RULE. To double the square of the middle diameter, add the square of the diameter of one end; from the sum subtract four tenths of the square of the difference between these diameters; multiply the remainder by the length of the Frustum, and that product by

.2618.

PROB. 150.-To find the cubic contents of the middle or lower FRUSTUM of a Pyramid, or Cone.

RULE.-Multiply the areas of the two bases, or ends, together; to the square root of the product add these two areas, and multiply the sum by one third of the height or length of the Frustum.

PROB. 151-To find the cubic contents of an IRREGULAR BODY whose dimensions cannot be taken. RULE. Put the body into a regular vessel, and pour in as much water as will just cover it; then take out the body, and measure how much the fall of the water is, and so find the cubic contents of that part of the vessel.

NOTE. The body and the vessel must both first be wet, so that no water may be absorbed by either.

GAUGING.

GAUGING is the art of finding the contents of boxes, tubs, casks, or other vessels. The contents are taken in cubic inches, or feet, or yards, &c. Divide the cubic inches by 231 for the contents in Wine gallons, by 282 for Ale or Beer gallons, by 265.8 for Dry gallons, and by 2150.4 for Bushels.

or Beer gallons; by 265.8 for Dry gallons, and by 2150.4 for Bushels.

NOTE. Finding the mean diameter reduces the cask to a Cylinder. The above is the rule generally followed by gaugers; but the following is far more accurate, and may be used for any cask of any vari ety. The arca in gallons is found by dividing the area in square inches by the number of cubic inches in a gallon.

RULE 2.-Add into one sum the areas in gallons of four circles; one, corresponding to the diameter of the middle of the cask; another to the diameter of the end, and the four others, each corresponding to the diameter at half the distance from the middle to the end; (all inside diameters ;) multiply the sum by the length of the cask; one sixth of the product is the content in gallons.

PROB. 153. To find the ULLAGE of a cask.

NOTE.-The Ullage is what the cask contains when only part full. It is found in two positions, viz.:~ when the cask is lying on one side; and when standing on one end. As in the latter position the Ullage can be far more accurately found than in the former, we shall only give a rule for the latter.

RULE.-Multiply the difference between the squares of the middle, and end diameters, by the square of the distance of the surface of the liquor from the mid dle of the cask; divide the product by the square of half the length of the cask subtract one third of the quotient from the square of the middle diameter; multiply the remainder by .7854, and that product by the distance of the surface of the liquor from the middle of the cask; the last product is the quantity (in cubic inches) above, or under half the content of the cask, according as the cask is more or less than half full. PROP. 154. To gauge a SHIP, or to find its TONNAGE OR BURTHEN.

Mensuration of Solids and Gauging are nearly the same thing. If a person understands the former, a knowledge of the latter may be acquired with few or no instructions. The contents of most vessels are found by the rules for finding the solidity or cubic contents of the Frustum of a Cone, Globe, Spheroid, Conoid, Spindle, or Pyramid. The art of gauging is principally confined to casks, as Barrels, Hogsheads, NOTE 1.-There is such a variety in the form of &c. Gaugers generally divide all casks into four va- Ships, that no general rule can be given that will an rieties, which depend upon the curvature of the staves.swer in all cases; the following is the most common. In the 1st variety, the staves are straight, or nearly so, from the middle of the cask, to the head, or end, and the cask is in the form of two equal Frustums of two equal Cones, whose larger bases or ends are placed together.

In the 4th variety, the staves are as bulging, or nearly, or quite as much curved, or arched from the middle to the end, as they can be, and are a part of an entire circle, and the cask is in the form of a part (the middle frustum) of a globe or sphere.

The other varieties have a curvature intermediate between these. The Gauger must determine by his own judgment to what variety the cask belongs."

In the 2d variety, the cask is in the form of the middle frustum of a Parabolic Spindle. There are more casks of this variety than of any other variety. In the 3d variety, the staves are a part of an entire ellipse or oval, and the cask is in the form of a part the middle frustum) of a spheroid.

In order to determine the contents of a cask, the following dimensions of the inside of it, must first be taken in inches and decimal parts. 1. The bulge or middle diameter. 2. The end or head diameters. 3. The perpendicular length or height.

