I'll 



SURVEYING. - 



SURVEYING. 



the number of the graduation, these being read from in the direction 

 sni/, will be greater than 180: let it be 256 (or 180 + 76); in that 

 case the observed angle is N. 76 E., and it expresses the bearing of 

 the line K c from the meridian n K s, or from the meridian n H s. If 

 the telescope in moving from K H should be directed to an object at E, 

 thon. the index of the vernier being supposed to be at z, the number 

 of the graduation will be less than 180* : let it be 110 (or 180 70); 

 in that case the observed angle is N. 70 W., and it expresses the bear- 

 ing of the line K E from the meridian n K s or n H i. 



Let the theodolite be removed to c, a staff being left at K, and turn 

 the whole instrument, the index of the vernier remaining at N. 76" E., 

 till the object-glass of the telescope is directed to K, and the inter- 

 section of the wires appears to coincide with the staff there ; then the 

 point n of the needle should lie over the zero of the graduations. Now 

 turn the upper horizontal plate till the object-glass of the telescope is 

 directed to L, and the intersection of the wires appears to coincide with 

 the object there ; then the telescope, in turning from the position c K 

 to c L, passing over and beyond s, the number of the graduation coin- 

 cident with the index of the vernier will (reckoning from zero at n) be 

 lew than 180 ; let it be 133 : in that case the observed angle is 

 I) . or S. 47 E., and it expresses the bearing of the line c L 

 from the meridian net or n us. If the telescope should not pass 

 beyond , and should be in the position c p, for example, the number 

 of the graduation, reckoned from n, will be greater than 180 ; let it be 

 208, i.r 10* + 26' : in that case the observed angle is 8. 26 W., or 

 N. 206 E., or N. 154 W., and it expresses the bearing of the line c i> 

 from n a or nm. In this manner the process of the survey is con- 

 tinued to the end of the road, or till, having passed completely round 

 the wood, the instrument returns to H, from whence it set out. 



As, from local attractions or other causes, the polarity of the needle 

 may not be constant, it is scarcely to be expected that the needle 

 xhijiild, when the telescope is directed back to a preceding station, 

 be exactly coincident with the north and south line in the compass- 

 box ; yet a near approach to such coincidence will serve to detect the 

 existence of considerable errors in the observed angles ; and a com- 

 plete verification of the whole series of operations will be obtained, 

 should the observed bearing of H from the meridian line n A at the 

 lat statiijii A, that is, the angle BAH, be found to agree with the 

 observed bearing of A from the meridian line H at the first station 

 n. When this agreement takes place the work is said to close 

 accurately. 



The urvey of a road or an enclosure, by following the course of the 

 i , or the contour of the latter, may be performed by simply 

 observing with a surveying-compass or a circumferentor the bearings 

 of the several station-lines from the magnetic meridian, and measuring 

 their lengths; and one of these instruments is generally employed 

 when great accuracy is not required. 



The plane table, which is also occasionally employed for surveying 



ground, is a square board fitted upon a tripod-stand and furnished 



w ith compass, and with an alidade, or ruler carrying " sights " at the 



extremities. Drawing-paper is made fait to the board or table, and the 



instrument being set up at any part of the ground which may be 



thought convenient, a point is marked on the paper to represent the 



place. The alidade is next turned about that point, so that the line of 



the ighU may be directed to any remarkable objects whose situations 



are to be determined, and lines are drawn by the edge of the ruler 



in its several positions; then the distance from the instrument to 



' 'e of those objects being measured, and laid down on its line of 



ion by a convenient scale, the place of that object on the paper 



lined. The table i then removed to that object, and fixed by 



edle in the compasg-box, so that its edges may be parallel to 



thi-ir former |*n<iti<.in ; that is, till the alidade placed on the line 



-; the places of the two objects of the paper is in a direction 



.; to tlii former place of the instrument. In this position, the 



le being turned about the point which represents the actual place 



of the instrument on the ground, lines are drawn as before along the 



edge of the ruler, towards the several objects which had been observed 



at the preceding station; the intersections of these lines with the 



others will determine the places of the objects on the paper. 



The length of every line which is to be measured must be obtained 

 in a direction parallel to the horizon between its extremities; and 

 termination of this length is generally a work of considerable 

 difficulty mi n, ...nint of the inequalities of the ground. 



