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A, the instrument is set up at B, another staff at C, at the same distance from B that B is from A. The readings of the two staves are then noted; the horizontal lines connecting the staves with the instrument represent the visual ray or line of sight. The instrument is then conveyed to D, and the staff which stood at A is now removed to E, the staff C retaining its former position, and from being the forward staff at the last observation, it is now the back staff; the readings of the two staves are again noted, and the instrument removed to F, and the staff C to the point G; the staff at E retaining the same position, now becomes in its turn the back staff, and so on to the end of the work, which may thus be extended many miles; the difference of any two of the readings will show the difference of level between the places of the back and forward staff; and the difference between the sum of the back sights and the sum of the forward sights will give the difference of level between the extreme points; thus:

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showing that the point G is 2 feet and higher than



the point A.

The foregoing process is called compound levelling. The following is an example of simple levelling, being performed at one operation, and therefore subject to the correction for curvature and refraction to obtain a correct result.




Suppose it were required to drain a pond and marsh A, by making a cut to a stream at B, a distance of thirty chains; let a level be set up at C, and directed to a staff held upright at the edge of the water at B. The horizontal line C D represents the line of sight which would cut the staff at D, the reading being 17.44 feet; the height of the instrument above the ground was 4 feet, and the depth of the pond 10 feet; therefore the difference of level between the bottom of the pond and the surface of the stream was as follows:

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To present, in the clearest possible manner, the practical application of the principles of levelling, we propose describing some operations in detail. We shall, therefore, commence with a case of a simple kind, which will prepare the way for more complicated examples. When a section of a line of country has been completed (for any purposes whatever), it is in most cases necessary to check its accuracy by repetition; but in doing this, it is seldom requisite to level over precisely the same line of ground, unless there is cause to suspect its general correctness, but to follow the most convenient and nearest route, and at intervals to level to some known points on the exact line of section, which will give their differences of level; the points thus selected are generally what are called bench marks, and are nothing more than marks or notches cut upon gateposts, stumps of trees, mile or boundary stones, or any similarly immovable objects, contiguous to the line of section, and at frequent intervals. These bench marks are made by the person who takes the section in the first instance, and are some

times previously determined upon. When the section is complete, their relative heights with regard to the base line or datum of the section become known; consequently, they may be considered as so many zero or fixed points on the line, easily recognizable, from whence any portion of the work may be levelled over again; or branch lines of level may be conducted in any direction, and the levels of such branches be comparable with those of the main line.

When, in checking the principal levels, by proceeding in the most convenient direction from bench mark to bench mark, it is found that the differences of level prove identical with those on the section, or within the limits of probable error, it may be presumed that all the intermediate heights are likewise correct; it is, however, just possible that equal errors of an opposite kind may have been committed, when, the sum of each being of the same magnitude, a balance of errors would cause the extreme points to be right, whilst the intermediate levels would be incorrect; but the probability is so much against such an occurrence, that we believe, unless there be some particular reasons for so doing, the whole exact line of a section is seldom levelled a second time for the purpose of checking the former results only.

From what has been remarked, it will appear evident that in taking running or check levels, there is no necessity for the use of the chain, or the compass attached to the instrument, the distances and bearings

having all been determined at the time the principal levels were taken.

The example we are about to give of this kind of operation is represented in the engraving, Plate I., which shows both the ground plan and the section. The strong black line on the plan is that of the section to be checked, and proceeds from a bridge in the town of A, in a circuitous direction along a valley, and nearly parallel to the course of a river, to a bench mark in the town of B; this originally formed a portion of a more extensive survey. We have selected this portion of the line as explanatory of our present subject; the route taken in proving the work is represented by the dotted line, and was confined to the public roads, that being considered the most convenient, because it would altogether exclude the necessity of passing through private property, as the surveyor would most likely have been ordered off, a great feeling of opposition existing among the owners and occupiers of the said lands; and further, the public road crossed the line several times, by which a number of intermediate points could be checked. Before giving the particulars of this example, we shall explain in detail the method of conducting the necessary obser


In the first instance the staff-holder must place his staff on the bench mark from whence the levels are to commence. (In the case of our example the staff was first placed on a peculiarly shaped stone on the crown

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