In taking these dimensions, the Gauger will have to exercise his judgment in determining the thickness of the staves. A deception is sometimes practised in the formation of casks, by making the ends of the staves, and the bung stave and one opposite to it, thinner than the rest; by this means, if great care is not taken, the true dimensions will not be obtained. The Gauger should also examine carefully whether the ends or heads of the cask are truly circular and equal if not, a proper allowance must be made.

PROB. 152.-To gauge, or find the content of any

CASK.

RULE.-If the cask is of the 1st variety, multiply the difference between the bulge or middle diameter, and the head or end diameter, by .55

If of the 2d variety, by .6-
If of the 3d variety, by .65-
If of the 4th variety. by 7-

Add the product to the head or end diameter: the sum is the mean, or average diameter of the cask Multiply the square of the mean diameter by .7854, and the product by the length of the cask, the last product is the content of the cask in cubic inches, which divide by 231 for Wine gallons; by 282 for Ale

RULE 1.-Take the dimensions in feet: multiply the length of the keel by the breadth of the ship at the midship bend; multiply this product by the depth of the hold; divide the last product by 95 for mer chant ships, and by 100 for ships of war; the quotient is the burthen in tons.

RULE 2.-The weight of a ship's burthen. is half tire weight of the water she will hold.

NOTE 2.-It is found that the weight of a cubic foot of pure water at a mean temperature, (55° Fahrenheit) is just 624 lbs. Avoirdupois; and any moderate change in temperature, will but insensibly affect the accuracy of this result.

[The following Problems were accidentally omitted in their proper place; they are therefore inserted here.] PROB. 155. To construct a HORIZONTAL DIAL, for any place.

RULE.-On any centre describe a circle, and draw a radius to the north part of it, for a meridian, or noon line: to find the angle, the shadow, or the edge of the shadow, makes with the noon line at any time before, or after noon, proceed as follows by Trigonometry. To the sine of the latitude of the place, add the tangent of as many degrees as are equal to the time from noon; from the sum subtract radius, and the remainder is the tangent of the angle required.→ In this manner find the angles or arcs for the hours, half hours, &c. and mark them on the edge of the diagram. It will not be necessary to make the calcu lations to beyond 6 hours from noon, for the distances from 12 to 6 in the forenoon, are the same as from 12 to 6 in the afternoon; and if the hour lines be continued through the centre of the dial they will point out the opposite hours.

An erect South Dial is made in the same way, only instead of the latitude, take the complement of lati tude of the place, and set the forenoon hours on the Erect Dial, where the afternoon hours are on the Horizontal Dial; and the afternoon hours on the Erect Dial where the forenoon hours are on the Horizontal Dial. Fix the Erect Dial for use, so that the plane of its face or plate shall be perpendicular to the horizon, and in a due east and west direction; and the wire for the gnomon, or the edge of the gnomon if it is a triangular plate, in both Dials, will be parallel to the axis of the earth.

PROB. 156.-To find the time when the Sun or any other Heavenly Body is due East, or West, at any given place.

RULE.-Add the Co-Tangent of the Latitude of the given place, to the Co-Tangent of the distance of the body from the Pole of the Hemisphere, in which the given place is situated; subtract Radius from the sum; the remainder is the Co-Sine of the distance of the body from the meridian: this distance changed into time, shows how much before, or after, the body passes the meridian, it is due E. or W.

its declination, and the Latitude of the given place' are of the same name: but if they are of different names, add the declination of the body to 90°.

PROB. 157. To find the AMPLITUDE of any HEAVENLY BODY.

RULE. AS Radius is to the Co-sine of the Latitude of the place. so is the Sine of the declination of the NOTE.--The distance of a body from the pole of body, to the Sine of the Amplitude; which will be of the hemisphere, in which the given place is situated, the same name (North or South) with the declinais found by subtracting its declination from 90°, when tion.

GLOSSARY,

OR EXPLANATION OF ASTRONOMICAL AND MATHEMATICAL TERMS, A KNOWLEDGE OF WHICH IS THE FOUNDATION OF ASTRONOMY.

[The index shews where other definitions are given.]

Air; atmosphere, a fine invisible elastic fluid, surrounding the earth on all sides, and extending several miles above its surface.

Altitude; height, or elevation in degrees, &c. above the horizon.

Amplitude; distance in degrees, &c. of a body at rising or setting, from the east or west.

for several months in summer. The northern includes the north frigid zone, and the southern the south. They are as far from the poles as the tropics are from the equator; their places, and also the places of the tropics, are determined by the obliquity of the ecliptic or the sun's greatest declination.

