tween the index mirror and the fore horizon glass. They may be taken out when necessary, and placed at N between the index mirror and the back horizon glass. 94. This instrument which is in form an octant, is called a quadrant, because the graduation extends to 90 degrees, although the arc on which these degrees are marked is only the eighth part of a circle. The light coming from the object is first reflected by the index glass C, (Fig. 17,) and throws upon the horizon glass E, by which it is reflected to the eye at G. If the index be brought to 0, so as to make the index glass and the horizon glass parallel; the object will appear in its true situation. (Art. 92. Cor. 2.) But if the index glass be turned, so as to make with the horizon glass an angle of a certain number of degrees; the apparent direction of the object will be changed twice as many degrees. Now the graduation is adapted to the apparent change in the situation of the object, and not to the motion of the index. If the index move over 45 degrees, it will alter the apparent place of the object 90 degrees. The arc is commonly graduated a short distance on the other side of 0 towards P. This part is called the arc of excess. 95. The quadrant is used at sea, to measure the angular distances of the heavenly bodies from each other, and their elevations above the horizon. One of the objects is seen in its true situation, by looking through the transparent part of the horizon glass. The other is seen by reflection, by looking on the silvered part of the same glass. By turning the index, the apparent place of the latter may be changed, till it is brought in contact with the other. The motion of the index which is necessary to produce this change, determines the distance of the two objects.* 96. To find the distance of the moon from a star.-Hold the quadrant so that its plane shall pass through the two objects. Look at the star through the transparent part of the horizon glass, and then turn the index till the nearest edge of the image of the moon is brought in contact with the star. This will measure the distance between the star and one edge of the moon. By adding the semi-diameter of the moon, we shall have the distance of its center from the star. For the adjustments of the quadrant, see Vince's Practical Astronomy, Mackay's Navigation, or Bowditch's Practical Navigator. The distance of the sun from the moon, or the distance of two stars from each other, may be measured in a similar man ner. 97. To measure the altitude of the sun above the horizon.— Hold the instrument so that its plane shall pass through the sun, and be perpendicular to the horizon. Then move the index till the lower edge of the image of the sun is brought in contact with the horizon, as seen through the transparent part of the glass. The altitude of any other heavenly body may be taken in the same manner. 98. To measure altitudes by the back observation.-When the index stands at 0, the index glass is at right angles with the back horizon glass. (Art. 93.) The apparent place of the object, as seen by reflection from this glass, must therefore be changed 180 degrees; (Art. 92. Cor. 1.) that is, it must appear in the opposite point of the heavens. In taking altitudes by the back observation, if the object is in the east, the observer faces the west; or if it be in the south, he faces the north; and moves the index, till the image formed by reflection is brought down to the horizon. This method is resorted to, when the view of the horizon in the direction of the object is obstructed by fog, hills, &c. 99. Dip or Depression of the Horizon. In taking the altitude of a heavenly body at sea, with Hadley's Quadrant, the reflected image of the object is made to coincide with the most distant visible part of the surface of the ocean. A plane passing through the eye of the observer, and thus touching the ocean, is called the marine horizon of the place of observation. If BAB' (Fig. 13.) be the surface of the ocean, and the observation be made at T, the marine horizon is TA. But this is different from the true horizon at T, because the eye is elevated above the surface. Considering the earth as a sphere, of which C is the center, the true horizon is TH perpendicular to TC. The marine horizon TA falls below this. The angle ATH is called the dip or depression of the horizon. This varies with the height of the eye above the surface. Allowance must be made for it, in observations for determining the altitude of a heavenly body above the true horizon. In the right angled triangle ATC, the angle ACT is equal to the angle of depression ATH; for each is the complement of ATC. The side AC is the semi-diameter of the earth, and the hypothenuse CT is equal to the same semi-diameter added to BT the height of the eye. Then AC: R::TC: Sec. ACT-ATH the depression.* 100. Artificial Horizon.