Where great precision is required, it would be proper that tliu 

 direction of the line to be measured should be indicated by pickets 

 uly planted at intervals along it; a cord may be stretched tight 

 between the two first pickets, and the measurement may be performed 

 by means of a graduated deal-rod 15 or 20 feet in length, which should 

 be applied successively to the cord, the place of each extremity of 

 the rod being marked by a pin pressed into the cord. But when 

 the gnmud is nearly level, a measuring-chain is laid upon the 

 ground iUelf in the direction of the line to be measured, the leading 

 man proving into the ground, at the end of each chain's length, an 

 in 'ii pin, which being taken up by the person who follows, the number 

 * so taken up serves to show the number of chains in the 

 length of the line measured. In ascending or descending any gentle 

 elevation of the ground, the chain should be held up at the lower end 

 till it is in a horizontal position, as nearly as the chain-holder can 



estimate it ; and a plummet being suspended from that extremity, so 

 as to touch the ground vertically under it, the measurement thus 

 obtained is in general sufficiently near the required horizontal length 

 of the line. When the slope of the ground is too great to admit of 

 this simple method being put in practice, the chain must be stretched 

 on the ground, and then the angle at which it is inclined to the 

 horizon being found by some instrument (a small spirit-level furnished 

 with a graduated arc), the horizontal value of the chain's length must 

 be computed. And if, at the same time, the vertical height of one 

 end of the chain above the other be also computed, there will be 

 afforded sufficient data for determining on paper the form of a vertical 

 section of the ground in the direction of the measured line. 



Where the rise or fall of the ground is considerable, the operation 

 will be most conveniently and accurately performed by the use of a 

 theodolite ; for this purpose pickets should be set up in the ground, in 

 the direction of the fine to be measured, at every place where a change 

 occurs in the inclination of the ground to the horizon, and marks made 

 on them at heights above the ground equal to that of the telescope 

 belonging to the theodolite ; then, while the chainmen are employed 

 in measuring the length of the line on the ground, the surveyor takes 

 the angular elevations or depressions of the marks on the pickets, with 

 respect to the horizon. From the data thus obtained the horizontal 

 distances between points of ground, and the positions of the points 

 above or below any assumed horizontal plane, can be computed. In 

 order to save the trouble of making trigonometrical computations, the 

 vertical arch of the theodolite usually carries two series of graduations, 

 from which, by inspection, when the telescope is directed to an object, 

 the portion of the measured line which should be subtracted from it 

 in order to reduce it to the corresponding horizontal length may be 

 found ; and also the portion of that horizontal length to which the 

 vertical height or depression is equal. 



This method may be conveniently put in practice when it is required 

 to exhibit sections of the ground, for the purpose of guiding the civil 

 engineer in the choice of a line for a road or canal ; the great accuracy 

 with which the section might be determined by a spirit-level not being 

 requisite. It is now the practice to represent on a plan of the ground 

 a vertical section in the direction of a proposed line of road, for the 

 purpose of showing the depths to which the excavations are to be 

 carried, and the heights to which the embankments are to be raised ; 

 a strong line, as of, b', d', representing the surface of the proposed 

 road : on one side of this line, as at a", d", are shown the profiles of 

 the requisite excavation ; and on the other side, as at b", are shown the 

 profiles of the embankments : both the heights and depths being deter- 

 mined with relation to the surface of the road. This method was first 

 proposed by Mr. Macneil. 



The principal and secondary station-lines constitute a triangulation 

 on the plan of the ground ; and when the lengths of these lines have 

 been ascertained by admeasurement, the superficies of the whole track 

 may be found by the rules of mensuration. The area of each triangle 

 should be calculated separately from the measured lengths of the lines, 

 and the several results added together, if all the triangles lie within 

 the given bonndaries of the tract ; should any of them lie on the 

 exterior of the boundary, the areas must of course be subtracted. 

 But as the boundaries of the several fields, &c., seldom coincide exactly 

 with the station-lines, offsets must have been measured from every 

 such line to each remarkable bend in the nearest boundary; and 

 between the station-line, the boundary, and every two offsets from the 

 former, there exists a small trapezoid, whose area must be computed 

 separately, and either subtracted from or added to the areas of the 

 triangles formed by the measured station-lines, according as it lies 

 within or on the exterior of these triangles. 



The accurate method just described is not always put in practice by 

 surveyors. When the boundaries of a field or tract of ground have 

 numerous small bends, a straight line is sometimes drawn through 

 portions of the boundary in such a manner that the small areas on 

 the exterior of the line shall be equal to those which fall in the interior, 

 this equality being estimated by the eye : the complex figure of the 

 contour line is thus reduced to one more simple ; and the area of the 

 field or tract is then computed. For this purpose either the plan is 

 divided into two or more triangles, or by a geometrical construction 

 the whole irregular figure is reduced to one triangle of equal magnitude, 

 and in either case the lengths of the sides are measured by the scale 

 of the plan. 



When a road, river, or any boundary-line is surveyed with the 

 theodolite and chain, the successive operations are registered in a book 

 according to a particular form, by which a person without any know- 

 ledge of the ground may be enabled with facility to lay the work 

 down on paper. This is called the ' Field-Book,' and the manner of 

 entering in it the series of operations will be best explained by means 

 of an example. Let a, Q, B, D, be the principal bends in the direction 

 of a road, and the stations at which, in succession, the theodolite is 

 placed for the purpose of observing the bearings of the several lines 

 o q, Q it, and K D, from the magnetic meridian passing through the 

 first station a. 



At o let the bearing of the object, or mark set up at Q, be observed ; 

 let the line o i; bo measured with the chain, and let offsets be measured 

 perpendicularly to that line up to any remarkable points near it. At 

 o, let the bearing of a staff at B be observed ; also let the length of 



