21	8 1 4	21 38	9	21 40	9	21 42	9	21 45	9
5	D	20 10	8 0 4	21 28	10	21 31	10	21 33	9	21 35	10
6	E	19	7 58 5	21 18	10	21 21	10	21 23	10	21 26	9
7	F	18 0	7 57 5	21 8	10	21 11	11	21 13	10	21 16	••0
8	G	17 19	7 56 5	20 57	11	21 00	11	21 3	10	21 5	11
9	A	16	7 55 5	20 46	11	20 49	12	20 52	11	20 54	11
10	B	15 8	7 54 5	20 34	12	20 37	11	20 40	12	20 43	11
11	C	14 4	7 53 5	20 23	11	20 26	12	20 29	11	20 31	12
12	D	12 17	7 52 5	20 11	12	20 14	12	20 17	12	20 20	11
13	E	✶	☉ in ♌	19 59	12	20 2	13	20 5	12	20 8	12
14	F	11 5	7 49 5	19 46	13	19 49	13	19 52	13	19 55	13
15	G	10	Swithin.	19 33	13	19 36	13	19 39	13	19 42	13
16	A	9 1	7 46 5	19 20	13	19 23	13	19 26	13	19 24	13
17	B	7 14	7 45 5	19 6	14	19 10	14	19 13	13	19 16	13
18	C	✶	7 43 5	18 52	14	18 56	14	18 59	14	19 2	14
19	D	6 10	Dog d. beg.	18 30	14	18 42	15	18 45	14	18 48	14
20	E	5	7 40 5	18 23	15	18 27	15	18 30	15	18 34	14
21	F	4 0	7 39 5	18 8	15	18 12	15	18 15	15	18 19	15
22	G	3 11	Magdalen.	17 53	15	17 57	16	18 00	15	18 4	15
23	A	2	☉ 10 ♌	17 37	16	17 41	16	17 45	15	17 49	15
24	B	1 8	7 34 4	17 21	16	17 25	16	17 29	16	17 23	16
25	C	29 20	S. Jam. Ap.	17 5	16	17 9	16	17 13	16	17 17	16
26	D	28 14	7 0 5	16 49	16	16 53	16	16 57	16	17 1	16
27	E	27	7 29 5	16 33	16	16 37	17	16 41	16	16 45	16
28	F	26 5	7 27 5	16 16	17	16 20	17	16 24	17	16 28	17
29	G	✶	7 25 5	15 59	17	16 3	18	16 7	17	16 11	17
30	A	25 1	7 24 5	15 41	18	15 45	18	15 50	17	15 54	17
31	B	23 14	7 22 5	15 23	18	15 27	18	15 32	18	15 36	18

A Table of the Sun's Declination.