Argument; a quantity by which another quantity or equation is found.

Arithmetical complement of a number; the differbetween the number and an unit, with as many ciphers annexed to it as there are figures in the number.

Analemma; a figure on the artifical globe drawn from one tropic to the other; on it, are the months and days of the months corresponding to the sun's declina-ence tion for every day in the year. On some globes it shows also the equation of time for every day in the year.

Angle; corner; meeting of two lines in a point; or the opening between two lines or planes that meet. Angles are greater or less, according as the opening of the lines that form them, is greater or less: they are of three kinds; viz. right, acute, and obtuse; a right angle is when the lines are perpendicular to each other, or so situated that if a circle is described round the angular point, 90 degrees of the circle, or one quarter of it, is contained between the lines; an acute angle is less than a right angle; or it is such that if a circle is described round the augular point, less than 90 degrees of it are contained between the lines; an obtuse angle is greater than a right angle, or contains more than 90°. When three letters express an angle, the angular point is at the middle letter.

Anomaly; distance in degrees, &c. from the apogee. Antarctic circle; a circle parallel to the equator round the south pole, 23° 28 from the pole.

Antipodes; inhabitants of the opposite side of the earth, whose feet point directly towards our feet. If two places are Antipodes to each other, the difference of their longitude is 180°, and one is in the same latitude north, that the other is, south: it is noon at one when it is midnight at the other; and it is summer at one when it is winter at the other, if the places have summer and winter.

Artificial numbers; a series of numbers that do not increase regularly by constantly adding one.

Ascending signs; those the sun is in while his meridian altitude is daily increasing; that is, those signs the sun is in while he ascends higher and higher every day at noon.

Ascension, right; the distance east on the equinoxial from the first point of aries; or the time any body comes to the meridian after the first point of aries.

Ascension, oblique; the time any body rises after the first point of aries. The ascension in time may be changed into degrees, &c. by reckoning 15° to an hour.

Ascensional difference; the difference between right ascension and oblique ascension. It shows how much less or more than 6 hours, a body rises before it culmi

nates.

Aspect; the distance in longitude between two bodies; or the situation of one body with respect to another as seen from the earth.

Asteroids; four small primary planets lately discovered between the orbits of Mars and Jupiter.

Astronomical time; time reckoned from the noon of one day up to 24 hours, to the noon of the next day; this December 24th. 22h. 50 minutes, astronomical time, is December 25th, 10 h. 50m. morning in common reckoning, or civil time; that is the astronomical day be gins at noon and is not divided into evening and mornAntaci; people, or two places in the same longi-ing, but is reckoned on from midnight to 13 hours, 14 tude and at the same distance from the equator, but hours, 15 hours, &c. or 13 o'clock, 14 o'clock, 15 o'clock, one north and the other south. If two places are An- &c. up to 24 o'clock, or 24 hours, the noon or beginning tæci to each other, it is winter at one when it is sum of the next astronomical day. Any astronomical day mer at the other; but their time before or after noon is is made up of the last 12 hours of the same civil day, the same. and the first 12 hours of the next civil day.

Aphelion, or Apogee; the point in a planet's orbit which is at the greatest distance from the body the planet moves round.

Apparent; when applied to time, it is the time shown by the sun.

Apsides, line of the; a right line from the apogee to the perigee; a right line through the foci of an ellipse or orbit from one side of it to the other.

Apsis; either apogee or perigee.
Aquarius; the 11th sign of the ecliptic.
Arc, or arch; any part of the circumference.
Aries; the first sign of the ecliptic; the first point
of aries, is where the sun is at the vernal equinox.
Aries is also a constellation of the zodiac.

Atmosphere; the air that surrounds the earth. Attraction; the power of one body to draw another towards it.

Austral; southern.

Aurora; the morning, or the morning twilight.

Axis; a line through the centre of a body, round which the body turns, or revolves; the axis of the earth continued to the heavens is called the axis of the heavens. The axis of any circle, as the ecliptic, or the axis of the moon's orbit, &c. is a right line through the centre of the circle and perpendicular to the plane of the circle.

Azimuth; the distance of a body in degrees, &c, from the meridian, or from the south or north point of the horizon.