-Hadley's Quadrant is particulaly adapted to measuring altitudes at sea. But it may be made to answer the same purpose on land, by means of what is called an artificial horizon. This is the level surface of some fluid which can be kept perfectly smooth. Water will answer, if it can be protected from the action of the wind, by a covering of thin glass or talc which will not sensibly change the direction of the rays of light. But quicksilver, Barbadoes tar, or clear molasses, will not be so liable to be disturbed by the wind. A small vessel containing one of these substances, is placed in such a situation that the object whose altitude is to be taken may be reflected from the surface. As this surface is in the plane of the horizon, and as the angles of incidence and reflection are equal, (Art. 91.) the image seen in the fluid must appear as far below the horizon, as the object is above. The distance of the two will, therefore, be double the altitude of the latter. This distance may be measured with the quadrant, by turning the index so as to bring the image formed by the instrument to coincide with that formed by the artificial horizon. 101. The Sextant is a more perfect instrument than the quadrant, though constructed upon the same principle. Its arc is the sixth part of a circle, and is graduated to 120 degrees. In the place of the sight vane, there is a small telescope for viewing the image. There is also a magnifying glass, for reading off the degrees and minutes. It is commonly made with more exactness than the quadrant, and is better fitted for nice observations, particularly for determining longitude, by the angular distances of the heavenly bodies. A still more accurate instrument for the purpose is the Circle of Reflection. For a description of this, see Borda on the Circle of Reflection, Rees' Cyclopedia, and Bowditch's Practical Navigator. See Note I, and Table II. SURVEYING. SECTION I. SURVEYING A FIELD BY MEASURING ROUND IT. ART. 105. THE most common method of surveying a field is to measure the length of each of the sides, and the angles which they make with the meridian. The lines are usually measured with a chain, and the angles with a compass. 106. The Compass.-The essential parts of a Surveyor's Compass are a graduated circle, a magnetic needle, and sight holes for taking the direction of any object. There are frequently added a spirit level, a small telescope, and other appendages. The instrument is called a Theodolite, Circumferentor, &c. according to the particular construction, and the uses to which it is applied. For measuring the angles which the sides of a field make with each other, a graduated circle with sights would be sufficient. But a needle is commonly used for determining the position of the several lines with respect to the meridian. This is important in running boundaries, drawing deeds, &c. It is true, the needle does not often point directly north or south. But allowance may be made for the variation, when this has been determined by observation. See Sec. V. 107. The Chain.-The Surveyor's or Gunter's chain is four rods long, and is divided into 100 links. Sometimes a half chain is used, containing 50 links. A rod, pole, or perch, is 16 feet. Hence 1 Link =7.92 inches of a foot nearly. =161 = 108. The measuring unit for the area of a field is the acre, which contains 160 square rods. If then the contents in square rods be divided by 160, the quotient will be the number of acres. But it is commonly most convenient to make the computation for the area in square chains or links, which are decimals of an acre. For a square chain =4×4=16 square rods, which is the tenth part of an acre. And a square link=1×10=100 of a square chain=' ̄ ̄ ̄ of an acre. Or thus, 625 links, or 2721 feet 1 square rod, =1 chain or 16 rods, =1 rood or 40 rods, 100000 43560 =1 acre or 160 rods. 109. The contents, then, being calculated in chains and links; if four places of decimals be cut off, the remaining figures will be square chains; or if five places be cut off, the remaining figures will be acres. Thus the square of 16.32 chains, or 1632 links, is 2663424 square links, or 266.3424 square chains, or 26.63424 acres. If the contents be considered as square chains and decimals, removing the decimal point one place to the left will give the acres. 110. In surveying a piece of land, and calculating its contents, it is necessary, in all common cases, to suppose it to be reduced to a horizontal level. If a hill or any uneven piece of ground, is bought and sold; the quantity is computed, not from the irregular surface, but from the level base on which the whole may be considered as resting. In running the lines, therefore, it is necessary to reduce them to a level. Unless this is done, a correct plan of the survey can never be exhibited on paper. If a line be measured upon an ascent which is a regular plane, though oblique to the horizon; the length of the corresponding level base may be found, by taking the angle of elevation. Let AB (Fig. 30.) be parallel to the horizon, BC perpendicular to AB, and AC a line measured on the side of a hill. Then, the angle of elevation at A being taken with a quadrant, (Art. 4.) R: Cos. A::AC: AB, that is, As radius, to the cosine of the angle of elevation; |