AUGUST XXXI.
North Declination.					Leap-ye.		First.		Second.		Third.		North Declination.
				1664		1665		1666		1667
				1668		1669		1670		1671
				1672		1673		1674		1675
				1676		1677		1678		1679
				1680		1681		1682		1683
				1684		1685		1686		1687
				1688		1689		1690		1691
				1692		1693		1694		1695
Da. Mo.	D. Week.	☽ Epact. Hour.	☉ Ris. & Setting.	Deg. Min.	Differ.	Deg. Min.	Differ.	Deg. Min.	Differ.	Deg. Min.	Differ.
1	C	*	Lamas.	15 5		15 10		15 14		15 19
2	D	22 3	7 19 5	14 47	18	14 52	18	14 56	18	15 1	18
3	E	21 0	☉ 20 ♌	14 29	18	14 34	18	14 38	18	14 42	19
4	F	20 0	7 16 5	14 10	19	14 15	19	14 19	19	14 24	18
5	G	18 12	7 14 5	13 51	19	13 56	19	14 00	19	14 5	19
6	A	*	7 12 5	13 32	19	13 37	19	13 41	19	13 46	19
7	B	17 8	7 10 5	13 13	19	13 18	19	13 52	19	13 27	19
8	C	15 20	7 8 5	12 54	19	12 59	19	13 3	19	13 08	19
9	D	14 17	7 7 5	12 34	20	12 39	20	12 43	20	12 48	20
10	E	13	Laurence.	12 14	20	12 19	20	12 23	20	12 28	20
11	F	12 5	7 3 5	11 54	20	11 59	20	12 3	20	12 8	20
12	G	11 18	7 1 5	11 33	21	11 38	21	11 43	20	11 48	20
13	A	10	☉ in ♍	11 13	20	11 18	21	11 23	20	11 28	20
14	B	9 14	6 58 6	10 52	21	10 57	21	11 3	20	11 7	21
15	C	8	6 56 6	10 32	20	10 36	21	11 42	21	10 47	20
16	D	7 3	6 54 6	10 11	21	10 15	21	10 21	21	10 26	21
17	E	*	6 52 6	9 50	21	9 54	21	10 00	21	10 5	21
18	F	6 0	6 50 6	9 28	22	9 33	21	9 38	22	9 44	21
19	G	4 12	6 48 6	9 6	22	9 12	22	9 17	21	9 22	22
20	A	*	6 46 6	8 44	21	8 50	21	9 55	22	9 1	21
21	B	3 0	6 44 6	8 23	22	8 29	22	8 33	22	8 39	22
22	C	1 20	6 42 6	8 1	22	8 7	22	8 12	21	8 17	22
23	D	*	☉ 10 ♍	7 39	22	7 45	22	7 50	22	7 55	22
24	E	29 9	Barthol.	7 17	22	7 23	23	7 28	22	7 33	22
25	F	28 5	6 36 6	6 56	23	7 00	23	7 5	23	7 11	22
26	G	26 18	6 34 6	6 32	22	6 38	22	6 43	22	6 45	23
27	A	*	6 32 6	6 10	23	6 15	23	6 21	22	6 26	22
28	B	25 14	Dog d. end.	5 47	22	5 53	22	6 58	23	6 4	22
29	C	24 6	6 29 6	5 25	23	5 30	23	5 35	23	5 41	23
30	D	23 3	6 27 6	5 2		5 8	22	5 13	22	5 18	23
31	E	22 15	6 25 6	4 39	27	4 44	24	4 50	23	4 55	23

A Table of the Sun's Declination.

SEPTEMBER XXX.
North Declination.					Leap-ye.		First.		Second.		Third.		North Declination.
				1664		1665		1666		1667
				1668		1669		1670		1671
				1672		1673		1674		1675
				1676		1677		1678		1679
				1680		1681		1682		1683
				1684		1685		1686		1687
				1688		1689		1690		1691
				1692		1693		1694		1695
Day Mo.	Da. Week	☽ Epact Hour.	☉ Ris. & Setting.	Deg. Min.	Differ.	Deg. Min.	Differ.	Deg. Min.	Differ.	Deg. Min.	Differ.
1	F	21	Giles.	4 16		4 22		4 27		4 32
2	G	20 12	6 21 6	3 53	23	3 59	23	4 4	23	4 9	23
3	A	19	☉ 20 ♍	3 30	23	3 35	24	3 41	23	3 46	23
4	B	18 0	6 17 6	3 7	23	3 12	23	3 17	24	3 23	23
5	C	17 20	6 15 6	2 43	24	2 49	23	2 54	23	3 00	23
6	D	16	6 13 6	2 20	23	2 26	23	2 31	23	2 37	23
7	E	15 9	6 12 6	1 57	23	2 3	23	2 8	23	2 13	24
8	F	14 6	Lady Fair.	1 33	24	1 39	24	1 45	23	1 50	23
9	G	12 18	6 7 6	1 10	23	1 16	23	1 21	24	1 27	23
10	A	*	6 5 6	0 46	24	0 52	24	0 58	23	1 3	24
11	B	11 7	6 3 6	0 23	23	0 29	23	0 30	24	0 40	24
12	C	10	6 1 6	0 1	22	0 5	24	0 10	24	0 16	24
-	13	D	9 3	☉ in ♎	South 24	23	South 18	24	South 13	7	South 7	9	Aequinoctial.
South Declination.	14	E	7 16	5 57 7	0 48	24	0 42	23	0 36	23	0 31	24	South Declination.
15	F	*	5 55 7	1 11	23	1 5	24	1 00	26	0 54	23
16	G	6 12	5 53 7	1 35	24	1 29	24	1 23	23	1 18	24
17	A	5	5 51 7	1 58	23	1 52	23	1 47	24	1 41	23
18	B	4	5 49 7	2 22	24	2 16	24	2 10	23	2 5	24
19	C	3	5 47 7	2 45	23	2 40	24	2 34	24	2 28	23
20	D	2	5 45 7	3 9	24	3 3	23	2 57	23	2 52	24
21	E	1 9	Matth. Ap.	3 32	23	3 27	24	3 21	24	3 15	23
22	F	29 22	5 42 7	3 56	24	3 50	23	3 44	23	3 38	23
23	G	28 18	☉ 10 ♎	4 19	23	4 13	23	4 7	23	4 2	24
24	A	27	5 38 7	4 42	24	4 36	23	4 30	23	4 25	23
25	B	26 17	5 36 7	5 06	23	4 59	23	4 54	24	4 48	23
26	C	*	5 34 7	5 29	23	5 23	24	5 17	23	5 12	24
27	D	25 3	5 32 7	5 52	23	5 36	23	5 41	24	5 35	23
28	E	23 16	5 30 7	6 15	23	6 09	23	6 4	23	5 58	23
29	F	*	Michael.	6 38	23	6 32	23	6 16	22	6 21	23
30	G	22 4	5 26 7	7 01	23	6 55		6 49	23	6 44	23

