REMARKS ON CONTRACT SECTION. 301 carry the construction to the proper height; settlement in the masonry will of course take place, but unless the work is very bad, or the foundation vicious, the difference of level occasioned by this settlement will be immaterial: by attending to the following advice the heights of the crowns of the arches will be found to be perfectly accurate. Let A B, Fig. 140, be a gradient of 1 in 100 along the extrados of a set of arches of 13 feet span and 13 feet rise, with voussoirs 2 feet thick; the piers up to springing must all be built up to a height of 13 + 2 below formation, that the line under the springers may be parallel to formation. Let formation at A be 240 00, surface height 245.00, or a cutting of 5 feet; near this a permanent post, or B.M. 243.59, or 3.59 above formation at A; plant the level and let the staff be held on the B.M., read off, say 5.25; send the staff on to A, or to b, which will make the work much shorter, and this point may be pretty nearly ascertained by the eye; supposing the staff therefore at or near this latter point, read off, say 8.00; 8.005.95 = 2.75 fall, and 243 59-27524084, or 84 higher than 240.00, and also, therefore, 84 higher than a point level with the required formation; now by moving the staff lower down, so that 8.84 be read off, we shall have a point level with formation at A, for 8.84-5.25 = 3·59 fall, and 243.59-3.59 = 24000. Now measure the distance from stump 240.00 to the point where the staff was last held, and say it is 15 feet; the inclination for this distance being 15 rise, the required height for formation will be 240-15; but the height of B.M. is 243.59-240-15 3·44, and when the staff is held on the B.M., we read from the level 5.25; add to this 3:44, when we get 8.69. Now drive in a stout stake, iron hooped, at the said distance, until the staff being placed upon it we read off 869, and it will be at the required height, for 869-5.25 3.44 fall, and 34359-3.44 240·15. It has been already observed, that a line drawn along the tops of the piers and abutments under the springers must be 15 feet below formation height; now it will not be sufficient to deduct this 15:00 from 240-15, giving 225·15, and drive in a stump at that height, because we cannot do so vertically under b, and at c an allowance must be made for the inclination of the gradient corresponding to distance. But by levelling from b downwards to c, we can find the height 225 15, which will be level with a point 15.00 below b; measure the distance from A to c, call it 30 feet, the inclination for which being 30 we shall have 340-30 for formation at this point, and 240.30-15.00 = 225.30, to which height drive in a stake as before, and then check by levelling back to B.M. 243-59, which height exactly we shall get if the work has been done correctly. From the appearance of Fig. 140, the reader may be led to think that the above mentioned stakes = = = are driven on the centre line, but as in this position the excavators would dig them up, they are driven in some 15 feet on one side; in rock or sound soil these bed moulds are little liable to disturbance, but they are not so safe in a loose ground, and it is always better occasionally to check their heights. If at the other side B of the viaduct the ground was similarly high, we should have but to repeat a set of levelling operations analogous to the last, to get the lines A B and c d, but being an embankment this cannot be done, and we must employ another method; we will suppose that at abutment C, and pier D, the masons have reached the heights marked by the dotted lines, we must first ascertain the formation heights at those points; let these be 241.66 and 242-45, and these minus 15.00 will give 226-66 and 227-45 for the heights at the springers. By levelling from a B.M. we find that the height of the abutment at C is 290-05; 227·45-190·05 = 37 40, or the height below springers to which the masons have reached, that is that they have 37.40 feet of masonry to put on to reach springing height, and this height, 37.40 should be entered in feet and inches by the engineer on a memorandum book with the date and afterwards on the section. At pier D the height of masonry is ascertained by levelling to be 17776; and 226-66-177-764890, the depth at D below springing, and this depth should be similarly entered; and in both cases a crow's foot mark should be made on the face of the masonry where the levelling-staff has been held, that it may be found at any future period. When the piers have reached within a few feet of their due height, it is well again to take the levels, as by then giving the height to be added, the masons or bricklayers, but of course more particularly the former, can regulate to a nicety the depth of their courses, and some allowance will have been made for settlements. Contour Levelling.-The foregoing observations on the practice of setting out levels, will be of material service in explaining the subject of contour. If we can imagine a valley with the water steadily rising in it, and leaving a mark of its presence at every five or ten feet rise, we shall have the most perfect idea of setting out contour levels, for the bubble of the spirit-level defines the horizontal line which would be assumed by the water, and if we remove the level higher and higher each time, the axis of the telescope performs, as regards this, the same process as the rising water; but it is necessary to drive in a number of stumps in order that the contour lines may be found on a future occasion. If the lines of contour levels are all set out at any given number of feet one above the other, and a survey of these lines is afterwards made, then the plot of such a survey will give a plan and also a section, as far as representing the relative CONTOUR LEVELLING. 303 height of levels over the ground, and according to the pains bestowed on the work, a section more or less accurate may be plotted from the plan. Let A B C D E F G, Fig. 141, be a valley which it is re quired to contour level with a rise of 5 feet, with the lowermost contour also 5 feet above the point X; remembering that not only the levels have to be set out, but a survey to be obtained by some means in order to lay down the contours on the plan. Range out the lines A G, H B, HC, &c., all of which are carefully fixed by their respective angles; plant the level at a, with the staff first set on X, where a permanent bench mark has been established; say that the reading is 12:50; this reading, minus 5 feet, equal to 750, and minus 10, equal 2.50; let the staff-holder move up the hill toward G, until the observer from his telescope reads 7.50, then drive in a stake; let the staff-holder then move on higher up, until the observer reads 2:50, and then drive in a stake. Let the staff be now moved towards a, until 2.50 is again read off, which will be another