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into three equal parts, each representing one chain, and on a scale 12 inches long, there will be 36 chain divisions; now each of these being subdivided into ten, the same as a chain, it follows that each subdivision is equal to 10 links; in a 4 chain scale the inch is divided into four, and again each division into 10, and such a scale a foot long will contain 48 chains, and so on with a 5, 6, or a 10 chain scale. Suppose, now, that from such a scale you have to mark off the following distances in chains, 600, 740, 1257; lay your scale along the pencil line with 0 at the beginning; with a needle-point prick off 600 at the 6th main division marked 6; for 740, it will be 4 subdivisions beyond the main division marked 7, four subdivisions being equal to 40 links; for 1257, it will be, first 12 main divisions and 5 subdivisions, plus 7 links, being a little less than a third short of the sixth subdivision. In the same manner these measurements may be taken off with a pair of compasses having the pencil leg at one end, and arcs of circles described from one end and the other of a chain line already laid down ; lines drawn from the end of this line to the intersection will give two more chain lines.

CHAPTER II.

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Chain Surveying.-Triangulation.-Systems to be pursued

under varying circumstances.--Setting out Buse Lines.Poles and Ranging Rods.Difficulties to be overcome. Perambulating the Boundaries.General Bearings of Bases of Operation and Conditions that will alter Systems of Triangulation.-Suggestions as to the Study of Land

Surveying. CŅAIN surveying, that is, with the chain only, is that to which the beginner should at first confine himself. When with this he can correctly and easily make a survey of a hundred acres or so, and produce a correct plan of his work, when he no longer finds any difficulty in chàining correctly, in reading the chainage, keeping his field-book, taking the offsets (however numerous), laying down the chain lines and offsets, then it will be time to apply himself to the use of instruments and extensive surveys. In this system of surveying we are obliged to divide the survey into a series of triangles, and again dividing and subdividing these triangles until the work is filled in; as our only means of laying down the chain lines is with three given lines to form a triangle. Some of our best plans have been produced from field-work done with the chain only, and yet circumstances occasionally occur when it is difficult on extensive surveys to produce satisfactory work by this means alone. In the course of this chapter we shall have occasion to point some of these out.

Whether the lands to be surveyed consist of one field only, or of half-a-dozen, or of one or two thousand acres, the system to be followed out is the same; the area must be divided into or inclosed by triangles, or both; the angles as subtended by the sides must be checked by tie-lines, and all the lines must be laid out to the greatest advantage, so as to secure as few stations as possible ; triangles as nearly equilateral as may be, and consistently with these two conditions, the offsets as short as possible, practically speaking. It is, however, but seldom we can secure equilateral triangles, and we must be content with having as few very acute or very obtuse angles as we can manage according as the work lays. In Fig. 1, the exterior boundaries might be the

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enclosures of one field only, instead of a few fields, or they might include a considerable estate. We should still have the same process to go through, or the same system to adopt, for one field as for the two latter cases, only that we should have fewer interior lines for taking the offsets to the fences, or filling in. With any three given lines a triangle may be described, and therefore any triangle BDC might be laid down, though neither of the lines DB, BC, CD, had been correctly measured. The only check upon this would be to measure a tie-line, from either of the angles to the subtending side ; but if the straight line, CD, be produced and measured on to E, then the measurement of E F will also be a check; for if DC or BC be not correctly laid down, EF will not measure on the plan as it is actually on the ground. Also in the triangle A GH, the accuracy of the three sides will be tested by the tie-line GI, as also by the line JKL, which at K and L, stations fixed on the lines CA and GH, must measure on the plan the given length KL on the ground between them, and J KL must be in one straight line on the plot as on the ground. To save time, the surveyor has to lay out these check or tie-lines so as to be able to take up offsets at the same time that he checks the chainage of his triangles; and to do this practice and care are required.

It is not possible to give the reader instructions as to the different systems of triangulation he may have to adopt according to the outline forms of the districts he may have to survey, as he may never perhaps meet two alike. The five figures, 2, 3, 4, 5, and 6, will enable him to form some idea of the different forms that may arise, but in all of which the same principle is carried

In the first figure, A B, is a tie-line; so is D E, being CD produced, which also checks the measurement of CF. In the second figure it will be seen that A B being produced to C, the whole connexion of the chain lines is checked by the intersection at D, and by C D and EF. In the third figure we have the base A B, and first the triangle A CD, which is checked by the prolongation of DC to E and the measurement of E A. The small triangle B FH being thrown up, it is checked by the measurement of FD, and FB being produced to G, by the measurement of GE. An infinity of such examples might be given, but after a little consideration the reader can lay them down for himself. The subject is deserving of study as one of importance to the engineer and surveyor, for by the production of lines, and by visual as well as by measured intersections, maps may not only be checked, but the position of distant and inaccessible objects may be often laid down on paper with such accuracy as to form a very correct map.