A Table of the Sun's Declination.

OCTOBER XXXI.
South Declination.					Leap-ye.		First.		Second.		Third.		South Declination.
				1664		1665		1666		1667
				1668		1669		1670		1671
				1672		1673		1674		1675
				1676		1677		1678		1679
				1680		1681		1682		1683
				1684		1685		1686		1687
				1688		1689		1690		1691
				1692		1693		1694		1695
Da. Mo.	D. Week.	☽ Epact. Hour.	☉ Ris. & Setting.	Deg. Min.	Differ.	Deg. Min.	Differ.	Deg. Min.	Differ.	Deg. Min.	Differ.
1	A	21	5 24 7	7 24		7 17		7 12		7 06
2	B	20 0	5 22 7	7 46	22	7 40	23	7 35	22	7 29	23
3	C	18 13	☉ 20 ♎	8 9	23	8 2	22	7 58	23	7 52	23
4	D	*	5 18 7	8 31	22	8 25	23	8 20	22	8 15	23
5	E	17 9	5 16 7	8 53	22	8 47	22	8 42	22	8 37	22
6	F	22 22	5 14 7	9 15	22	9 9	22	9 4	22	8 59	22
7	G	14 18	5 12 7	9 37	22	9 32	23	9 27	23	9 21	22
8	A	13	5 10 7	9 59	22	9 54	22	9 49	22	9 43	22
9	B	12 7	5 8 7	10 21	22	10 16	22	10 10	21	10 5	22
10	C	11 19	5 6 7	10 43	22	10 37	21	10 32	22	10 27	22
11	D	10	5 4 7	11 04	21	10 59	22	10 53	21	10 48	21
12	E	9 16	5 2 7	11 25	21	11 20	21	11 15	22	11 10	22
13	F	8	☉ in ♏	11 46	21	11 41	21	11 36	21	11 31	21
14	G	7 4	4 59 8	12 7	21	12 2	21	11 57	21	11 52	21
15	A	*	4 57 8	12 28	21	12 23	21	12 18	21	12 13	21
16	B	6 0	4 55 8	12 48	20	12 44	21	12 39	21	12 34	21
17	C	4 13	4 53 8	13 9	21	13 4	20	12 59	20	12 54	20
18	D	*	Luke.	13 29	20	13 24	20	13 20	21	13 14	20
19	E	3 1	4 49 8	13 49	20	13 44	20	13 40	20	13 34	20
20	F	2	Tres. Mic.	14 9	20	14 4	20	13 59	19	13 54	20
21	G	1 0	Except.	14 28	19	14 24	20	14 19	20	14 14	20
22	A	29 11	Ret. Brev.	14 48	20	14 43	19	14 38	19	14 34	20
23	B	28 7	Term beg.	15 7	19	15 2	19	14 57	19	14 53	19
24	C	26 19	4 40 8	15 26	19	15 21	19	15 16	19	15 12	19
25	D	*	Crispin.	15 44	18	15 40	19	15 35	19	15 31	19
26	E	25 16	☉ 13 ♏	16 2	18	15 58	18	15 53	18	15 49	18
27	F	24	Mens. Mi.	16 20	18	16 16	18	16 11	18	16 7	18
28	G	23 4	Sim. Jude.	16 38	17	16 33	17	16 29	18	16 25	18
29	A	22 17	Ret. Brev.	16 55	17	16 51	18	16 47	18	16 32	17
30	B	21	Appear.	17 12	17	17 8	17	17 4	17	17 00	18
31	C	20 13	4 2 8	17 29	17	17 25	17	17 21	17	17 17	17

A Table of the Sun's Declination.

