companies' regulations, will weigh about 6 tons each empty. Composite six compartment passenger carriages will weigh about 12 tons each empty.

2. Speed. The most economical speed for goods is 20 miles per hour.

3. Locomotive Power and Train Resistance. - The tractive power of a locomotive is given by—

where D=

P =

diameter of cylinder in inches.

mean pressure of steam in cylinders in lbs. per square inch.

L= length of stroke in inches.

w= diameter of driving wheel in inches.
Ttractive force in lbs.

(1)

The tractive power is, however, limited by the adhesion of the locomotive drivers to the rails. In ordinary English weather the adhesion of a locomotive may be taken at 450 lbs. per ton of weight on drivers, or about one-fifth. When the tractive power developed by the cylinders exceeds the adhesion, the adhesion must be taken as the tractive power. In addition to the tractive power the boiler capacity is a dominant factor in determining the working load which a locomotive will take.

The resistance of a train on the level may be found from the following formulæ :

where T = weight of train in tons; v = velocity in miles per hour; A = area of frontage of train in square feet; B = volume of train in cubic feet; R = resistance in lbs. on a level. As compared with experiment, equations (2) and (3) give results too high for low speeds.

The average train resistance may be taken at about 10 lbs. per ton at about 20 miles per hour, on the level.

In addition to the above train resistance on the level, the resistance due to gravity in ascending an incline must be cal

culated upon. Let G = gradient, so that = inclination of gradient,

G

I

-=

i.e., for 1 in 60

I

and let w = weight of train. Then the com

G

60'

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

(4)

W X

..

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 x .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