considered in modern practice, as by equalising the distance between the staff at each end and the instrument the necessity for making the allowance would be obviated. If only back and fore sights are required it will not be difficult to arrange for the equidistance of the staff, but it does not necessarily follow that the instrument must be exactly in line with the staves. Alselect some a ways eligible position upon which to plant your level, so as to command as large range of your work as possible consistent with the necessity to have the back and fore sights equidistant. In Fig. 241 I give a simple illustration, which really deals with the whole question, however complicated. In the line of section from A to D it is assumed that EQUALISING BACK AND FORE SIGHTS. 193 ates, and finally at B for a fore sight, the same distance (or thereabouts) as from A. Now by keeping A and в the same distance from A' we have fulfilled the condition required by curvature and refraction, and if the instrument is in perfect adjustment the depths of the intermediates a, b, c, below the line of collimation ▲ B, although of different radii to A and B, yet for all practical purposes will be suf LEVEL ficiently accurate. This will be possibly better understood by reference to Fig. 242. Here let me say that, whilst it is absolutely essential that the back and fore sights should be most accurately observed, because the difference of their sum will be the actual rise or fall from the commencement to the termination, yet for all practical purposes it is not necessary (except in the case of the level of water, existing railways, or road crossings) to read nearer than tenths. Thus 1.43 would be booked 1.40, and 1.47 would appear 1.50. By so doing a great deal of unnecessary labour and complication in making up the book is avoided, and seeing that even with the largest scale in practice it is impossible to plot less thanth of a as foot, it is a needless waste of time to observe so minutely in the field. Passing back to the consideration of Fig. 241, having observed the fore sight at в (0·59), and previously taken care that the staff is held upon some firm place, the face thereof being now turned towards B', to which point the instrument has been transplanted, and when adjusted the reading of the back sight at в is 9.80, and now follow the various points along the line, d (2·30), e (4-30), ƒ (5·90), g (8.30), h (10·00), j (7-30), k (4.90), 7 (5.30), m (0-10), and n (10-50), all intermediates, whilst c (12.53) is the fore sight. The same principle as previously explained equally applies, and so on ad infinitum, showing at the finish of the section ι This is only a very simple illustration, but it may be adopted either for a great length of section or for a few chains. Instructions to Staff-holder.-It is desirable that the surveyor should direct the staff-holder as to the points at which it is necessary to take "readings," especially for back and fore sights, and unless he has some trustworthy person to read the distances on the chain-line he should ascertain the longitudinal measurements himself; certainly he must personally superintend the establishment of bench-marks, and see that the staff is not only held on the highest point, but that it is the same place which is described in the "remarks" column. Plenty of Information.-Another point is that the remarks should be in as much detail as possible, accompanied by neat and graphic sketches of any important features met with in the section, especially with regard to the bench-marks. A sight should certainly be taken at the end of every chain except under exceptional circumstances. It may be well here to explain, that it is not by any means necessary that there should be any longitudinal measurements at either a back or a fore sight, but if it be found convenient to change at a point on the line of section which is to be determined by measurement, then the distance will appear opposite the foresight and opposite the next back sight (which represents the same spot). There will be no distance, but for facility in after work a dash should be drawn across the column. Thus, referring for illustration to Fig. 241, if at в it had been intended to have another intermediate, but the surveyor found that the rise of the ground would hardly justify his changing further, instead of entering 0.59 as an intermediate, he would book it as a fore sight, and put the distance upon the chain-line opposite, as in Fig. 243, and having moved the level to B' in sighting the staff held at the same place (viz. в) would read and enter in the first column the back sight 9.80, so that at 1.60 the distance was 1 chain (100 links), at 1.45 200, at 1.55 = 300, at F s 0.59 400, at в S 9.80= 000, at 2:30 430 links, and so on. I should explain that in Fig. 241 the back and fore sights at A, B, C, and D are, for particular illustration of a system, shown upon the line of section, but there is no absolute rule for this, as provided the prin = LEVELLING WITH THEODOLITE. 195 Back Inter- Fore Dis- 6.30 ciple of having the back and fore sights equidistant, they may be at any point right or left of the line. Then again, I have been frequently asked if the first back sight is the commencement of the section? I say, no. The first back sight must necessarily be upon a bench-mark, in as near proximity to the commencement of the section as possible; but as a general rule the zero of the chainage is an intermediate; and the same applies to the last fore sight, which may be some distance from the termination of the section, involving a number of back and fore sights before the bench-mark is reached. And when this has been done, then the difference between the sum of the back sights and fore sights will represent 000 1.60 100 1-45 200 1.55 300 0.59 400 9.80 2.30 430 4.30 500 and so on. Fig. 243. (or should do) the difference between the levels of the first and last bench-mark. Again, as the intermediate sights are the depths below the varying lines of collimation (which only are regulated by the back and fore sights), and so long as they have been accurately observed, they are disregarded in making up the field-work, and are only affected in the rise and fall columns, as connected with the reduced levels. But let it be said that the accuracy of the section so far as its details are concerned is entirely dependent upon the care with which the intermediates are observed, especially in reading long distances, as a IX. may be easily taken for XI., which involves an error at this particular point on the section of two feet, but does not in any way affect the whole section. Patience and care will obviate such an unpardonable error. Taking the Level of Water.-In taking the level of the surface of water it is best to so place a stone on the fore-shore that it is only just covered with a film of water, and then hold the staff upon the stone. This applies only to standing water; but for a tidal stream the exact time of the observation should be chronicled, and, from a nautical almanack or by other means, the exact position of high and low water may then be determined. Levelling with Theodolite. Except under circumstances which are unavoidable, the use of the theodolite for levelling purposes should be confined to ascertaining inaccessible points or for the heights of mountain sides, for which the ordinary operations are inadmissible. In Austria, when working against time, I was compelled to use the theodolite for taking cross-sections of a ravine, the results of which were afterwards at leisure fairly confirmed by the level. A point at the bottom of the slope must be accurately determined by the ordinary means, and above this the height of the axis of the theodolite must be carefully ascertained. Thus, as in Fig. 244, the dotted line A B will represent the hypotenuse of the rightangled triangle BA F', and with the distance & b' it is possible to calculate the height в B', and deducting from that в b, and adding to this result the height A G or B'b', we get the height b b'. A simple illustration of this will be found in Fig. 245. Here the angle caɗ 25°, and the distance & c measured along the slope is 500 feet. Then co = AC X sin. 25° = 500 × ·42262 = 211·31 feet; but a is 5 feet above G, and c is the same height from c, and so is C'H 5 feet. Therefore c H 211 31. as follows: = GHAC (or G c) × sin. 65° = 500 × And Ac or G H is found 90631 = 453·15 ft.* And the heights c c', d d', e e', and b b', and the distances & c', & ď, G e', and G b' (Fig. 224) may be found in a similar manner, by treating the cases as right-angled triangles, CA O', DA D', E A E', and B A B', and plotting the calculated heights and distances from the datum line G H. In the case of going down hill you reverse the triangle, making в A the base and F B A the angle. * In these calculations we take the sine and cosine of the complement of 25° or those of 65°. |