NOVEMBER XXX.
South Declination.					Leap-ye.		First.		Second.		Third.		South Declination.
				1664		1665		1666		1667
				1668		1669		1670		1671
				1672		1673		1674		1675
				1676		1677		1678		1679
				1680		1681		1682		1683
				1684		1685		1686		1687
				1688		1689		1690		1691
				1692		1693		1694		1695
Da. Mo.	D. We••k.	☽ Epact. Hour.	☉ Ris. & Setting.	Deg. Min.	Differ.	Deg. Min.	Differ.	Deg. Min.	Differ.	Deg. Min.	Differ.
1	D	19	All Saints.	17 46		17 41		17 38		17 32
2	E	18 2	All Souls.	18 2	16	17 58	17	17 54	16	17 50	17
3	F	*	Crast. An.	18 18	16	18 14	16	18 10	16	18 6	16
4	G	17 0	Except.	18 33	15	18 30	16	18 26	16	18 22	16
5	A	15 11	Powder Tr.	18 48	15	18 45	15	18 41	15	18 37	15
6	B	14 7	Appear.	19 3	15	19 00	15	18 56	15	18 53	16
7	C	12 19	4 16 8	19 18	15	19 14	15	19 11	15	19 8	15
8	D	*	☉ 25 ♏	19 32	14	19 29	14	19 25	14	19 22	14
9	E	11 8	4 15 8	19 46	14	19 43	14	19 39	14	19 36	14
10	F	8	4 13 8	19 59	13	19 56	13	19 53	14	19 50	14
11	G	9 4	Martin.	20 13	14	20 10	14	20 6	13	20 3	13
12	A	7 17	Crast. Ma.	20 26	13	20 23	13	20 19	13	20 16	••••
13	B	*	Except.	20 38	12	20 35	12	20 31	12	20 29	13
14	C	6 13	Ret. Brev.	20 50	12	20 47	12	20 43	12	20 41	12
15	D	5	Appear.	20 2	10	20 59	12	20 55	12	20 53	12
16	E	4 2	☉ 4 ♐	21 13	11	21 10	11	21 7	12	21 5	12
17	F	3 14	4 3 8	21 23	10	21 21	11	21 18	11	21 16	11
18	G	2	Oct. Mar.	21 34	11	21 31	10	21 29	11	21 26	10
19	A	1 11	Except.	21 44	10	21 41	10	21 39	10	21 36	10
20	B	29 23	Ret. Brev.	21 54	10	21 51	10	21 49	10	21 46	10
21	C	28 20	Appear.	22 3	9	22 00	9	21 58	9	21 56	10
22	D	27	☉ 10 ♐	22 11	8	22 09	9	21 7	9	22 5	9
23	E	26 8	3 56 9	22 20	9	22 18	9	22 16	9	22 13	8
24	F	*	3 55 9	22 28	8	22 26	8	22 24	8	22 22	9
25	G	25 4	Qu. Mar.	22 35	7	22 34	8	22 31	7	22 30	8
26	A	23 17	Except.	22 42	7	22 41	7	22 39	8	22 37	7
27	B	✶	Ret. Brev.	22 48	6	22 48	7	22 45	6	22 44	7
28	C	22 6	Term ends.	22 54	6	22 54	6	22 52	7	22 50	6
29	D	21	3 51 9	23 00	6	22 59	5	22 58	6	22 56	6
30	E	20 2	Andrew.	23 05	5	23 4	5	23 03	5	23 2	6

A Table of the Sun's Declination.