Arctic Circle; a circle round the north pole 23° 28′ from the pole. The arctic and antarctic circles are frequently called the polar circles. Within them the sun does not rise for several months in winter, nor setCancer; the 4th sign of the ecliptic.

Body; the word is used to signify either, or any, of the celestial orbs.

Capricorn; the 10th sign of the ecliptic. Cardinal Points; east, west, north, and south points. Celestial Poles; the earth's axis produced to the heavens.

Centrifugal force; projectile force; or tendency of a body to move forward in a straight line.

Centripetal force; the power or force by which a body is attracted, or drawn towards another body, or point, round which it revolves; gravity; attraction; or the tendency of a body to move to the centre of gravity, or to the centre of its motion. The centrifugal and centripetal forces balance each other, and cause the planets to move in circles or ellipses.

known very nearly during the next cycle. That 8, if the various calculations respecting any planet, are made accurately for any given year, these calcula tions will answer very nearly for the year found by adding the planet's cycle to the given year, (the transits of Mercury and Venus excepted.) The Cy cle of Mercury is 79 years; Venus 8 years; Mars 79 years; Jupiter 83 years, and Saturn 59 years: the other planets not being visible to the naked eye, their cycles are not computed.

Cycle of the Sun; 28 years; after which the same days f the month return to the same days of the week; and the Sun's place to the same degrees and minutes of the ecliptic as on the same year of the preceding cycle, or 28 years before; except when inter rupted by the omission of a leap year. In the year of Christ, 1, the cycle of the sun was 10.

Chord: a right line from one end of an arc to the other. The sine of an arc of 90°, the chord of 60°, and the tangent of 45, are each equal in length to the radius of the circle of which the arc is a part. The Cycle of the Moon; or Golden Number; 19 years; ccant of the smallest arc, is as long, and a little after which the new and full moons, and other aspects longer than the radius. The tangent of a small arc, is of the moon, return to the same days of the month only a little longer than the arc; the secant and tan-(when five leap years are included,) as on the same gent both increase in length as the are increases, till year of the preceding cycle, or 19 years before, This the arc is 90°; when the secant and tangent extend in was discovered by Meton 432 years before Christ, and length to infinity. on this account is sometimes called the Metonic CyCircle; a round figure bounded by a curve line call-cle. In the year of Christ 1, the Golden Number was 2 ed the circumference; circles of the spliere are of two kinds, great and small; a great circle divides the sphere into two equal parts, a small circle into two unequal parts.

Circle of illumination; the circle that divides the enlightened from the dark hemisphere.

Cylinder; a round figure or solid, of equal size from end to end; as a round column, or a rolling stone of a garden, or a piece of stove pipe; whose bases or ends are circles, and parallel and equal.

Declination; nearest distance in degrees, &c. from the equator, or from the plane of the equator: decli nation in the heavens corresponds to latitude on the

Circumference; periphery; the bounding line of a circle; every part of the circumference is equally dis-earth. tant from a point within the circle, called the centre. The circumference of every circle is supposed to be divided into 360 equal parts called degrees; each degree into 60 equal parts called minutes, and each minute into 60 equal parts called seconds.

Colures; those two meridians or great circles, which pass through the equinoxial and solstitial points of the ecliptic.

Degree; the 360th part of the circumference of a circle; or the 90th part of a quadrant. A degree is of no determinate length; but the 360th part of any cir cle, whether great or small.

Diagonal; a right line between two opposite angles. Dial; an instrument to show the hour of the day by the sun. A horizontal dial is a diagram drawn on any level plane, with a stile or index, or gnomon, to cast a shadow to the different hours of the day markstraight wire from the centre on which the diagram is Complement of an arc, or of an angle; what it drawn, towards the pole of the heavens; or making wants of 90°.

Comet; a blazing star, a planet with a vapour-like appendage, or luminous train, or tail, moving rounded on the edge of the diagram. The gnomon is a the sun in a very eccentric orbit.

an angle with the horizon equal to the latitude of the Concave: hollowing in a circular manner. place or the gnomon may be made of a thin plate of Cone; a circular figure or solid, growing propor-brass, or thick tin, in a triangular form, and so fitted tionably smaller till it ends in a point; and may be as to fill up the space occupied by the wire, and be represented by a tapering pole or round stick of tim- tween the wire and the meridian, or noon line. ber; the plane of the base being perpendicular to a Dichotomized; halved; a term applied to the right line from its centre to the vertex, or small end. moon when she is in her quadratures. Conjunction; meeting, or coming together, or being in the same part of the heavens; or being in the same direction from the earth; or in the same longitude, though not always in the same latitude. Each of the inferior planets has two kinds of conjunction with the sun, viz. Inferior and Superior. Inferior is the conjunction when the planet is between the earth and the sun; Superior is the conjunction when the earth is on one side of the sun, and the planet on the other.

