Befides which, there is another kind of Leap-Year to be obferved in the Gregorian Account, viz. The Year 2000, 2400, 2800, and every Fourth Hundredth Year in this Succeffion are to be efteemed Leap-Years, and all other even Hundreds, which by Old Style are accounted Leap-Years, are in the prefent not to be accounted for Leap-Years.

Note, The common Year hath 365 Days in it, but Leap-Year of both Kinds 366, and then February hath 29 Days, which in common Years hath but 28 Days..

Rule 1. For the Jalian common Leap Years.

Divide the Year by 4, what's left shall be,

For Leap-Year, o, for paft, 1, 2, or 3.

Example 1. The Year 1757 is it a Common Year, or LeapYear?

4)1757(1 the Remainder; or is it Year after Leap-Year. 439

Example 2. The Year 1760; is it a Common Year, or LeapYear?

4)1760(0

440

Remainder; is therefore Leap-Year.

Rule 2. For the Gregorian Leap-Years.

As every Fourth Hundredth Year (beginning from the Year 2000) is Leap-Year, and all the other even Hundreds, Common Years; cut off two Cyphers towards the Right-hand, and divide the other Figures by 4, the Remainder, if o, points out LeapYear; but if 1, 2, or 3, fignifies it to be a common Year, and the ift, 2d, or 3d Year after the Centennial Leap-Year.

Example it. The Year 800, is it a common Year, or LeapYear!

4)1800(2

4

Remainder; is therefore a Common Year, and 2d Year after Centennial Leap-Year. Example 2. The Year 2000, is it a Leap-Year, or a Common Year?

4)20loo(o Remainder; is therefore Centennial Leap-Year.

5

=

Problem IV. To find the Dominical Letter until the Year 1799 inclufive.

Definition 1. The Week Days in Calenders, or Almanacks, are exprefled by the firft feven Letters of the Alphabet; the Letter A, conftantly anfwering to the firft Day in the Year; that Letter then that ftands against the first Sunday in the Year is called the Dominical Letter.

The Rule. Divide the Year, and 4th thereof by 7;
What's left, fubtract from 7, the Letter's given,

Note, 1. When it's Leap-Year, there are two Dominical Letter's, one serves to the clofe of February, the other from thence to the Year's-end; 'tis the latter that this Rule finds.

2. The Dominical Letter goeth backward in a Common Year one Letter, but in Leap-Year two Letters.

3. As faid before, the Years 1800, 1900, 2100, &c. are LeapYears according to the Julian, but common Years according to the Gregorian Calendar, therefore will have but one Letter inftead of two, and confequently the Order of the Dominical Letters will then be changed.

Examp. For the Year 1757. I demand the Dominical Letter? The Operation.

The given Year is (by Prob. 3.) the firft Year after 1957

It's fourth Part is

The Sum is

7)2196(313
(5

439

2196

Quotient and Remainder is 5; which fubtract from 7, refts 2 for the Dominical Letter; that is, B.

Problem V. By the 19 Epacts, to find Eafter Limit from the beginning of March, inclufive.

Definitions. 1. Eafter-Limit is the 14th Day of the Pafchal New-Moon (or the New-Moon nearest the Vernal Equinox) after the first of March.

2. The Vernal Equinox, by the Gregorian Calendar is fix'd on the 21ft of March.

The RULE.

Find the Epact by Problem 2.

If that be less than 24, fubtract it from 44; but if more than 24, fubtract it from 74; if juft 24, fubtract from 73; alfo if it be 25, and the Golden Number more than 11, fubtract from 73; the Remainder is Eafter-Limit, or the Day of the Pafchal Fuli Moon, from the 1ft of March inclufive.

Example. I demand Eafter-Limit, for the Year 1757.
The Operation.

The Epact for the Year 1757 (by Problem 2.) is
Which fubtracted from

9

44

Remainder is Eafter-Limit from the 1ft of March 35 Days, or the 4th Day of April for the Year 1757.

Problem VI. To find Eafter-Day for any Year. Definition. Eafter-Day, is next Sunday after Eafter Limit, or Day of the Pafchal Full Moon, and is never before the 22d Day of March, nor after the 25th Day of April.

The RULE.

1. Find the Dominical Letter by Problem 4.
2. And Eafter Limit by the laft Problem.
3. The Letter more by 4, from Limit take:

What's left from neareft Sevens fhall Eafter make.
Example. For the Year 1757, I demand Eafter-Day.
The Operation.

Dominical Letter (by Prob. 4) is B, or

To it add

The Sun. is

Which fubtract from Eafter Limit (found by Prob. g.)

Remainder is

Which fubtract from the neareft Sevens

Remainder is

35

29

35.

6

Which added to Eafter-Limit 35, Sum is 41, from which subtract March 31 Days, remains 10, fo that Eafter-Day is the 10th Day of April for the Year 1757.