DECEMBER XXXI.
South Declination.					Leap ye.		First.		Second.		Third.		South Declination.
				1664		1665		1666		1667
				1668		1669		1670		1671
				1672		1673		1674		1675
				1676		1677		1678		1679
				1680		1681		1682		1683
				1684		1685		1686		1687
				1688		1689		1690		1691
				1692		1693		1694		1695
Day Mo.	Da. Week	☽ Epact Hour.	☉ Ris. & Setting.	Deg. Min.	Differ.	Deg. Min.	Differ.	Deg. Min.	Differ.	Deg. Min.	Differ.
1	F	18 15	☉ 20 ♐	23 10		23 09		23 08		23 06
2	G	✶	3 50 9	23 14	6	23 13	4	23 12	4	23 11	5
3	A	17 11	3 49 9	23 18	4	23 17	4	23 16	4	23 15	4
4	B	15 23	3 48 9	23 21	3	23 20	3	23 20	4	23 19	4
5	C	14 20	3 48 9	23 24	3	23 23	3	23 23	3	23 22	3
6	D	13	3 48 9	23 26	2	23 26	3	23 25	3	23 25	3
7	E	12 8	3 47 9	23 28	2	23 28	2	23 27	2	23 27	2
8	F	11 21	Days are at a stand.	23 30	2	23 29	1	22 29	2	23 28	1
9	G	10	23 31	1	23 30	1	23 30	1	23 30	2
10	A	9 17	23 31	0	23 31	1	23 31	1	23 31	1
11	B	8	☉ in ♑	23 31	0	23 31	0	23 31	0	23 31	0
12	C	7 6	Days in∣crease.	23 30	1	23 31	0	23 31	0	23 31	0
13	D	✶	23 29	1	23 30	1	23 30	1	23 30	1
14	E	6 2	3 47 9	23 28	1	23 29	2	23 29	1	23 29	1
15	F	4 15	3 47 9	23 26	2	23 27	2	23 27	2	23 27	2
16	G	✶	3 48 9	23 24	2	23 25	2	23 25	2	23 25	2
17	A	3 3	3 48 9	23 21	3	23 22	3	23 22	3	23 23	2
18	B	2	3 49 9	23 18	3	23 19	3	23 19	3	23 20	3
19	C	1 0	3 49 9	23 14	4	23 15	4	23 16	4	23 16	4
20	D	29 12	☉ 9 ♑	23 9	5	23 10	5	23 12	4	23 12	4
21	E	28 8	Thomas.	23 5	4	23 6	6	23 7	5	23 8	5
22	F	27	3 50 9	23 00	5	23 1	6	23 2	5	23 3	5
23	G	26	3 51 9	22 54	6	22 55	6	23 57	5	22 54	5
24	A	25 17	3 52 9	22 48	6	22 49	7	23 51	6	22 52	6
25	B	24	Christmas.	22 41	7	22 43	8	22 45	6	22 46	6
26	C	23 6	Stephen.	22 34	7	22 36	8	22 38	7	22 39	7
27	D	22 18	John.	22 27	7	22 21	8	22 31	7	22 32	7
28	E	21	Innocents.	22 19	8	22 20	8	22 23	8	22 25	7
29	F	20 15	3 56 9	22 11	8	22 12	8	22 15	8	22 17	8
30	G	19	3 57 9	22 9	8	22 4	9	22 6	9	22 8	9
31	A	18 3	3 58 9	21 53	6	21 55	9	21 57	9	21 59	9

To find the Sun's Declination upon every Day of the Year.

THe Sun's Year (that is, the time that the Sun goeth out of a certain Point of the Ecliptick, and returneth again to the same) is not of 365 days just; but about 5 Hours and 49 Minutes more (that is, little less than 6 Hours;) Wherefore after three Years, there is always added to the fourth four times 6 Hours, that is, a Day more in February, for to count the Year or the Revolution of the Sun in even Days; therefore that fourth Year is called Leap-year: Therefore when we de∣scribe the Sun's Declination in Tables, we always use to make four several Tables, for four such Years following one the other; and yet by reason of the foresaid difference, that four Revolutions of the Sun do not justly make up one Day, but wants about 48 min. bringeth in process of time so great a difference in the Declination, that it is needful every twenty Years to renew such Tables.

How to find the Leap-years, it is thus: Divide the Year of our Lord above 1600. by 4; If the Division doth fall out even, without any over-plus, that Year then is a Leap-year of 366 Days: But if out of the Division there remain any Number, that Remainder sheweth how many Years that Year propounded, is after the Leap-year.

For EXAMPLE.

I desire to know what Year the Year 1666. is. Leaving 1600, I divide 66 by 4, and find there remains 2; for 16 times 4, or 4 times 16, is 64; that taken from 66, there remains 2; whereby I find the Year 1666. to be the second Year after the Leap-year. In the like manner you must work for any other Years: Only note this, If nothing remaineth upon the Division out of the Quotient, then it is a Leap-year if it be even.

As for EXAMPLE.

It is required to know what Year 1692 is. Leaving the 1600, divide the 92 by 4, and nothing remains upon the Division, but is even 23 in the Quotient; where∣by I find that Year 1692. is a Leap-year.