Constellation; properly an assemblage, or collection of stars in the immediate neighbourhood of each other.

Convex; protuberant; swelling out in a circular 'thanner.

Cube; a square solid of six sides, all equal. The 3d power, or root.

Culmination of a body; passing the meridian, or the highest point of the body above the horizon. Culminate; to pass the meridian.

Cycle; a period of time in which the same phenomena er circumstances of a body begin to occur again in the same order.

The Cycle of a Planet is a number of years, during which, the planet passes through all its various posi tions with respect to the sun and earth; that is, the Cycle is the time from the planet's leaving some particular position with respect to the sun and earth, till its return to the same again on the same day, and at the same time of the day, (very nearly,) of some future year. All the different aspects of the planet, times of rising, setting, and coming to the meridian of any place, occur during the time of the cycle; and all these positions happen in the same order, and on the same days of the month, and nearly at the same times of the day, during the next cycle; so that if these are known, for every day of one cycle, they are

Diameter; a right line from one side of the cir cumference of a circle, through the centre, to the other side.

Digit; the 12th part of the diameter of the Sun, or Moon.

Direct; according to the order of the signs. Dyonisian Period; 532 years; found by multiply. ing the cycle of the Sun by the Golden Number. Disk; the body, or round flat face, or surface of the Sun or Moon, as seen from the earth; or of the earth, as seen from the Sun or Moon.

Diurnal Arc; the arc, or time of a body from its rising to its setting; or while the body is above the horizon.

Dominical Letter; or Sunday Letter: the letter that stands in the calendar, against the Sundays of the year; found by setting the first seven letters of the alphabet against the seven days of the week; A against the first day of the year; B, against the second day, &c., and then repeating the same through the year.

East; the point of the horizon, or the heavens, on the right hand when we face the pole star, equally distant from the north and south.

Easter Day; as now celebrated, is always the first Sunday after the Paschal, or mean Full Moon, which happens on, or next after the 21st of March: and if the Full Moon happens on Sunday, Easter Day is the Sunday after. Easter means to rise; it was the Sunday next after the Paschal Full Moon, on which Christ arose from the dead.

Eccentric; elliptical; deviating from a circle into an ellipse or parabola.

Eccentricity; distance from the centre of an ellipse to either of its foci.

Ecliptic; the earth's orbit; or the path in which the earth moves round the Sun'; or the path in which

the San appears to move round the earth, once a year: the plane of the earth's orbit: on the artificial globe. it is a great circle crossing the equator at an angle of 23 28'; and divided into signs and degrees.

part of the equator is equally distant from the poles. It divides the earth into two equal parts, called the Northern and Southern Hemispheres.

Equinocial Points; the first point of aries and the first point of libra; that is, those points of the ecliptic where the plane of the equator cuts, or intersects the ecliptic.

Equinox; the time the Sun enters either of the . Equinoxial points; the Spring Equinox is called the Vernal Equinox; and the other, the Autumnal Equinox: at these times the days and nights are equal all over the world.

Era, or Epoch; a particular point, or date of time, from which events are reckoned.

Evection; an inequality in the motion of the moon, by which, at her quarters, her mean place differs from her true place, by about 2 more than at her syzygies. Firmament; the heavens, or orb of fixed stars. Fixed Stars; those stars which always preserve the same situation with regard to each other. They all probably resemble the sun in matter and magnitude, and are each the centre of a system similar to the Solar System. In some of them, there has been discovered a very slow (indeed) motion, called their proper motion; whence it is conjectured that not only the bodies belonging to the innumerable systems of stars, are in motion round their respective centres, but that all the systems of bodies in the universe, are themselves in motion round some common centre; and that thus they are prevented from approaching each other, which, from their mutual attraction, they must otherwise do.