Problem VII. To find the Moon's Age.

Definition. The Moon's Age is, how many Days are paft fince the Day of her Change, which Age never exceeds 30 Days. The Rule. 1. Find the Epact by Problem the 2d.

2. To the Epact add to the Day of the Month, and the Number of the Month; the Sum if exceed not 30, is her Age, but if it doth, fubtract 30 as oft as you can, and the Remainder is her Age. Note, The Numbers of the Months are these,

January, February, March, April, May, June,

2,

4,

July, Auguft, September, October, November, December.

2, 3,

5: 6,

8,

8,

10,

Example. The 21st of May, 1757, I demand the Moon's Age?

The Operation

The Epact (by Prob. 2.) for the Year 1757 is

To it add the Day of the Month

And the Month May's Number

The Sum is

Which being more than 30 b is the Moon's Age required.

9

21

3:

33 Days. 3 Days.

Problem VIII. To find the Moon's Southing.

Definition. The Moon's Southing, in the Time of her coming to, or upon the Meridian; which, from the New Moon to her Full, is after Noon; but from the Full to the Change is before Noon.

The Rule 1. Find the Moon's Age by the laft Problem.

2. Multiply her Age by 4, and divide the Product by 5; the Quotient is Hours, and the Remainder is fo many times 12 Minutes of an Hour, and both together is her Southing.

Example. The 21st of May, 1757; I demand the Moon's Southing?

The Operation.

The Moon's Age (by Prob. 7.) is

Multiply by

The Product is

3 Day's

12

That divided by 5, the Quotient is two Hours, and the Remainder is 2, which makes 24 Minutes; fo that the Moon's Southing is 2 Hours 24 Minutes in the Afternoon,

Prob. IX. To find the Time of Full Sea, or High Water, at any Place.

The Rule 1. Find the Moon's Southing by the laft Problem. 2. To the Southing, add the Point of the Compafs making Full Séa, (on the Full and Changé Day) for the Place propofed; that Sum is the Time of Full Sea, or High Water."

Note, The Point of the Compass making Full Sea on the Full and Change Days, may be found (in the Tide-Table) in the Mariher's Calendar.

Example. The 21ft of May, 1757; I demand the Time of High Water at London.

The Operation. The Moon's Southing (by Prob. 8.) for the

21ft of May, 1757 is

To it add London SW. and NE.

Sum is the Time of High Water

2h. 24m. Afternoon.

Sect, II. The Use of the Plane-Chart, or Plot.

IT's requifite to understand the Plane-Chart before the Cafes of Plane-Sailing: For it conduces much to the Knowledge thereof; and for the better understanding of it, mind the following

Definitions. 1. The Plane Chart fuppofeth the Earth and Sea to make one flat Superficies, or Long-fquare; in which the Meridians are Parallel, and the Degrees of Latitude and Longitude, equal in all Places; which is only true in the Equator.

2. The Equator is a Line drawn Eaft and Weft, and is 90 Degrees diftant from each Pole; From it Latitude beginneth, and on it Longitude is counted.

3. The Poles are two oppofite Points, one called the North Pole, the other the South Pole; and lie North and South from each other; at them is the greatest Latitude 90 Degrees.

4. The Meridians are Lines (in this Chart) parallel to each other, and perpendicular to the Equator, and lie North and South; on which are counted the Degrees of Latitude.

5. Parallels of Latitude, are Lines parallel to the Equator, and lie Eaft and Weft.

6. Latitude is the Breadth, or Distance of any Parallel of Latitude from the Equator; from whence its counted both ways to each Pole, ending in 90 Degrees, the greatest Latitude.

7. North Latitude, is on that fide of the Equator towards the North Pole and South Latitude towards the South Pole.

8. Difference of Latitude is the Breadth, or nearcft Distance of any two Parallels of Latitude; and fheweth how far one Place lies to the Northward, or Southward of the other; it never exceedeth 180 Degrees.

9. Longitude (in the Plane Chart) is reckon'd on any Parallel of Latitude, and increafeth to the Eastward, till it end in 360 Degrees, the greatest Longitude.

10. Difference of Longitude, Meridian Distance, and Departure from the Meridian, fignify (in the Plane Chart) one and the fame thing, and is the neareft Diftance of any two Meridians it fheweth how far one Place is to the Eaftward, or Weftward of another.

The Ufe of the Plane Chart.

Prob. 1. To find the Latitude of any Place in the Chart,

Rule 1. Take the nearest Distance of the Place to any Parallel or East and Weft Line.

2. Lay that Distance on the graduated Meridian, fetting one Foot of the Compaffes in the faid Parallel, and turning the other Foot the fame Way, the propofed Place lieth from it; the laft Foot fheweth the Latitude required.