point to be staked off, and then lower down until 7.50 is again read, which will give a fourth point to be marked. The stumps for this work may be much lighter than the stumps we have already mentioned; in fact, if no time is lost, mere laths are sufficient. Let the observer thus range out with tolerable longsights up to the line H F, getting the staff held exactly on the line, so as to have the stumps to answer here the purposes of stations; of course, after the first remove, the reading on the staff will be different; for instance, when the level is first planted and the staff set up at the last stump driven in-say on the first 5 feet contour-it may, perhaps, read 11 feet; then 1100 will be the reading to continue this lower contour, and 1100 minus 5, equal to 600 will be the next. With a long staff and 5 feet contours we may always arrange, with a little judgment, to set out three different heights at each fresh plant of the instrument; but, until experience is acquired, it is advisable to be satisfied with two. On reaching a contour-stump on the line H F, set up a flag-pole, when an assistant, who has already ascertained the starting-point of the contours with reference to the line X G, and the distances of the first and second from the point X, takes up the chaining with a good prismatic compass, and taking the bearings, measures with the offset staff, or better, with the tape or another chain, up to all the stumps driven in, until he reaches the line H F, at the same time he ascertains the distance from H or HF, where the flag-pole has been set up. In the meantime the level has gone on from the line H F to HE; the assistant follows with the chain, and so one set after another is set out with the level, and then chained. If in chaining and offsetting the assistant is careful to obtain horizontal distances, more particularly with the offsets, a very correct plan will be produced, which will be very useful in moderately undulating countries. One line of contours being taken all round, the work is recommenced. To effect the same object approximatively, sets of cross sections may be taken, as the undulations may require, and the positions of these cross sections very carefully shown on the plan. The differences in the readings of the level-staff must, as before, be 5 feet each time, or 10 feet if the contours are to be ten feet above each other. Improved Dumpy Level.-The most experienced observers with the level have remarked the difficulty that exists with every instrument to get it to reverse well; that is, without any alteration in the position of the bubble; and when taking long sights or levels about which there happens to be more than ordinary anxiety, it is often a constant source of discomfort. When after several removes of the instrument over very steep ground, the parallel plate screws have been so worked as to bring the plates into a very oblique direction, this difficulty in getting the telescope to reverse correctly generally increases, so much that it is often necessary to readjust the screws so as to bring back the plates to their parallel positions. To this it may be observed that in planting the instrument even on very inclined ground, we should roughly level with the legs first, as we have pointed out in our observations on the use or rather application of the instrument; but when levelling operations are hurried, as they often are, attention to this very important point as regards this rough levelling of the instrument is often neglected. The improved level, as constructed by Elliott, to which we now call attention, in a great measure removes these defects, both as regards the degree of tightness with which the telescope portion of the instrument is screwed on to that part which consists of the parallel plates and axis, as also with regard to the difficulty arising from the levelling of the instrument on very steep ground. In the improved dumpy level, the telescope and the parallel plates are all in one, and a little circular level is applied, the object of which is to bring the instrument into rough adjustment; for by attending to the bubble of the circular level occupying its proper centre while setting up with the legs only, this rough adjustment. is secured; instead of the ordinary ball and socket fitting usually applied to the level, the ball and socket joint of the theodolite has been adapted, by means of which the inconvenience arising from steeply inclined ground is done away with. These improvements are so considerable that we fully intend to adopt this improved level in our own practice. In appearance when set up it does not differ from the ordinary level, or we should have given an illustration of it. APPENDIX. THE TRANSIT INSTRUMENT. As the name of this instrument implies, it is used principally astronomically, for observing the passage of celestial objects across the meridian. We give an illustration of it at Fig. 142, because in long tunnels with deep shafts it may be used to considerable advantage, as giving the means of setting out with minute accuracy the main line of direction and the vertical axis of every shaft. The telescope is in two parts, connected together at the sphere A, which also receives the ends of the conical axis, CC, at right angles to that of the telescope. The other two ends of the conical axis, consisting of cylindrical pivots, rest in Y's at the summits of the vertical standards, SS, in which the axis of the telescope turns. A level across the conical axis denotes when it is horizontal. The standards are fixed to a circle which rests upon parallel plate-screws, by which the instrument is levelled. The two braces from the top of the standard to the beam across the above-mentioned circle are for the purpose of steadying the motion of the telescope. The vertical limb, L, is fixed to one of the pivots of the conical axis, and turning with it, denotes the angular elevation of the telescope by means of the two horizontal verniers, which are adjusted in their horizontal position by means of the spirit-level shown above them; the adjustments are effected by means of the arms and screws, y and a; the wires of the diaphragm, placed near the eye, and of the telescope, are illuminated for night observations by means of a lamp, which throws its light through the pierced cone on to a reflector within the sphere A. The lantern is so constructed that the power of the light may be tempered to suit circumstances. COPYING AND REDUCING PLANS-THE PENTAGRAPH-THE Copying and Reducing Plans.-To persons unacquainted with the routine business of an office, and to the accuracy that is required to be combined with despatch, the mere copy of a field-plan, or of the plan of a townland survey, must appear a matter of the greatest simplicity, and, but for the necessary correctness, so it would be; notwithstanding, however, that it is a most mechanical operation, it |