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it can easily be seen that time would be chains and 79.6 feet; it is always written saved by making the two setting up. thus on the hub stakes. The degree of Before commencing the chopping, the a curve should be made as small as postransitman decides how many stations sible, for the longer the curve the shorter he will lay off and sets a picket on each the line; the "lay of the ground” nearly extreme chord (BC and BF in the case always decides the degree of curvature taken above) at a short distance, say to employ in connecting two tangents, twenty feet from the instrument, so as that curve being chosen which will give to serve as a guide for the axemen. One the best profile, or in case of a choice slight difference between laying out a between rock and earth excavation, the curve in the field and the explanation least expensive line, the limiting value of usually given in text books for doing it, the degree of curvature, of course, being should be noticed. In text books the never exceeded. This limiting value was first chord is taken to be one hundred decided upon at the same time as that feet, while in practice it very rarely oc- for the grades. Where a grade and a curs that a B.C. (beginning of curve) curve occur together, a resistance to comes at an even station, so that the first motion is caused by each, so to make the chord is nearly always less than a full effect not exceed that due to the maxichain, and the first deflection angle will mum grade on a straight line, the limit be equal to the difference between the of the former has to be changed. It has

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chainage of the B.C. and that of the been found experimentally that a onenext full station divided by one hundred degree curve causes as much resistance and multiplied by one-half the degree of as a 2.4 feet rise per mile, so that the the curve; for example, if the chainage limiting value for grades will have to be of the B.C. is 1021 + 54.6, and it is a reduced by that amount for every degree three-degree curve, the first deflection of curvature. The value 2.4 was found

1022-1021 + 54.6 X 1°30' for a speed of twenty miles per hour. angle will be

Locations are sometimes made by tak100

ing the angles and distances directly 45.4

X 1° 30'=0° 40' 52" nearly, or in from the plot and laying them out upon 100

the ground, but the ordinary way is to practice 0° 41'. The second angle of de- use the plot simply as a guide, and to flection will be 2° 11', the third 3° 41' run in the tangents and put in curves to etc. If the length of the curve be 925 fit. In going around a rocky shore the feet (=100 1:30), the chainage of the intersection points often fall in the waE.C. (end of curve) will be 1030 + 79.6, ter, as shown in Plate I., Fig. 2. To run the last chord will therefore be 79.6 feet in the curve FC, run the random lines A long and the corresponding deflection E and E D, measuring the angles B A angle, or increase of deflection angle, as Eri, G ED=i, and II D Kri, then L

79.6 the case may be, will be +1° 30' =

BD=I=i+i, + In the triangle EA 100

D, EA, ED and the angle A Ë D are 1° 114'. By 1030+79.6 is meant 1030 known, so that D A and the angles E A

CONSTRUCTION.

D and E D A can be computed. This see an article on the subject in the “Pi will give the angles BAD and BD A, Eta Pamphlet” of 1878-9. so that in the triangle B AD, the sides He should next re-establish the center B A and B D can be found. After de- line, for most of the stakes and perhaps ciding upon the degree of the curve, the some of the hubs will have been destroyed sub-tangent can be calculated in the during the clearing. While doing this ordinary manner, the differences between he should reference all hubs at the bethis distance and the lengths AB and ginnings and ends of curves, and on tanBD be laid off from the points A and D, gents at least one in every two thousand and the curve run in as usual.

feet, and at apices in the grade, in order If several location lines have been run to facilitate the finding of the center line in the same neighborhood, the stakes on after the grading is finished. The ordithe one adopted should be painted, so as nary method of referencing is to turn to readily catch the eye.

off an angle of 45° to the tangent, set a hub at 100 feet, driving a hub stake

beside it with R. H. marked thereon, reThe first steps to be taken after the verse the instrument and place another final location has been decided upon is in the same manner; then turn off an the clearing of the right of way. The angle of 45° to the other side of the width of clearing should be about one tangent and proceed as before. Should hundred and thirty feet, in order to allow the natural features of the country or for high banks and wide side ditches, any other cause prevent the setting of and for the erection of a telegraph line, hubs on both sides of the line, it will be which should be placed on the berme, or necessary to set two hubs on each referspace between the foot of the slope of the bank and the side ditch, and always on the same side of the line. As a wide clearing is necessary to prevent trees

Fig.3. from falling on the wires, the center line of the road should not pass through the middle of the clearing, but far enough to one side to allow the telegraph line to occupy that position. Assuming the average fill to be three feet, the top width of bank to be seventeen feet and the slope ratio of the sides to be one and ence line, as shown in Plate I., Fig. 3. a-half horizontal to one vertical, this Care should always be taken that the would make the slope stakes extend thir. hubs are placed in positions where they teen feet from the center line, so if the would not be liable to be disturbed. latter be fifty feet distant from one side I have employed the following method of the clearing and eighty feet from the and prefer it to any other, although it other, the telegraph line could occupy was not in accordance with the instructhe center. If by reason of a high bank tions given to the section engineer of or a deep cutting the telegraph line be the road on which I was working: Set brought too near one side of the clearing, up the instrument over the hub to be the latter should be widened there; and referenced, turn it until two trees are in any case, all trees which by falling, found on line with the hub, and cut would strike the wires should be cut down the most convenient one close to down. The trees felled on the clearing the ground, so that the instrument can should be winrowed and burned, and be set up over the stump. After having any logs left by the fire should be hauled clamped the plate, set a nail on the into the bush or be burned a second time. stump, then reverse and set another on a After the line has been properly cleared, blaze upon the other tree. Turn the inand not until then, should the section en- ' strument at about right angles to this gineer commence operations. His first reference line, find to other trees on line duty should be to lay out the off-take and proceed as before. By this means drains, for full directions concerning the hubs are set so permanently that which, and railroad drainage in general, even fire will not destroy them. Their