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Although in the above figures we have by the dotted lines laid down a system of triangulation suitable to each under certain conditions, it is to be understood that it is perfectly possible that, in consequence of other considerations, the triangulations might have to be laid out in a totally different manner; for instance, it would be by no means desirable that the intersections D or G should fall in the midst of a wood or village ; again, a range of hills might so run across that it would be extremely difficult and inadvisable to sight the bases by the eye alone, as we are now working, from low to high ground, and down to low ground again, unless there happened to intervene a considerable space of table-land, so as to be able to make sure of the direction of the line along the high ground. If this were not the case, we should have to lay down a different system of triangles, and probably make one base run along the range of hills, and work right and left of it. It is only necessary to mention all these possible and continually arising contingencies to an intelligent mind to show the necessity of a general study of a locality, and the consequent advantages and disadvantages of assuming one series of triangles instead of another.

We must now say a few words as to the means of sighting a long line, for unless this be carefully done, it is better to make the survey in smaller triangles one after another, a method, however, not to be advocated.

The poles or ranging rods used on surveys should be about about eight or nine feet long, perfectly straight,* and cut from well seasoned stuff; about one inch and a half in diameter at bottom, and tapering at top; shod with iron tipped with steel ; instead of making them round, they are better with the corners merely chamfered off, as this gives a better hold, and they should be painted white; fastened to the top should be a small flag. Not less than a dozen or two of these are required on an extensive survey to be carried out on a broad system of triangulation.

With regard to the station poles to be fixed at the ends of the base lines, they will require to be often as much as thirty to forty feet in length; they should be clean, straight, natural spars, of which a more detailed description will be found under the head of “Station Poles,” in the chapter on Surveying by Instrumental Observation.

Two of these poles being temporarily set up at the proposed ends of a base—that is a line crossing a district from end to end, or running by one whole side of it-it is sometimes possible to

* When you find one of your ranging rods warped, break it to prevent your men from using it.

RANGING BASE LINES.

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select two stations on rising ground, half or three-quarters of a mile apart, from each of which the main station poles at each end of the proposed base are visible, though both of them cannot be seen from either of the intermediate spots selected ; in such a case a surveyor and his assistant may, by waving their flags right and left, bring themselves on the line proposed. In such a case, the two main poles may at once be firmly and permanently fixed, as also the two intermediate ones last found; the same operation may now be repeated so as to find intermediate stations to chain upon, when the base is laid out, and the greatest care should be taken that the poles are fixed perfectly upright. It is not always, however, that such favourable circumstances occur, and it is often necessary to find roughly at first where the intermediate poles must come; when the approximation has thus been made, then the situations of the poles may afterwards be accurately fixed.

Sometimes it happens that you are obliged to lay out your line from one point or main station pole only, and to guess, as it were, as well as you can from a general map, from some old plan, or only from observation, where a line will take you ; if on reaching the other end of the district to be surveyed, you come to such a point that you can from it lay out your other lines, the thing is settled, and you have only to re-examine your work to see that the line be perfectly straight, or to make it so. But, on the other hand, if you are too wide of the mark sought, you have nothing left but to begin over again. This is one of the

. most tedious operations you have to perform on an extensive survey to be enclosed in as few triangles as possible, and induces many surveyors to give up the system, which, however, is certainly the most minutely correct as to the whole of the survey, as well as the details. Without

Without any instruments, such as a compass or theodolite, much time is unavoidably lost in carrying out this principle in all its integrity, when the survey is very large, say three or four thousand acres; but on lesser occasions, say one half of this, it may generally be done even with the chain alone, without meeting with such obstructions as to induce one to lay the system aside. Where, however, you have to deal with

, a country where there is much wood, you will have to give it up, as, practically speaking, the obstructions are insurmountable, In calm weather you will often receive assistance at first starting the sighting of a line by tying two poles strongly together, but care must be taken that they are firmly fixed upright in the ground; I have often tied them in a hedge fast to some stout stem; to make sure they are perfectly upright, try the plumb line upon them in two or three directions, for if a pole leans in

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