The Longitude of the earth, or the place of the earth in the ecliptic, is always the opposite point to that in which the sun appears. About the 21st of March the earth enters the 1st degree of Libra, an I the sun being always 6 signs distant, enters the 1st degree of Aries: this is the Vernal Equinox in the northern hemisphere: the sun is now vertical at the equator, and about to pass north of it. While the earth passes through Libra, Scorpio, and Sagittarius, the sun passes through Aries, Taurus and Gemini; these last are called Spring signs. because the sun is in them in the spring months. About the 21st of June, the earth enters the 1st degree of Capricorn, and the Sun the 1st degree of Cancer: this is the Summer Solstice in the northern hemisphere; the sun is now vertical at the northern Tropic, and ahout to commence his return to the south. As the earth passes through Capricorn, Aquarius, and Pisces, the Sun passes through Cancer, Leo, and Virgo: these last are called Summer signs, because the sun is in them in the Summer months. About the 23d of September, the earth enters the 1st degree of Aries, and the Sun the 1st degree of Libra: this is the Autumnal equinox in the northern hemisphere; the sun is now vertical at the equator, and about to pass south of it. As the earth passes through Aries, Taurus, and Gemini, the Sun passes through Libra, Scorpio, and Sagittarius; these last are called Autumnal signs. About the 22d of December, the earth enters the 1st degree of Cancer, and the sun the 1st degree of Capricorn; this is the Winter Solstice in the northern bemisphere; the sun is now vertical at the southern Tropic, and about to commence his return to the north. While the earth passes through Cancer, Leo, and Virgo, the sun passes through Capricorn. Aquarius, and Pisces: these last are called Winter signs. Aries, Taurus, Gemini, Cancer, Leo, and Virgo, are called northern signs, because the sun while in them, is north of the equator; the others, Libra, Scorpio, Sagittarius, Capricorn, Aquarius, and Pisces, are called southern signs, be cause the sun while passing through them is south of the equator Capricorn, Aquarius, Pisces, Aries, Taurus, and Gemini, in the northern hemisphere, are called Ascending signs; because the sun while in them is daily ascending to the north: his meridian altitude is daily increasing, or he is daily ascending higher and higher above the horizon at noon. The others, Cancer, Leo, Virgo, Libra, Scorpio, and Sagit-into two branches, and again unites, the Shield of tari:6, are called Descending signs.

Egress; coming out; emersion.

Element; fundamental principle; arguments terial time or quantity, by, or from which something else is found.

Elevation; height, or altitude.

Foci, the plural of Focus; the points round which an ellipse is drawn.

Focus; one of the points round which an ellipse is drawn.

Frigid Zone; the portions of the earth around the poles within the polar circles.

Frustum; a piece cut off from a regular figure by a plane parallel to the base: or it is what remains after a piece is cut off of each end of a regular figure.

Galaxy the milky way; a girdle of white light, or luminous zone, which makes a complete circle in the heavens. Beginning at the head of Cepheus, it traverses the constellations Cassioepia, Perseus, Auriga, the east shoulder of Aries, the feet of Gemini, the great Dog, the middle of the Ship, where it is most luminous, the Centaur, the Cross, the Southern Triangle, the Altair, the tail of Scorpio, the bow of Sagittarius, a part of Ophincus, where it separates

Sobieski, the Serpent, the Eagle, the Arrow, the Fox and Goose, and the Swan, to where it began. This rema-markable belt has maintained the same position in. relation to the Stars, from the earliest ages of antiquity; and when examined through powerful glasses, (strange as it may appear,) is found to consist entirely of fixed stars, scattered by millions, like glittering dust, on the dark back ground of the general heavens. Geocentric; as seen from the earth; as respects the earth.

Ellipse or ellipsis; an oval, or oblong circle. To describe an ellipse, see Problem 110. That diameter of an ellipse which passes through the foci, is called the conjugate diameter: the diameter perpendicular to this, and which passes through the centre of the ellipse, is called the transverse diameter.

Elongation; angular distance of a planet from the Sun, as seen from the earth.

Emersion; re-appearance; or coming out from obscurity; the appearing of a body from behind another body, or from out of the shadow of another body.

