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desirable; and these readings, being entered both as back and fore readings, will produce the same effect as back and fore readings of the same points obtained in different positions of the instrument. The distances from the instrument of these points should be omitted from the second column; but, the distances between them being entered successively in the first column, their respective distances from the instrument may at any time be determined, if required. The height of the in strument itself may be entered in this way as an intermediate sight; and, as the same height that is added as a back reading is subtracted again as a fore reading, any error in this reading will not at all affect the levels afterwards taken, and, provided it be not greater than the limit within which distances can be laid down and estimated upon the plot, is of no moment Now, in taking the section of a line of any considerable extent, the scale is seldom sufficiently large to admit of less than six inches being laid down or estimated upon the plot, and conse quently an error of two or three inches in the intermediate sights would be immaterial. When observations are made out of the line, to be levelled, in order, for instance, to obtain the height of this line above neighbouring rivers, canals, roads, &c., the readings are to be entered in the same manner as for other intermediate sights; and, the column of bearing and distance being left blank, no mistake can be made in drawing the section. The bearing and distance of such points, if desirable to be noted, must be entered in the space left for remarks.

For the purpose of reference on any future occasion, in order either to check the accuracy of the levels already obtained, or for the convenience of commencing a new series in some other direction, marks should be left upon some convenient fixed points upon which the staff has been held, and the reading noted with the greatest possible care. These bench marks, as they are called, should ordinarily be left at about every half-mile of distance, and may be either on or off the line. In the latter case the readings are to be recorded in the manner already explained for points out of the line. The hooks and tops of gates, copings, sills, or steps of doors, &c., are commonly used for bench marks, and the mark must be made exactly on the point upon which the staff has been held. A stout stake may be driven into the ground for a bench mark, and is by many persons preferred to any other.

When a section of considerable length is to be plotted, the horizontal distances cannot be laid down on as large a scale

as is necessary for the vertical heights above datum, in order that the section may be of any practical use, without making the plot of most unwieldy dimensions. It is therefore usual to make the vertical scale much larger than the horizontal one: thus 4 inches to a mile for the horizontal distances, with one inch to 100 feet for the vertical distances, is a usual combination. In the accompanying figure we have drawn the portion of a section from the portion of the field book at page 109, making use of a scale of 1 inch to 800 feet for the horizontal distances, and of a scale of 1 inch to 200 feet for the vertical distances

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A G is ruled for the datum line; on it are set off from A, the horizontal distances at the points B, C, D, E, F, G, according to the horizontal scale of 1 inch for each 800 feet, and through the points A, B, C, D, E, F, and G, are drawn lines Aa, вb, &c., perpendicular to A G; on these lines are set off the vertical distances to the points a, b, c, &c., according to the vertical scale of 1 inch for each 200 feet; and the line a g, passing through all the points a, b, c, &c., will represent the required section. A line is drawn between the stations E, F, at the proper distance from the datum line to represent the level of the canal; and proceeding in this manner, and making any remarks that may seem desirable, opposite the corresponding points of the section, the work will be completed.

Having now explained the construction and use of the most accurate instruments for tracing the level of any portion of country, we proceed to notice the water level, a very simple instrument, adapted to give a rapid delineation of any portion of country, an object frequently of greater importance than accuracy. It can be made by any workman, will cost but a few shillings, and requires no adjustment when using it.

"A B is a hollow tube of brass, about half an inch in diameter,

and about 3 feet long; c and d are short pieces of brass tube of larger diameter, into which the long tube is soldered, and are for the purpose of receiving the two small bottles, e and f. the ends of which, after the bottoms have been cut off, by tying a piece of string round them when heated, are fixed in their positions by putty or white lead; the projecting short.

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axis, g, works (in the instrument from which the sketch was taken) in a hollow brass cylinder, h, which forms the top of a stand used for observing with a repeating circle; but it may be made in a variety of ways, so as to revolve on any light portable stand. The tube, when required for use, is filled with water (coloured with lake or indigo), till it nearly reaches to the necks of the bottles, which are then corked for the convenience of carriage. On setting the stand tolerably level by the eye, these corks are both withdrawn, which must be done carefully, and when the tube is nearly level, or the water will be ejected with violence; and the surface of the water in the bottles, being necessarily on the same level, gives a hori zontal line in whatever direction the tube is turned, by which the vane of a levelling staff is adjusted."

