The axis QR, of a small pencil of light from an object q, directly in front of the face BC, passes straight through this face, and falls upon the face D c, making with it an angle of 22° 30'. It is there reflected into the direction RS, and falling upon the face DA, at the same angle, is again reflected into the direction ST, perpendicular to the face AB, and consequently passes straight through this face without refraction. Looking down through the aperture in the metal plate, an image of the object q is seen at P, at a distance from A B equal to the distance of the object itself from B c; and if A в be placed, by means of the sliding rod before mentioned, at a distance from the table equal to the distance of the object from the prism, and a sheet of paper be laid upon the table at P, the apparent place of the object, as seen through the prism, will coincide with the actual place of the paper, seen through the projecting part of the aperture, and an accurate drawing of the object may be traced upon the paper. If the object Q be distant, its image may be brought nearer, and thus made to coincide with the place of the paper, by placing a concave lens before the face BC of the prism. PART III.-SURVEYING INSTRUMENTS. SURVEYING instruments may be divided into three classes: 1. Instruments for measuring distances. 2. Instruments for measuring angles. 3. Instruments for laying down the survey upon paper, or, as it is called, plotting the survey. Under the first of these classes we propose to describe 1. The chain. 2. The spirit level and levelling staves. * When a ray of light passes from a denser into a rarer medium it is refracted farther from the perpendicular to the refracting surface, so that, if be the angle which the ray in the denser medium makes with the perpendicular to this surface, and o' the angle which the ray in the rarer medium, after refraction, makes with the same perpendicular, μ sin. Ø = sin. ', the refracting power being greater than unity. If, then, the angle be increased, the angle ' is also increased, and becomes a right angle, when becomes equal to the angle whose sine is equal The ray then is re 1 μ fracted directly along the surface, and neither emerges, nor is reflected; but, if be still farther increased, the ray of light is reflected back into the denser medium, according to the ordinary law of reflection. With ordinary crown glass, for which, this takes place when exceeds 41° 49', or the ray makes with the surface an angle less than 48° 11'. Under the second we shall include 1. The prismatic compass. 3. The optical square. 2. The box sextant. 4. The theodolite. And under the third, in addition to the instruments already described in Part I. of this Work, we shall say something of 1. The large circular protractor. 2. The T square and semicircular protractor. 4. The station pointer. THE LAND CHAIN. Gunter's chain is the instrument used almost universally for measuring the distances required in a survey. For extensive and important surveys, however, such as those carried on under the Board of Ordnance, a base of about 5 or 6 miles in length is first measured by some more accurate instrument, and all the principal lines, and the distances of the extreme points, are calculated from triangles connecting them with this base. An instrument which has been known to answer well for this purpose is a steel chain 100 feet long, constructed by Ramsden, jointed like a watch chain. chain is always stretched to the same tension, supported on troughs laid horizontally, and allowances are made for changes in its length made by temperature, at the rate of 0075 of an inch for each degree of heat from 62° of Fahrenheit. This To return, however, to Gunter's chain ;—it is 66 feet, or four poles in length, and is divided into 100 links, which are joined together by rings. The length of each link, together with the 66 × 12 rings connecting it with the next, is consequently 100 inches, or 7.92 inches. To every tenth link are attached pieces of brass of different shapes for more readily counting the links in distances less than a chain. The following tables exhibit the number of chains and links in the different units of lineal measure, and the number of square chains and links in the different units of square measure, made use of in this country : A TABLE OF LINEAR MEASURES. Sq.Mile. 64,000,000 2,787,400 3,097,600 | 102,400 6,400 2,560 640 1 As, then, an acre contains 100,000 square links, if the content of a survey, cast up in square links, be divided by 100,000, the quotient gives at once the content in acres, and decimals of an acre. But the division by 100,000 is performed by merely pointing off the five last figures towards the right hand for the decimals of an acre, and the remaining figures towards the left hand are the acres in the content required. 1175 1175 5875 8225 12925 13.80625 The decimals thus pointed off being then multiplied by 4, and the five last figures pointed off as before, the remaining figures are the roods; and the five decimals cut off from this product, multiplied by 40, give the poles, or perches, and decimals of a pole, the same number, 5, of digits being again pointed off, including the zero, which arises from the multiplication by 40. Thus, if the side of a square field measured 11 chains, 75 links, or 1175 links, the area of the field would contain 1175 x 1175, or 1,380,625 square links, which is equivalent to 13.80625 acres. Then 80625 acres is equivalent to 80625 × 4, or 3.22500 roods; and, again, 22500 roods is equivalent to 22500 × 40, or 9.00000 poles. The field consequently would measure 13 acres, 3 roods, 9 poles. 