Epact; the age of the moon at the commencement of the year; or the number of days since the time of the lust mean new moon. NOTE. The age of the moon to the nearest day in our Almanacks is generally reckoned from the time of true new moon. The true new moon sometimes differs about 14 hours from the mean; therefore the age of the moon on the first day of the year as put down in the Almanack, sometimes differs a day from the Epact. The foundation of the Epact is the difference between the Solar year and the Lunar year. This difference is about 11 days; that is 10 days, 21 hours, 0 minutes, 15 seconds; found by subtracting 12 Lunations, or 354 days, 8 hours, 49 minutes, 34 seconds, from the Solar year, 365 days, 5 hours, 48 minutes, 49 seconds.

Equation; a quantity to be applied to mean time, place, or motion, in order to find the true.

Equator, or Equinoxial; a circle round the centre of the artificial globe; or an imaginary great circle Found the centre of the earth from east to west. Every

Gibbous; the shape of the enlightened part of the moon, between the first quarter and the full, and the full and the last quarter.

Globe; a round substance; a circular body; a ball or sphere: an artificial globe is a round body fitted up with appurtenances, by which many astronomical problems may be performed; there are two kinds, the Terrestrial, and Celestial; the Terrestrial globe exhibits the earth with its natural and political divisions: the Celestial, the firmament of Constellations and Stars. In using the globes. set them level, and so that the plane of the meridian may extend north and south; and stand on the east side. In inspecting the representations on the globes, the eye is supposed to be at some point on, or over the Terrestrial, and in the centre of the Celestial.

Golden Number; the Cycle of the Moon.

Gravitation; or gravity; attraction, or that power at or near the centre of the earth, that draws every thing about the earth towards it; the nature of this power, or what it is, has never been discovered. Harvest Moon; the Full Moon nearest the autumnal equinox.

Heliocentric; seen from the sun.

Hemisphere; half the globe; or half the celestial sphere.

Horizon, sensible; the level of any place; or the

circle round the place where the earth and sky appear to meet; or it is the plane of this circle.

Horizon, rational; the plane of a circle round the centre of the earth, dividing the earth into two equal hemispheres. The rational horizon is parallel to the Bensible horizon at the distance of the semi-diameter of the earth from it. The horizon of the artificial globe (representing the rational horizon of the earth) is a broad flat ring on which are drawn several concentric circles, as the circle of the signs and degrees of the ecliptic, and of the days of the month answering to each degree of the sun's place in the ecliptic, &c. Though the rising and setting of the heavenly bodies respect the rational horizon, yet it holds true also of the sensible horizon, (within a few seconds,) the distance of these bodies being so great, (except the moon,) that the earth's semi-diameter seen from them is no more than a point.

"Horizontal; level; or parallel to the horizon. Immersion; the disappearing of a body behind another body; or in the shadow of another body. Inclination; angle.

Index; a moveable hand on the pole of the artificial globe, fixed to point to the hours of the day in a circle round the pole.

Ingress; entrance.

Julian Period; 7980 years; found by multiplying the Cycle of the Sun, the Golden Number, and the Roman Indiction together. The Julian Period began 706 years before the supposed time of the creation, for no later could the three cycles of which it is composed begin together. The birth of Christ was 4713 years after the commencement of this period.

Neap Tide; the least Flood and Ebb Tide. Nocturnal arc; arc described below the horizon. Nonagesoimal degree; highest point of the ecliptic above the horizon; which is 90° from either point of the horizon that is cut by the ecliptic.

North; the point of the horizon or the heavens in front of us when we face the pole star, as far from the point where the sun rises, as from the point where it sets on the 21st of June, or 21st of December. Node; the point of the Moon's, or a planet's orbit, that is cut, or intersected by the plane of the ecliptic. There are two Nodes; the one where the body as cends above, or to the north of the plane of the eclip tic, is called the Ascending Node; the other, the Descending Node.

New Style; that reckoning or computation of time, whereby every fourth year is a leap year, with the exception of 3 leap years in every 400 years. (See Leup Year.)

Number of Direction; a number of days which being added to the 21st of March, shows on what day either of March or April Easter Sunday falls.

Oblique; acute; or obtuse; indirect; not perpendicular.

Obliquity; deviation from parallelism; or from perpendicularity.

Occultation; an eclipse of a star, or planet; or the disappearance of a star or planet behind the moon ; or behind a planet or comet.

Octant; the aspect of two planets when they are 45° apart.

Old Style; that reckoning or computation of time when every fourth year is a Leap year. (See Leap Year.)