positions should be accurately noted in the ground; does not slope greatly, add the field book.

together (for earth cuttings and embankThe next step should be to to run over ments) one-half the width of road bed the levels very carefully, placing benches (ordinarily 11 feet for cuts and 84 feet at every thousand feet on the edge of for fills), the center cut or fill and half the clearing most distant from the cen- the latter quantity ; measure off the dister line, so as to be out of the way of tance so found at right angles to the the graders. Benches should be always center line, estimate the rise or fall in placed at both ends of heavy cuttings that distance, add to or subtract from for easy reference in driving grade plugs, the distance three halves of the rise or during the progress of the work. fall and hold the rod at this new disWhere the line does not pass through tance. The level having been previouswooded country and no convenient ob- ly set up and the height of instrument ject can be found for a bench mark, one above grade determined, sight to the rod, should be made by sinking a post in the subtract the reading from the latter ground five or six feet in order to be be. quantity, and add to it one-half the low frost, and marking the elevation of width of road bed and one-half of the a nail driven in the top of it upon a quantity itself. Should the sum thus stake placed alongside. Plugs two obtained equal the distance of the point, inches in diameter and six or eight long where the rod is held, from the center should be driven at the foot and directly stake, set the slope stake there; if not, in front of each center stake. They try again until the two quantities agree should be made level with the service of within two or three tenths of a foot. the ground, and upon them the leveling Set the ditch stake outside of the slope rod be held when levels are taken. stake at a distance equal to the width Should the plugs not be driven to the of berme, which varies from six to fifteen surface, it will cause a large discrepancy and even twenty feet, according to the between the actual quantity of material stability of the material, the most comexcavated and that called for by the pro- mon value being ten feet. On the slope file. If the section engineer would like stakes should be marked s. s., and their to avoid all chance of receiving an over- distance from the center line; the ditch hauling from the office, on account of stakes should be marked D. În grading such discrepancy, he can do so by clear- side ditches it is a good plan to drive a ing away from the foot of each stake all plug four or five feet outside of the moss and spongy material and driving ditch stake and mark on the latter the the plug down to solid ground. In this cut below the former. way the true level of the base of the At the same time that the slope stakes embankment would be recorded, for all are being set, elevations should be taken the moss, etc., is compressed to almost on every cross section at distances not nothing by the weight of the superin- equal to the semi-width of road bed, cumbent earth. It may be unnecessary and wherever the slope changes; they labor, but it is well to look ahead a little, should be taken, too, at some distance especially if those in charge of affairs beyond the ditch stakes. Cross sections are at all inclined to be unreasonable. should be taken and slope stakes set

After the profile of the line has been wherever the slope of the ground or the made on profile paper to a scale of 200 grade changes. Cross sections should be feet to the inch horizontal, and 20 verti- set out instrumentally at right angles to cal, the gradients should be carefully the center line on tangents; and on established. The objects to be attained curved portions at right angles to the in fixing them are an equality of cuts tangent of the curve. and fills to as great an extent as is judi The levels on the cross sections should cious, and the avoidance of long hauls be taken in the same manner as those on and irregularities in the continuous grade the longitudinal line, commencing on a line.

bench mark, and using the same datum; The next thing to be done is to write they should be continued through a sethe cuts and fills on the center stakes, at ries of cross sections till another bench the same time setting the slope and mark is reached, on which a level should ditch stakes. To set the former when be taken to test the accuracy of the work.

Grade plugs should be driven at the change in the height of formation level ends of cuttings, where the grade cuts must be taken into account every time the natural surface, both on the center that the rodman moves the rod in the line and at a distance on each side equal direction of the line. It is sometimes to the semi-width of road bed in cut- customary. to drive, at the ends of large tings. Driving a grade plug where the cuttings, grade plugs two or three feet grade is level is quite an easy matter, long and as many inches in diameter, the for all that is necessary is to make the upper end being bound with an iron ring rodman hold his rod, at different points, so as to be useful as a rough reference until the rod reads an amount equal tó during the course of the work. The the difference between the height of in- form of level book used on construction strument and formation level: but when differs somewhat from that used on prethe grade is a rising or a falling one, the liminary, and is given below.