3.22500 40 9.00000 Ten arrows must be provided with the chain, about 12 inches long, pointed at one end, so as to be easily pressed into the ground, and turned at the other end, so as to form a ring to serve for a handle. In using the chain marks are first to be set up at the extremities of the line to be measured. Two persons are then required to perform the measurement. The chain leader starts with the ten arrows in his left hand, and one end of the chain in his right, while the follower remains at the starting point, and, looking at the mark, or staff, at the other extremity of the line to be measured, directs the leader to extend the chain in the direction of this mark. The leader then puts down one of his arrows, and proceeds a second chain's length towards the end of the line, while the follower comes up to the arrow first put down. A second arrow being now put down by the leader, the first is taken up by the follower, and the same operation is repeated till the leader has expended all his arrows. Ten chains, or 1000 links, have now been measured, and, this measurement having been noted in the field book, the follower returns the ten arrows to the leader, and the same operations are repeated. When the leader arrives at the end of the line, the number of arrows in the fol lower's hand shows the number of chains measured since the last exchange of arrows, noted in the field book, and the number of links extending from the last arrow to the mark, or staff, at the end of the line being also added, gives the entire measurement of the line. Thus, if the arrows have been exchanged 9 times, and if the follower have 4 arrows, and from the arrow last laid down to the end of the line measure 63 links, the whole measurement 9463 will be 9463 links. 9000 400 63 To assist in preserving the line straight, as well as to serve for a check upon the number of chains measured, it is a good method to set up a staff at each ten chains, when the arrows are exchanged. In using the chain care must be taken to stretch it always with the same tension, and, as it will give when much used, it must occasionally be examined, and shortened if necessary When the ground over which the measurement is taken rises or falls, or both alternately, the horizontal distances are what we require for plotting the survey, and not the actual distances measured along the line of the ground. For many ordinary purposes the horizontal measurement may be obtained by holding one end of the chain up, so as to keep it, as nearly as can be judged, horizontal, the arrow being placed vertically under the end so held up; but, when a more accurate survey is required, the distances must be measured along the line of ground, and, the angles of elevation and depression of the several inclined parts of the line being afterwards taken with the theodolite, or the vertical risings and fallings being taken by the process of levelling with the spirit level and staves, the correct horizontal distances must thence be computed. The following table shows the number of links to be subtracted from every chain, or 100 links, for the angles there set down, being in fact the versed sines of those angles to a radius of 100. The correction for each 100 links, for any angle whatever, may at once be taken from a table of natural versed sines, by considering the first two figures as integers. The correction may also be taken from a table of natural cosines, by subtracting each of the first four figures from 9, and reckoning the first two figures as integers, and the last two as decimals: thus, to find the correction for an inclination of 8° 19′, take the first four figures of the cosine of 8° 19′, which will be 9894, and, subtracting each of these four figures from 9, we obtain 0105: then, considering the first two figures of this result as integers, and the last two as decimals, we have 1.05 for the correction due to the inclination 8° 19' for every 100 links. If the last figure in the correction thus found be increased by 1, whenever the fifth figure of the cosine is less than 5, the result will be more accurate. TABLE showing the Reduction in Links and Decimals of a Link upon 100 Links for every half Degree of Inclination from 3° to 20° 30'. The advantage of Gunter's chain is its adaptation to the superficial measure of land in acres, &c.; but, when a survey is to be made for the purpose of linear measurements only, or when it may be more convenient to compute the area in square feet, a chain 100 feet long, divided into links of a foot long, is to be preferred. Such a chain is best adapted to military surveying. Offsets, perpendicular to the main line, to hedges and remarkable objects on either side of it, are measured from the chain as it lies stretched upon the ground, by means of an offsetting staff. This staff should be 10 links in length, and |