For to know the same by the foregoing Tables, it is thus. Each Month hath 12 Co∣lumns; The first thereof shews the Days of the Month; The second Column, having the Dominical Letters, shews the Days of the Week; The third Column having two Rows of Figures, the first of them shews the Epact of the Moon, and the other the Hour of the Day, reckoning the said Hours always from Noon; the fourth Column shews the Chief Days of the Year, and the Terms and their Returns which are fixed and certain; and in the void places it shews the Rising and Setting of the Sun in this Latitude, and the Place of the Sun every 10 Day or Degree. These four Columns of themselves are fit for Mens ordinary use, and may be made with a little Art and Pains to perform all the Conclusions which the yearly Almanacks shew and teach, as you shall see by the following Rules and Observations.

The fifth Column of the foregoing Tables shews the Sun's Declination for every Day of the Year, for all these Years in the first Column under-written, which are all Leap-years. The sixth Column shews the Daily Difference of the Sun's Declination. The seventh Column shews the first Year from the Leap-year: The eighth, the Daily Difference of the Sun's Declination in that Year. The ninth shews the second Year from the Leap-year; The tenth, the Difference; The eleventh, the third Year from the Leap-year; The twelfth, the Difference every Day of the Sun's Declination, as you see in the Tables. This Table following shews the Leap-years, First, Second, and Third Years, as they are plainly expressed in the Head of each Table.

Leap-years.	First.	Second.	Third.
1664	1665	1666	1667
1668	1669	1670	1671
1672	1673	1674	1675
1676	1677	1678	1679
1680	1681	1682	1683
1684	1685	1686	1687
1688	1689	1690	1691
1692	1693	1694	1695

For to find the Sun's Declination, Look for the Day of the Month in the left hand of the Table, and in the common Angle of meeting you will find the Declination which you seek after.

I. EXAMPLE.

I desire to know the Sun's Declination for the 22 of May, in the Year 1693. being the first Year after the Leap-year. In the Head of the Table I find the Month and Year; on the left hand of the Table I find the Day; and in the Common Angle or Line of Meeting, I find the Declination I look for to be North 22 deg. 13 min.

II. EXAMPLE.

Upon the 5th of November in the Leap-year 1692. I desire to know the Declina∣tion of the Sun. In the Head of the Table I find the Month and Day, and in the first Column to the left hand I find the Day of the Month, and in the Common Line of Meeting, under the Year, I find the Sun's Declination required, to be 18 deg. 37 m. South Declination; and his Difference in 24 Hours, 15 min.

The foregoing Tables of the Sun's Declination is rectified properly for the Meridian of the most famous and Metropolitan City of London. The Constant Kalendar I bor∣rowed out of Ingenious Mr. Philips's Purchaser's Pattern, at the end of page 247. With some addition it is very useful with the foregoing Tables.

Of the Difference and Aequa∣tion of Declination in di∣vers Places of the Earth.

A Table by which you may proportion the Sun's Declination to any other Meridian.

The Difference in Declination daily.	M	M	M	M	M	M	M	M	M
00	03	06	09	12	15	18	21	24
	M	M	M	M	M	M	M	M	M
Degrees of Difference of Longitude either East or West.	Deg. 15	0	0	0	0	0	0	1	1	1
30	0	0	0	0	1	1	1	2	2
45	0	0	0	1	1	2	2	3	3
60	0	0	1	1	2	2	3	3	4
75	0	0	1	2	2	3	4	4	5
90	0	0	1	2	3	4	4	5	6
105	0	1	2	2	3	4	5	6	7
120	0	1	2	3	4	5	6	7	8
135	0	1	2	3	4	5	7	8	9
150	0	1	2	3	5	6	8	9	10
165	0	1	2	4	5	6	8	10	11
180	0	1	3	4	6	7	9	11	12

NOte this, They that are more Easterly from the Meri∣dian of London, have the Decli∣nation less when the Sun de∣clineth from the Line, and in∣creaseth in Declination either Northward or Southward, as well between the 10th of March and the 12th of June, as between the 13th of September and the 12th of December; and more when the Sun returneth again towards the Line, whether it be North or South of the Line, as well between the 12th of December and the 10th of March, as between the 12th of June and the 13th of September.

On the contrary, They that are more Westerly from the Meridian of London, when the Declination increaseth North or South, have more Declination, and less when the Declination decreaseth; that is, when the Sun is going towards the Aequinoctial, ei∣ther on the North or South side of the Line; the reason is, because the Sun cometh to the Meridian Eastward, to them that live there, always before it doth to us; and them that live more Westerly, have him later to their Meridian.

EXAMPLE I. Of those that are more Easterly, which increase in Declination.