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The notes here given show the center they are doing piece work, so as to see levels and the cross sections taken to that the close cutting and grubbing are gether, as would be the case were the properly attended to, and that no poor benches run in by flying levels. In set- material, such as roots, moss or logs, is ting slope stakes in swamps it is not thrown in the bank. The last, unless necessary to use the instrument: simply very large, should be kept higher in the set them at the distances called for by middle than at the sides all through the the fills marked on the center stakes, al. progress of the work, and when finished lowing a little for the subsidence of the the upper surface should be rounded off surface, if it be thought advisable. so as to fall from four to six inches from

Before commencing to work a cutting, center to sides. It should be left considthe quantity of material in it and its erably above grade, so as to allow for quality should be determined, so as to subsidence, the amount being determdecide how much should be carried each ined by previous experience. way, and to ascertain how far it will By the term “grubbing” is meant complete the embankment at each end, tearing the stumps out by the roots, and due allowance being made for the by “close cutting," chopping them down shrinkage of the material. The ground nearly level with the ground. Grubbing is now ready for the contractor to set occurs on the off-take drains, on side the graders to work.

ditches, in embankments under two feet As stated in the article in the Pi Eta in depth, and in line cuttings, though it Pamphlet, already referred to, he should is not often paid for where the cutting commence operations at the ends of the exceeds three or four feet, or in borrow off-take drains and continue them across pits. Close cutting should be done in the right of way to the opposite side ditch, enbankments over two and under five or in order to start four gangs of men in six feet in depth. A safe rule to go by each large depression of the line to build is, never to allow a stump to reach the embankment from the side ditches. within two feet of grade,” for the latter While the embankment is being built, may some time be lowered if the bank both the contractor and engineer should should sink uniformly below the original keep an eye on the graders, especially if grade. It costs more to chop one pro

jecting stump out of the bank than to the horizontal section is one hundred close cut a dozen before commencing the square yards. If the average of the grading

differences of elevations at the four corBefore opening an earth cut the engi- ners of any square is twenty-seven fee neer should see that the side ditches are or nine yards the cubical content of the finished as far as the embankment will prism will be nine hundred yards.

Staextend, and that the material excavated tion grounds should be laid out, if possifrom the former is cast into the latter. ble, on long tangents where the grade is In shallow cuttings it is sometimes neces- nearly level; or at least does not exceed sary to excavate below grade in order to nineteen feet to the mile. If it is necesremove all the loose surface material,sary to place one on a curve, let the staand to fill either with ballast or firm tion house be situated near the apex, to earth taken from a deeper portion of the allow the station master to see trains cutting or elsewhere. “All large stones approaching both ways. Clearings of and boulders measuring less than 27 eight or ten acres should be made about cubic feet, and all loose rocks that may station houses to provide against danger be removed with facility by hand, pick from bush fires, if for no other purpose. or bar, without the necessity of blasting, Very unstable swamps or muskegs are are classed as loose rock." All stones occasionally crossed by the method and boulders measuring more than 27 called “logging,” which consists in placcubic feet, and all solid quarry rock are ing logs transversely to the line under classed as “solid rock.” In cuttings the bank, leaving their ends projecting composed of both earth and solid rock, at least six feet beyond the bottoms of a berme of six feet is to be left on the up- the slopes. When this is done, the per surface of the latter. Owing to its ground must not be broken for side removal, earth shrinks from eight to ditches. twenty-five per cent. of its volume, Sloping ground covered with pasture loose rock changes but little and solid should be ploughed to prevent sliding, rock occupies one and a half times the before the embankment be built thereon. space in embankments that it did in its Measurements of material removed, natural state. Earth cuttings and em- should, whenever possible, be taken in bankments have slopes of one and a half excavation, and, when taken in embankhorizontal to one vertical; rock cuttings, ment, due allowance should be made for one horizontal to four vertical, and rock both shrinkage and subsidence of the embankments one to one. Where the natural surface. Preliminary estimates side ditches and line cuttings do not fur. are made from the profile by averaging nish enough material for the banks, bor- end depths; quantities in ditches are row pits are rendered necessary. To lay taken out by the method of “end areas;" one out, fix a line far enough from the pit and in cuttings by either the last men. not to be disturbed by the excavation, tioned method, or by the prismoidal and divide up the surface of the ground formula,” which is given by the equation that is to be removed into squares, whose V=l:6(A +4M+B), where V is the sides are parallel and perpendicular to cubical content, 2 the length between the the line of reference, then take the ele sections, A the area of one cross section, vations of the corners of these squares B that of the other, and M that of the above the datum used on the line. Af- cross section, which is not measured on ter the borrow pit is finished, re-locate the ground. Its value can be obtained the corners of the squares and take their by reducing each end area to an equivnew elevations. This divides the vol- alent area between parallel bases by the ume removed into vertical square prisms, formula h=}(V6A+b*—b), where b is whose length can be found by averaging the width of road bed and h the depth the differences of the two elevations of the equivalent area, and calculating taken at each corner. If the length of the area corresponding to the mean of the sides of the squares be taken equal the two depths thus found. It is someto some multiple of three feet, the cal- times obtained by calculating the area of culation of the cubical content will be an assumed cross section, all the variable greatly facilitated. Thus, if the length dimensions of which are taken to be a of each side is thirty feet or ten yards, mean between the corresponding dimen

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