Opposition; opposite part of the heavens; two bodies are in opposition when their difference of lon

Julian Years; years of exactly 365 days; or years when every 4th year is a leap year, without interruption. Latitude of a place on the earth; the distance of the place in degrees, &c. north or south of the equa-gitude is 180°. tor. The distance from the equator to the pole being 90°, latitude can never exceed this.

Latitude of a celestial body; the distance in degrees, &c. of body, from the nearest part of the plane of the ecliptic.

Leap Year; (see page 28.).

Leo; the 5th sign of the ecliptic.
Libra; the 7th sign of the ecliptic.

Libration; the moon revolves round her axis in the same time she revolves round the earth, and consequently she always presents nearly the same side or hemisphere to the earth: her motion on her axis being always uniform and equal, and her motion in her orbit unequal, or accelerated and retarded monthfy, small portions of her eastern and western limbs appear and disappear alternately; this periodical oscil lation of her disk, is called the Libration of the moon. Line; what has length but no breadth; and is generated by the motion of a point.

Line of equal parts; see scale of equal parts. Longitude of a place on the earth; the distance of the place in degrees, &c. east or west of some particular meridian.

Longitude of a heavenly body; the distance of the body from the first point of Aries, reckoned on the ecliptic in signs, degrees, &c., according to the order of the signs, or from west to east, quite round to the first point of Aries again.

Orbit; path in which one body moves round another.
Oriental; eastern, or morning.

Oval; elliptical; the shape of the planets' orbits. Parabola; an ellipse whose foci are at an immense, or infinite distance from each other.

Parabolic Conoid; half of an Oblong Spheroid: the spheroid is divided by a plane to which the longer axis or diameter is perpendicular,

Parabolic Spindle; a figure or solid which will just fill the space occupied by a Parabola in revolving round its longer axis, or diameter.

Parallax of a body; the difference of the place of a body as seen from different points of view; as from different stations on the earth; or from the earth in different parts of its orbit; or Parallax is the angle at the body formed by two lines drawn from different places on the earth, or from different points in the earth's orbit. The relative places of bodies are always reckoned with respect to their centres. The apparent place of a body is where it appears as seen from the surface of the earth; the true place is where it would appear if it could be seen at the same time from the centre of the earth: Diurnal Parallax is the difference between the apparent and true place of a body; or it is the angle formed at the body by two lines, one drawn from one end of a semi diameter of the earth, and the other from the other end; it is evident that the Diuinal Parallax is greatest, when the body is in the horizon; and nothing when the body is in the zenith; and that the apparent place is always below the true place, except when the body is in the zenith. Horizontal Parallax is the Diurnal Parallax of a body in the horizon; or it is the semi-diameter of Mean; average, or middle; equal. the earth's disc as seen from the body. Annual Pa Meridian; the south, the zenith, or the north part rallax of a body, is the difference between the appaof the heavens; a line, or great circle of the sphere, rent place of it, as seen from different parts of the from north to south; or the plane of such a circle earth's orbit; or it is the angle at the body formed by passing through the poles of the earth, the zenith and two lines. one drawn from one side of the earth's orbit, nadir, and continued to the heavens. Every place on and the other drawn from the opposite side. It is ob the earth has its meridian, which is an imaginary cir-vious that the greater the distance of the body, the cle, or the plane of a circle passing through the place, the poles, the zenith, and the nadir, and the north and south points of the heavens. At noon at any place, the sun is on the meridian of that place: the meridian of the artificial globe is a hoop in which the globe is bung, and turns.

Lunar Month; the time from one New or Full

Moon to the next.

Lunation; 29 days, 12 hours, 44 minutes, 3 seconds: the mean or average time from one New, or Full Moon, to the next.

Milky-way; the Galaxy. Minute; the 60th part of an hour; or the 60th part of a degree: 60 seconds.

Nadir; a point in the heavens directly opposite the zenith; the point of the heavens, under our feet, on the opposite side of the earth.

less is its Parallax. The fixed stars are, all of them, at such an immense distance from us, that they have no sensible Diurnal, or even Annual Parallax.

Parallel; continued in the same direction at the same distance.

Parallelopipedon; a regular square solid, as a stick of timber, or a plank, whose opposite sides and ends are equal.

Paschal Full Moon; the mean Full Moon which happens on, or next after, the 21st of March: 80 call ed, because on the day it happened, the Jewish Feast of the Passover was eaten.