On the 26th of March, the first Year after the Leap-year, I desire to know the Declination of the Sun at Noon at Bantam in the East-Indies. 〈 math 〉〈 math 〉 I find by Globes, or the Plat of Mercator, that Bantam is to the Eastward of the Meridian of London about 110 Degrees; we do not esteem of a Degree or two, because it amounteth to nothing in this Practice. The Sun for his Course round the Heavens and Earth, which is 360 Degrees, hath need of 24 Hours; What time will 110 Degrees have? Facit 7 Hours, and something more not worth the noting; whereby the Sun comes to the Meridian 7 Hours sooner at Bantam, than it doth at London; That it is 12 a Clock at Noon at Bantam, when it is 4 of the Clock in the Morning with us at London. The Sun's Declination for the 26th of March, is 6 deg. 25 min.: The Difference of the Declination of the Day following, you find is 23 min. which it is increased; Therefore I say, If in 24 Hours the Declination increaseth 23 Minutes, How much then in 7 Hours? Facit almost 7 Minutes, that the Declination is less than it is at London. So that the Declination at Bantam that Day, is but 6 deg. 18 min. North: And on the contrary, when the De∣clination decreaseth, work, and you will have the Declination South, Eastward, or Westward.

EXAMPLE II. The Ʋse of the Table.

On the 17th of September in the same Year, I desire to know the Declination that day at Noon at Bantam. The Declination for the Meridian of London is that Day 1 deg. 52 min. and the Difference of the Declination of the Day following is 24 min. decreased; and, as was said before in the last E••••mple, the difference of Longitude is 110 deg. Therefore I look in the Head of the foregoing Table, for the nearest Num∣ber to the Difference 24, and find it to fall just even on the Head of the last Column; then look on the left hand of the Table for the Difference of Longitude, and I find 105 deg. nearest, and in the Common Angle of Meeting I find 7, which is to be substracted from the Declination in the Meridian of London abovesaid, 1 deg. 52 min. and the Remainder will be the Declination for the Meridian or Longitude I am in, which is 1 deg. 45 min. South: But if the Declination decreaseth, as it doth here in∣crease, then you must have added.

	deg.	min.
In the Meridian of London the Declination	01	52
The Minutes Proportional substracted	00	07
The Declination for 110 deg. Longitude of Bantam, East	01	45
The Declination of 110 deg. West of the Meridian of London	00	07
West	01	52

EXAMPLE III.

A Ship coming on the seventh of November, in the third Year after the Leap year, into the great South-Sea, thwart of the Coast of Peru, in Longitude 76 deg. The Pi∣lot desireth the Declination there at Noon in that Meridian.

	deg.	min.
In the Meridian of London the Declination is	19	08 South.
The Minutes Proportional added	00	03
In the Longitude 76 deg. the Declination	19	11 West.
In the Longitude of 76 deg. East, the Declination is	19	05

Two Ships being in Company, they parted at the Lands-end of England: The one Sails Eastwards, and cometh upon his Reckoning upon the 28th of September 180 Degrees on the other side the Globe of the Earth (being the first Year after the Leap-year) and by the foregoing Tables finds the Sun's Declination 5 deg. 57 min. The other Ship Sails Westwards, and meeteth the first Ship at the aforesaid place, by his Reckoning not the 28th, but on the 27th of September, and findeth the Decli∣nation in these Tables for that Day; so that they differ in the Time one Day, and in Declination 24 min. the which proceedeth from this cause: The first having Sailed against the Rising of the Sun 180 Degrees, hath shortned his time 12 Hours; the other hath Sailed with the Sun 180 Degrees, hath lengthned his time 12 Hours, and thereby hath one Night less than the first. Seeing then in 24 Hours increaseth 24 Minutes, he that Sailed Eastward must reckon 12 Minutes Declination less, and he that Sailed Westward 12 Minutes more than the Table doth shew; and so both of them shall keep one manner of Declination, to wit, 6 deg. 9 min.

A Table of the Refractions of the Sun, Moon, and Stars, according to the Observation of thrice Noble Tycho Brahe.

