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i.e., for 1 in 60

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G 60'

and let w = weight of train. Then the com

ponent of the weight of the train due to gravity may be taken as

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which is the resistance due to gravity to be overcome in ascending an incline in addition to the resistance of the train on the level for the given speed.

By equating the train resistance on the level for the proposed speed plus the resistance due to gravity in ascending a gradient in terms of G, equations (2) or (3) and (4), with the tractive power of the locomotive proposed to be employed and solving for G the ruling gradient may be found, or if the ruling gradient is fixed the tractive power of locomotive required may be found. In the latter case sufficient boiler capacity to take the maximum load up the longest steepest gradient at the proposed speed must be stipulated for.

Maximum Gradient.-1 in 30 is about the steepest gradient that may be worked under usual conditions with ordinary locomotives, and this may be taken as an exceptionally steep gradient.

"Pusher" Gradients.—In some cases it may be advisable to adopt different ruling gradients on different portions of the line, working the steeper gradients or "pusher" grades with auxiliary or special engines, or adopting one of the rack systems on the steep sections. This may be adopted on lines on which there are "valley" sections and "hill" sections.

Minimum Radius of Curve.-As regards minimum radius of curve, 10 chains radius is about the sharpest curve that will be used on main line 4 ft. 8 in. gauge. Rolling stock will go round curves of 5 chains radius and even less in station yards and sidings; 3 ft. gauge lines have been constructed with curves of 145 ft. radius, or 2 chains 13 ft.

Compensating Gradients on Curves. When gradients occur on sharp curves they should be compensated so as to make the joint resistance due to curve and gradient equal to the resistance due to gradient alone on the straight. This is effected by reducing the gradient where curves occur. The resistance of a 1° curve is estimated as being equivalent to the resistance due

to a gradient of from .025 to .06 ft. per 100 ft. As an average it may be taken as equivalent to a gradient of .04 ft. per 100 ft. For a 1° curve, therefore, the gradient should be reduced by .04 ft. per 100 ft. For any other curve the resistance is proportional to the degree of curve, i.e., for a 6° curve the resistance is 6×.04.24 ft. per 100 ft. to be deducted from the gradient. The degree of a curve is the angle subtended at the centre by a 100 ft. chord, i.e., twice the deflection angle of the curve for a 100 ft. chord.

Cost of Line, Light Railway.-£2,700 per mile is about the very lowest figure for which a single line of light railway can be constructed at home, and this in exceptionally easy country, not inclusive of cost of land and not including rolling stock. £3,000 or £4,000 per mile will be a more usual figure.

A single line, capable of handling 1,000 tons of freight per day, can usually be built anywhere in moderately easy country for £4,000 or £5,000 per mile, including equipment and rolling stock. This does not apply to lines abroad neither of whose termini are in connection with a seaport. Mr R. C. Rapier, of Messrs Ransomes & Rapier, in "Remunerative Railways," estimates the equipment of 40 miles of metre gauge single line at £86,708, or £2,168 per mile. This includes 40 lb. rails, wooden sleepers, seven engines 15 tons each, turntables, tanks, watercranes, weighbridges, sheer legs, signals, 35 passenger carriages and break vans, 150 waggons, workshop fittings and stores.

In another estimate for 40 miles of 3 ft. 6 in. gauge line, Mr Rapier gives the cost of equipment at £2,471 for 45 lb. rails and eight 18-ton engines. As regards the cost of ordinary double line railways, the cost will vary so much with the locality and special circumstances of each case that no general figures can be given.

Details of the Field Work of Working Survey and Pegging out: Instruments. With reference to the actual field work of the working survey and pegging out, first as regards instruments, the most convenient size of theodolite is a 5 or 6 in. theodolite, which, for the purposes of an ordinary railway survey, need not read closer than to single minutes. American instruments for ordinary railway purposes only read to single minutes, and the angles are read off without the aid of a microscope, a piece of white ivory or celluloid being fixed above the vernier

to reflect the light on it. A 6 in. theodolite of English make usually reads to 20", and is furnished with microscopes. This is of course useful for accurate work, but it takes more time to read than the American instrument reading to single minutes only, which is really all that is required for ordinary railway purposes.

