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11. Required the dimensions of an oblong garden containing three acres, and bounded by 104 perches of pale fence ?
Answ. 40 perches by 12. 12. How many acres are contained in a square meadow, the diagonal of which is 20 perches more than either of its sides?
Answ. 14A, 2R. 11P. 13. If a man six feet high travel round the earth, how much greater will be the circumference described by the top of his head than by his feet?
Answ. 37.69 feet. N. B. The required difference is equal to the circumference of a circle 6 feet radius, let the magnitude of the earth be what it may.
14. Required the dimensions of a parallelogram containing 200 acres, which is 40 perches longer than wide ?
Answ. 200 perches by 160. 15. What difference is there between a lot 28 perches long by 20 broad, and two others, each of half the dimensions ?
Ans. 1A. 3R.
Containing the Astronomical methods of finding the Latitude, Varia
tion of the Compass, c. with a description of the instruments used in these operations.
DAY and night arise from the circumrotation of the Earth. That imaginary line about which the rotation is performed, is called the Axis, and its extremities are called Poles. That towards the most remote parts of Europe is called the North Pole, and its opposite the South Pole. The Earthi's Axis being produced will point out the Celestial Poles.
The Equator is a great circle on the Earth, every point of which is equally distant from the Poles; it divides the Earth into two equal parts, called Hernispheres: that having the North Pole in its centre is called the Northern Hemisphereand the other, the Southern Hemisphere. The plane of this circle being produced to the fixed stars, will point out the celestial Equator or Equinoctial. The Equator, as well as all other great circles of the sphere, is divided into 360 equal parts, called degrees ; each degree is divided into 60 equal parts, called minutes, and the sexagesimal division is continued.
Note. The ancients having no instruments by which they could make observations with any tolerable degree of accuracy, supposed the length of the year, or annual rnotion of the earth, to be completed in 360 days: and hence arose the division of the circumference of a circle into the same number of equal parts, which they called degrees.
The Meridian of any place, is a semicircle passing through that place, and terminating at the Poles of the Equator. The other half of this circle is called the opposite Meridian.
The Latitude of any place, is that portion of the Meridian of that place, which is contained between the Equator and the given place; and is either North or South, according as the given place is in Northern or Southern Hemisphere, and therefore cannot exceed 90°.
The Parallel of Latitude of any place, is a circle passing through that place, parallel to the Equator.
The Difference of Latitude between any two places, is an arch of a meridian intercepted between the corresponding parallels of latitude of those places. Hence, if the places lie between the Equator and the same Pole, their difference of latitude is found hy subtracting the less latitude from the greater: but if they are on opposite sides of the Equator, the difference of latitude is equal to the suin of the latitudes of both places.
The First Meridian is an imaginary semicircle, passing through any remarkable place, and is therefore arbitrary. Thus, the British esteem that
to be the First Meridian which passes through the Royal Observatory at Greenwich; and the French reckon for their First Meridian, that which
passes through the Royal Observatory at Paris. --Formerly many French geographers reckoned the meridian of the island of Ferro to be their First Meridian; and others, that which was exactly 20 degrees to the west of the Paris Observatory. The Germans, again, considered the meridian of the Peak of Teneriffe" to be the First Meridian. By this mode of rechoning, Europe, Asia, and Africa, are in east longitude ; and North and South America, in west longitude. At present, the first meridian of any country is generally esteemed to be that which passes through the principal Observatory, or chief city of that country.
The Longitude of any place is that portion of the Equator which is contained between the first meridian, and the meridian of that place: and is usually reckoned either east or west, according as the given place is on the east or west side of the first meridian; and, therefore, cannot exceed 180°.
The Difference of Longitude between any two places is the intercepted arch of the Equator between the meridians of those places, and cannot exceed 180o.
There are three different Horizons, the apparent, the sensible, and the true. The apparent or visible Horizon is the utmost apparent view of the sea or land. The sensible is a plane passing through the eye of an observer, perpendicular to a plumb-line hanging freely; And the true or rational Horizon is a plane passing through the centre of the Earth, parallel to the sensible Horizon.
Altitudes observed at sea, are measured from the visible Horizon. At land, when an astronomical quadrant is used, or when observations are taken with a Hadley's quadrant by the method of reflection, the altitude is measured from the sensible Horizon; and in either case, the altitude inust be reduced to the true Horizon.
The Zenith of any given place is the point immediately above that place, and is, therefore, the elevated pole of the Horizon : The Nadir is the other pole, or point diametrically opposite.
A Vertical is a great circle passing through the Zenith and Nadir; and therefore intersecting the Horizon at right angles.
The Altitude of any celestial body is that portion of a Vertical, which is contained between its centre and the true Horizon. The Meridian Altitude is the distance of the object from the true Horizon, when on the Meridian of the place of observation. When the observed Altitude is corrected for the depression of the Horizon, and the errors arising from the instrument, it is called the apparent Altitude; and when reduced to the true Horizon, by applying the parallax in Altitude, it is called the true Altitude. Altitudes are express. ed in degrees, and parts of a degree.
The Zenith Distance of any object is its distance from the Zenith, or the complement of its Altitude.
The Declination of any object is that portion of its meridian which is contained between the equinoctial and the centre of the object; and is either north or south, according as the star is between the equinoctial and the north or south pole.