EXAM. A tub is to be made that shall contain 196.5 English ale gallons, the diameter of its greater base =60 inches, and of its leffer base=36 inches; required its perpendicular depth? Anf. 30 inches. CASE 2. When the depth and the diameter of one bafe are given, to find the diameter of the other base. Multiply .7854 by the perpendicular depth, and divide the given content of the veffel in cubic inches by the product, the quotient is the fquare of a mean diameter, which confifts of the product of the two di ameters, and one third part of the fquare of their dif ference; and, when the diameter of one base is given, the other is found by the solution of a quadratic equation; thus, Put a the given diameter, the diameter fought, and S the quotient of the given content, divided by the product of the depth into .7854. = 2 Then ax+ a- =S; that is, ax+aa—2ax+xx_s 3 3ax+aa—2ax+xx=38 =35-aa+=3S 3 aa xx+ax+= 35—aa+ ad 3aa 4 4 4. Multiply the given depth by .7854, and divide the content of the veffel by the product; multiply the quo of the fquare of the given tient by 3, and fubtract diameter from the product; extra& the fquare root of the remainder, and subtract one half of the given diameter from the root; the remainder is the diameter fought. EXAM. It is required to find the diameter of the lesfer base of a tub, which fhall contain 60 ale gallons; the diameter of the greater bafe being 40 inches, and the depth 24 inches? Ans. The diameter of the leffer bafe is 18.637 inches. ift, The content of the vessel is 282×60=16920 cu. bic inches. 2d, .7854×24=18.8496 and 16920 18.8496 =897.634. 3d, 897.634×3=2692.902, and 2 of 602 is 1200. 1492.902=38.637, and 38.637-20=18.637 The content of a cafk, with the bung and head diameters being given, to find its length; the cask being of the 3d variety. Multiply the fum of the squares of the bung and head diameters by .3927, and divide the content of the cafk in cubic inches by the product; the quotient is the length of the cask. EXAM. A cafk is to be made which shall contain 109.07 English ale gallons, its bung diameter =32 inches, and its head diameter 29 inches; what must its length be? Anf. 41.99, or 42 inches. SECT. SECT. VI: NAVIGATION. DEFINITIONS and PRINCIPLES, Fig. 80. AVIGATION is the art of conducting a ship NA in the fea from one port or place to another. 2. The earth and sea constitute one fpherical body, which differs very little from a perfect globe; its diameter is about 7964 miles, and its circumference 25020 miles. 3. The earth hath two motions, one round the fun in a year, called its annual motion; and another round its own axis from west to east, once in twenty-four hours, called its diurnal motion. 4. The annual motion of the earth, is the cause of the apparent annual motion of the fun; and its diurnal motion is the caufe of the apparent revolution of the fun, moon, and fixed ftars from caft to weft in the space of twenty-four hours. 5. Several circles are supposed to be described on the terraqueous globe, and alfo in the vifible heavens, which altogether are called circles of the fphere; and thefe are either great or small. 6. A great circle divides the globe into two equal parts, as the equator, meridian, horizon, ecliptic, and vertical circles. 7. A fmall circle divides the globe into two unequal parts, as the polar circles, tropics, and other parallels of latitude and declination. 8. the poles of the globe P and S are the extremities of its axis, or, they are the quiefcent points, when the globe turns round its axis; and oppofite to thefe are the celeftial poles in the visible heavens. 9. The equator is a great circle furrounding the globe in the middle between the two poles, as ÆQ 10. Meridians are great circles paffing through the two poles, and cutting the equator at right angles, as PmS, &c. 11. The ecliptic EC is the path of the earth's annual motion round the fun, or the path of the fun's apparent annual motion round the earth; one half of it lies on the north, and the other half on the fouth fide of the equator. The fun appears always fomewhere in this circle; for, this being the earth's orbit, in whatever point the earth is, the fun is feen in the oppofite point. The fun's daily progress is near one degree. 12. The interfections, or points where the ecliptic croffes the equator reprefented by the point A, are called equinoctial points; because, when the fun appears in either of thefe, the day and night are equal. 13. The points of the ecliptic, which are farth ft from the equator at E and C, are called folftitial points; because, while the fun paffes over a fmail part of the ecliptic on each fide of these points, he is for fome time nearly at the fame diftance from the equa tor, and fo feems to ftand ftill. 14. The meridian which paffes through the equi noctial points is called the equinoctial colur, as PAS, and that which paffes through the folftitial points is called the folftitial colure, as PES. These are the only two meridians which divide both equator and ecliptic into four equal parts. 15. The ecliptic is divided into twelve equal parts, called figns, each containing 30°, namely, Ω my ရာ Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricornus, Aquarius, Pisces. 16. The Zenith Z, is that point in the visible heavens directly over the spectator's head, and the Nadir N, is the oppofite point. 17. There are two horizons, the rationl and fenfible. The rational horizon HO, is a great circle furrounding the globe in the middle between the zenith and nadir, which are its poles. 18. The fenfible or visible horizon, is the boundary of the spectator's view, and is properly a plane touching the earth in the place where the fpectator ftands. 19. Latitude on the earth, is the distance of any place north or fouth from the equator,' reckoned on the meridian. Thus ZÆ is the latitude of Z. 20. Longitude on the earth, is the distance of any place eaft or weft from the first meridian, reckoned on the equator; or the longitude of any place is the arch of the equator between the firft meridian and the meridian of that place. |