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The instrument, however, with which observations upon the level of a country may be most expeditiously made, and generally with greater correctness than with the water level, is the reflecting level. This instrument consists merely of a piece of common looking-glass, ll, one inch square, set in a frame fixed against a plate of metal weighing about a pound, and suspended from a ring, r, by a twisted wire, w, so that it may swing freely, but not turn round on its axis of suspension. A fine silk thread, tt, is stretched across the center of the mirror, and a small opening, o, at one side of the mirror,

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The instrument is adjusted as follows It is suspended in a frame, constructed to hold it, and bring it soon to rest, at about 50 yards in front of a wall. The observer looks into the mirror, and brings his eye into such a position that its image is bisected by the silk thread, t t; and the point upon the wall, seen through the opening, o, which coincides with the silk thread, is marked upon the wall. The mirror is then turned round, and the point is also marked upon the wall, the reflection of which in the mirror now coincides with the silk thread, when this thread again bisects the image of the observer's eye as before.

Lastly, the middle point, between the two thus found, is marked upon the wall; and by turning a screw, s, the center of gravity of the instrument is altered, till the mirror hangs so as to bring the reflection of this last mark upon the thread, when the observer's eye is bisected by it. The instrument will now be in perfect adjustment, and, when the image of the eye is brought upon the thread, all points bisected by the thread, whether seen by reflection, or directly through the opening, o, will be on the same level with the eye of the observer. The observations may be made either by holding the instrument at arm's length, or by suspending it from the branch of a tree, or from any post or rail of a convenient height. Greater accuracy is obtained by suspending it by means of a frame fitting on a three-legged stand, such as already described as used for supporting the more accurate instruments; but it must not be forgotten that this instrument is not to be at all compared with them for minute accuracy; but that its advantages are the great rapidity with which it can be used, whether in a very confined space, or in an open country.

INSTRUMENTS FOR MEASURING ANGLES.

In every map and plan the distances and angles laid down are not the actual distances and angles between the points of which the relative positions are intended to be represented, but they are the distances and angles between the projections * of those points upon the same horizontal plane, and are called the horizontal angles and distances between the points. Now, if our surveying instruments were constructed to measure the actual angles subtended by different objects, the process of calculating all the horizontal angles from these observed angles would be very laborious; but, by having such instru

The projection of a point upon a horizontal plane is the point in which a vertical line through that point meets the horizontal plane.

ments as will at once determine by observation the horizontal angles, we are saved a vast amount of labour, and also from any errors which might otherwise creep into the calculations.

THE PRISMATIC COMPASS.

With this instrument horizontal angles can be observed with great rapidity, and, when used with a tripod stand, with a considerable degree of accuracy. It is, consequently, a very valuable instrument to the military surveyor, who can make his observations with it, while holding it in his hand, with all the accuracy necessary for a military sketch. It is also a useful instrument for filling in the detail of an extensive survey*, after the principal points have been laid down by means of observations made with the theodolite, hereafter to be described, and for any purpose, in short, in which the portability of the instrument and rapidity of execution are of more importance than extreme accuracy.

c is a compass card divided usually to every 20', or third part of a degree, and having attached to its under side а magnetic needle, which turns upon an agate center, o, fixed in the box B; n is a spring, which, being touched by the finger, acts upon the card, and checks

B

с

its vibrations, so as to bring it sooner to rest, when making an observation. s is the sight-vane, having a fine thread stretched along its opening, by which the point to be observed with the instrument is to be bisected. The sight-vane is mounted upon a hinge-joint, so that it can be turned down flat in the box when not in use. P is the prism attached to a plate sliding in a socket, and thus admitting of being raised or lowered at pleasure, and also supplied with a hinge-joint, so that it can be turned down into the box when not in use. In the plate to which the prism is attached, and which projects beyond the *The prismatic compass was used for this purpose by the officers engaged in making the Ordnance Surveys of the United Kingdom.

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