Steel Band and Tapes. For chaining out the line the ordinary steel chain 66 ft. long or steel band is used, the latter being the best for chaining out the centre line of a railway. Ten or more of the usual steel chaining arrows should be carried. A tape is also required for measurements from fence corners, buildings, &c., for fixing the position of the line to be run, odd measure ments, &c.

Ranging Rods, &c.-Two or three iron-shod ranging poles 10 or 12 ft. long are required for distant points in long lines, and about a dozen ordinary ranging rods.

For driving in the pegs a stout wooden mallet is best, as it does not split and break the heads of the pegs so much as an iron hammer. A couple of small plumb bobs and a stout cord line 1 or 2 chains long, together with some billhooks or knives for cutting through hedges and a small hand hammer, should be carried. It will be found expedient to have hedgers' gloves for the men when quickthorn hedges have to be cut through. An axe will occasionally be required to cut down small trees. One or two stout canvas bags should be provided for carrying these things.

Chainmen. As regards chainmen, it will be found expedient to have two men for chaining and one for carrying pegs, fetching back flags forward, &c. Three men will usually be sufficient.

Pegging out Centre Line. The surveyor commences operations by locating the beginning and the end of the first straight line, and fixes its position on the ground by ranging rods. This he will do by scaling off the 25 in. Ordnance map and measurement on the ground from existing objects, such as fences, buildings, &c., unless the exact position is indicated by some object intersected by the line. Having driven in the first peg at the commencement of the first line, set up the theodolite over it, level it up, and direct the cross hairs on to the ranging rod at the extremity of the line, and clamp the instrument firmly in this position. One end of the chain being held on the first peg, the leading chainman now holds a ranging rod at the other extremity

of the chain, and moves it to right or left as directed until it is bisected by the cross hairs, when he inserts the rod into the ground and then drives in a peg at the mark thus made. The surveyor will direct the peg to be knocked to right or left until it is bisected by the cross hairs and is correctly in line, and the leading chainman should then apply the end of the chain to the top of the peg and make a scratch on it along the chain handle with a chaining pin. Very often each peg is merely driven so that its centre is at the end of the chain as nearly as may be. In a long line it will be necessary to shift the instrument forward about every 15 chains or so, otherwise the pegs will get out of line, as the ranging rod and the pegs cannot be seen with sufficient distinctness to get them exactly into line at greater distances. In this case, by a signal prearranged with the leading chainman, the surveyor will range in a chaining pin held on the top of the peg, with which a point mark is made on it, and over which the theodolite may be set up. In this work the leading chainman should be the more intelligent of the two.

Chainages and Survey of Detail. The chainage of each road, fence, ditch, &c., intersected should be taken and booked, and any alterations from the 25 in. map in existing fences, new buildings, &c., must be surveyed. The box sextant will sometimes come in useful for the purpose of measuring the angles at which fences, &c., cross.

The chainages of roads, fences, ditches, and survey of alteration to existing detail may be taken by recalling the chainmen prior to moving the theodolite forward, and sending one of them forward with it, then with the assistance of the others the fence chainages, &c., are booked, and any details which require to be surveyed are taken. It is a good rule to take everything required as the work proceeds, as going over the ground again leads to loss of time. When, however, surveys of roads, rivers, &c., for some considerable distance on either side of the railway are required, a special survey of these must be made. One or more assistant surveyors should be a help and ought to expedite the work, but it is quite easy for one man to do all that is required if the time permit.

Bridges. When roads or rivers are crossed on the skew and a bridge is contemplated, the proper angle of skew for the bridge,

which will best suit the ground, should be measured on the ground with the theodolite, and a correct survey of the road or river for some distance on each side of the railway should be made. Levels and cross sections along the road will also be very useful in designing the bridge.

Setting out Curves.*-When the pegs have been driven nearly to the end of the first line, scale off the position of the

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tangent point of the first curve as nearly as may be from the 25 in. map on which the line is laid down, and direct the chainman to stop driving pegs when he gets to within a chain or two of where the tangent point will be, and continue the chaining with chaining pins until he gets a chain or two beyond the intersection point, lining in the chaining pins with the theodolite and leaving

*For classification of curves by "degree," see Chapter XI.

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