Alti∣tudes.	Sun.	Moon	Stars		Alti∣tudes.	Sun.	Moon
min.	min.	min.		min.	min.
0	34	33	30	18	06	06
1	26	25	21	19	05	06
2	20	20	15	20	04	05
3	17	17	12	21	04	05
4	15	15	11	22	03	04
5	14	14	10	23	03	04
6	13	13	00	24	03	04
7	12	13	08	25	02	03
8	11	12	07	26	02	03
9	10	11	06	27	02	03
10	10	11	05	28	02	02
11	09	10	05	29	02	02
12	09	09	04	30	01	02
13	08	00	04	31	01	02
14	08	08	03	32	01	01
15	07	08	03	33	01	01
16	07	07	02	34	01	01
17	06	07	02	35	01	01

THe Refraction of the Sun, Moon and Stars, causeth them to appear higher above the Horizon than they are: Therefore the Refraction is alway•• to be sub∣stracted from the A ••••ude ob∣served, that the tr•• ••ltitude may be had.

As for Examp

The Sun's Meridian Altitude by Observation being 9 Degrees, I require the true Altitude.

	deg.	mi.
Altitude by Observation	9	00
Refraction substract	0	10
The true Meridian Alti∣tude	8	50

Of the Refraction of the Sun, A Dutch Ship being upon the Discovery of a North-East Passage to the East-India, was forced to Winter in Nova Zembla: the Mariners beheld the Sun 14 days sooner than he should by his De∣clination, and by Computation 5 Degrees under the Horizon; which is caused by the gross Vapours, and thickness of the Air neer the Horizon.

The USE of the CONSTANT KALENDAR.

I. To know the Day of the Month.

THis is the Chief and most useful Observation of any Almanack, and may as well be performed by this, as by any other. To this purpose, you must by the general Kalendar at the beginning hereof, know the Dominical or Sun∣day Letter for the Year; then considering with your self, whether it be the beginning, midst, or end of the Month (as you must do in any Almanack) find this Letter in the beginning, midst, or end of the Month, and reckoning from it to the Day of the Week, either Munday, or Tuesday, or whatsoever other Day it is, right against the Day of the Week you shall find what Day of the Month it is. Here is no difficulty in this; only when it is Leap-year you see there is two Sunday Letters, the first of these you may use only to the 24th of February, and the other all the Year after.

For Example. In the 1668. the Dominical Letter ED the first Sunday in January, is at the first E, which is at the fifth Day of the Month; the first Sunday in February is at the second Day of the Month; but the first Sunday in March is at the first D, which is at the first Day of the Month, and so all the Year after.

II. To know what Day of the Week any Notable Day will fall upon, in any Year.

First find the Dominical Letter in the former Table; then find your Letter in your Month next before the Day you desire, and so from thence count the Days of the Week, till you come to the Day desired. Thus if you would know what Day of the Week Lady-day, or the Annunciation of the Lady Mary falls upon this Year 1668. the Dominical Letter is D; this is three Days before the said Day, therefore that falls upon a Wednesday.

But now in the Year 1669. when the Dominical Letter is C, Lady-day will be upon the Thursday. This will be in a short time as ready to you, as if these Letters were painted out for you in Vermilion.

III. To find the Time of Sun Rising and Setting.

This is set down for most of the Days in the whole Year, for London; and may serve for all the East, South, and West Parts of England: And this is done after somewhat a briefer manner than is usual, making the Minutes which are placed in the midst, to serve both the Hours of Setting and Rising; which you must understand thus: The 7th of February you shall find these Figures, 4. 59. 8. that is, the Sun that Day sets at 4 h. 59 m. that is 59 m. after 4. and riseth at 59 m. 8 h. that is 59 m. before 8. or almost 7 a Clock. And so you must account them always, remembring, That as the Minutes follow the first Figure, so they must be reckoned in Time after: as they stand before the last Figure, so they must be reckoned in Time before it.

And think it not preposterous that the time of the Sun's Setting is set down before the Rising; for the Sun's Setting is of most use, and the other serves in a manner for the filling up of the Column.

	ho.	min.
If you double this time of Sun Setting	04	59
You have the Length of the Day	09	58
If you substract it from	12	00
You have the time of Rising, differing in shew from the Kalendar	07	01
But all one in effect; and this doubled, shews the Length of the Night	14	02

IV. To find the Place of the Sun.

THis is set down in the Kalendar, about every tenth Day, to every tenth Degree; so that reckoning a Degree for each Day between, you shall have the Place of the Sun exact enough for most ordinary Uses. Thus the 10th of March the Sun enters into Aries; therefore the 15th Day, or five Days after, the Sun is in five De∣grees of Aries.

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.

Notes

• * 1.1

  When the Declination increaseth, then add; and for de∣creasing, substract.
• * 1.2

  8 d. 39 m. Declination 1 April 1689.