RULE. Find the Moon's southing, to which add the point of the compass making full sea, on the full and change days, for the place proposed, and the sum will be the time required.

EXAMPLE.

I demand the time of high water at Boston, January 25th, 1786, admitting the tide to flow and ebb N. W. and S. E. on the days of change and full?

We have before found the Moon's southing to be 7h. 12m. in the morning.

h. m.

Therefore to 7 12

Add 4 0 the point of the compass, and it

Gives 11 12 in the morning, for the time of high water.
PROBLEM XIX.

To find on what day Easter will happen.

it was ordered by the Nicene Council, that Easter Sunday should be kept on the first Sunday after the first full moon, which happened upon or after the twenty first day of March, the day on which they thought the Vernal Equinox happened. Though this was a mistake, for the Vernal Equinox, that year, fell on the twentieth of March. But yet, the full moon, which fell on, or next after the twenty first of March, they called the Paschal full moon. And by the introduction of the Gregorian, or New Style, the Equinox will now always happen on the twentieth or twenty first of March. And the feast of Easter is now to be kept on the next Sunday after the Paschal full moon, or the full moon which happens after the twenty first of March; but, if the full moon happens on a Sunday, Easter day is to be the next Sunday after.

RULE. Find the age of the moon on the 21st of March, in the given year, and if it be 14, then find the day of the week answering to it, and the Sunday following is Easter Sunday; but if the

moon's age on the 21st day of March be not 14, then reckon forward to the day on which the moon's age is 14, and find the day of the week answering to that day; the Sunday following will be the day required.

N. B. On leap year take the 20th of March.

EXAMP. When does Easter happen in the year 1786? 21 of March

29 Epact.

1 No. of the month.

51

Jan.

31

33

28

5 There

Take 31 days in March. fore the first of January being Sun

13th of April, the day of the full moon, or Easter limit.

day, reckon forward 5 days, including Sunday, and you will find the 13th of April falls on Thursday, consequently the next Sunday is the 16th, which is Easter Sunday.

Easter may be found, for any future time, by the following Table which is calculated from 1753, the time of the commencement of the New Style in America, and which shews, by the Golden Number, the days of the Paschal full moons; by which, and the Dominical Letter, the day on which Easter will fall, may be found.

The Use of the Table.

First, find the Golden Number as before taught, which seek in the column of Golden Numbers under the time in which the given year is included; right against the Golden Number of the year, in the last column but one, you have the day of the month on which the Paschal full moon happens, which is the limit of Easter; from thence run your eye down among the Dominical Letters, till you come to the Letter of the given year, and against it you have the day of the month, on which Easter falls that year.

EXAMPLE. To know when Easter falls in 1786.

The Golden Number for the year being one, and the Dominical Letter A ; therefore seek in the first column (the given year being included between the years 1753 and 1899) for the Golden Number: then cast your eye along to the last column but one, under the title Paschal full and you will find the thirteenth of April to be the day of the full moon; against which, in the last column, stands E, which shews it to be Thursday, therefore the next Sunday following is Easter Sunday, which, by going down the column of Letters to the next A, you will find to be the sixteenth of April.

GOLDEN NUMBERS FROM 1753 TO 1899, AND SO ON TO 4199;

INCLUSIVELY.

15 41515) 7 112 412 4 415

9

PLANE GEOMETRY.

DEFINITIONS.

1. A POINT in the Mathematicks is considered only as a mark, without any regard to dimensions.

2. A Line is considered as length, without regard to breadth or thickness.

3. A Plane or Surface has two dimensions, length, and breadth, but is not considered as having thickness.

4. A Solid has three dimensions, length, breadth and thickness, and is usually called a Body.

5. A line is either straight, which is the nearest distance between two Points; or crooked, called a Curve Line, whose ends may be drawn further asunder.

6. If two Lines are at equal distance from one another in every part, they are called parallel Lines, which, if continued infinitely, will never meet.

7. If two lines incline one towards another, they will, if continued, meet in a point: by which meeting is formed an Angle.

8. If one Line fall directly upon another, so that the Angles on both sides are equal, the Line, so falling, is called a perpendicular, and the Angles so made, are called right Angles, and are equal to 90 degrees, each,

9. All Angles, except right Angles, are called oblique Angles, whether they are acute, that is, less than a right Angle; or obtuse, that is, greater than a right Angle.

GEOMETRICAL PROBLEMS.

PROBLEM I. To divide a Line AB into two equal parts.

Set one foot of the compasses in the point A, and, opening them beyond the middle of the line, describe arches above and below the line; with the same extent of the A compasses, set one foot in the point B, and describe two arches crossing the former draw a line from the intersection of the arches above the line, to the intersection below the

line, and it will divide the line AB into two equal parts.

PROBLEM II. To erect a perpendicular on the point C in a given line.

Set one foot of the compasses in the given point C, extend the other foot to any distance at pleasure, as to D, and with that extent make the marks D, and E. With the compasses, one foot in D, at any extent above half the distance of D and E, describe an arch above the line, and with the same extent, and one foot in E, describe an arch crossing the former ;

draw a line from the intersection of the arches to the given point C, which will be perpendicular to the given line in the point C.

PROBLEM III. To erect a perpendicular upon the end of a line.

Set one foot of the compasses in the given point B, open them to any convenient distance, and describe the arch CDE; set one foot in C, and with the same extent, cross the arch at D: with the same extent cross the arch again from D to E; then with one foot of the compasses in D, and with any extent above the

A

C

B

E

half of ED, describe an arch a; take the compasses from D, and, keeping them at the same extent with one foot in E, intersect the former arch a in a; from thence draw a line to the point B, which will be a perpendicular to AB.

PROBLEM IV. From a given point, a, to let fall a perpendicular to a given line AB.

Set one foot of the compasses in the point a, extend the other so as to reach beyond the line AB, and describe an arch to cut the line AB in C and D; put one foot of the compasses in C, and, with any extent above half CD, describe an arch b; keeping the compasses at the same extent, put one foot in D, A, and intersect the arch bin b; through which intersection, and

the point a. draw a E, the perpendicular required.

B

D