bridges, as the same amount of waterway would have to be provided in each case.

The same remark applies to culverts and drains.

There would, on the other hand, be a small saving in the quantity of land to be acquired to the extent of a narrow strip or zone, represented by the difference in width between the narrow and standard gauges.

There would also be the same small proportionate saving in the embankments and cuttings to the extent of the difference in gauge.

Also a saving in the overline bridges and road approaches in consequence of less width and height of the opening through those bridges.

And a saving in the rails, sleepers, and ballast of the permanent way, to the extent consistent with efficiency. That some saving may be effected in these is undoubted, but it is necessary to exercise caution, and not rush to the opposite extreme by making the parts too light. A rail should be made not only strong enough to carry well the engines that have to pass over it, but it should also be heavy enough to stand the wear of several years. Narrow-gauge engines must be heavy in conformity with the loads they have to haul. The same amount of power must be exerted to haul a hundred tons on a given gradient, whether the gauge be narrow or broad. In some cases of narrow-gauge railways the original rails, which weighed only 45 lbs. per yard, have since been replaced with others weighing 60 and 65 lbs. per yard. The light 45 lb. rails were evidently not found to be sufficiently heavy to keep the road to proper line and level. The result of our everyday practice seems to prove that there is not only an advantage, but an economy, in adopting rails of a heavy section, and experience would therefore indicate that even for a narrow-gauge railway it may not be expedient to adopt rails weighing less than 65 lbs. per yard.

Gradients.-There are very few localities where the rails on any line of railway can be laid perfectly level or horizontal for more than comparatively short distances. By far the greater portion have to be laid on inclined planes of varying rates of inclination to suit the general formation of the district traversed, and the circumstances of the line to be constructed.

The degree, or rate of inclination, of these inclined planes, or

gradients, may be expressed in various ways. A very general method is to state the number of feet, metres, etc., which can be measured along the gradient before an increased rise or fall of one foot or metre, etc., is obtained. Thus a gradient of 1 in 200 signifies a rise or fall of 1 foot in 200 feet, or 1 metre in 200 metres.

Sometimes the rate of inclination is expressed by stating the number of feet of rise or fall in a mile. In this way a gradient would be described as falling at the rate of 30 feet in a mile, rising at the rate of 20 feet in a mile, etc. Twenty feet to a mile is equal to 1 in 264.

Another method is to give the percentage of rise or fall. In this way the inclination would be expressed as a 1 per cent. gradient, 2 per cent. gradient, per cent. gradient, etc., which for comparison would signify 1 in 100, 1 in 50, and 1 in 200 respectively.

The gradients of a railway most materially influence its facility and cost of working, and every effort should be used to make them as easy as possible consistent with the prospect of the line.

Steep gradients signify heavy locomotives, increased cost of motive-power, reduced speed, and light loads.

The following tabulated memoranda show the approximate loads, exclusive of engine and tender, which can be hauled on the level and on certain inclines at various speeds by engines of the quoted capacities and steam admissions. A medium-sized, ordinary type of passenger and goods engine has been selected for each of the examples. The working of the passenger engine and train is assumed to be under favourable circumstances, with fine weather, fairly straight line, first-class permanent way, modern rolling-stock with oil axle-boxes and perfect lubrication, and all the conditions most suitable to ensure the least resistance to the moving load. For the goods engine and train a greater resistance per ton of load is assumed, as the goods trucks are never so perfect or easy in the running as the passenger carriages. A certain amount of side wind is taken into consideration, and also an allowance for moderately sharp curves, the object being to indicate what may be looked upon as fair, average, workable loads.

The loads for engines of larger or smaller dimensions, or higher or lower pressures, may be obtained by working out the

proportion between the tractive force put down in any of the columns of the tabulated memoranda and the ascertained tractive force of any other engine under the same conditions of cut-off and speed.

NOTE.-The column loads in tons are exclusive of the weight of engine and tender.

From the above memoranda it will be seen how greatly the gradients affect the loads. For an important main trunk line, with a heavy and frequent train-service of passengers and goods, the introduction of steep gradients would not only reduce the speed of the train-working, but would probably involve the necessity of assistant engines over those parts of the line; and it may be prudent, where possible, to incur heavier earthworks, or considerable detours, or tunnels, to obtain more favourable gradients. For such a line the additional cost, and the extra distance caused by a detour of a mile or more, will be of far less importance than the interruption in the train service arising from a serious reduction in speed or taking on assistant engines. On many railways abroad there are very interesting examples of long detours of several miles, carefully studied out to obtain greater length and easier gradients, resulting in the construction of lines over which the traffic can be worked without necessitating auxiliary engine-power. On the other hand, there are situations where steep gradients cannot be avoided, where certain altitudes must be reached, and where there is no alternative but to face the inevitable.

On secondary lines, and short branch lines, where the traffic is not expected to be heavy, and where speed is not so important, it may be policy to economize outlay and introduce steepier gradients than on the main line.

Half a mile of a rather steep gradient is not felt so much when it is situate midway between two stations, because the attained speed of the train assists the engine over the short distance to the summit; but when it occurs as a rising gradient out of a station, it forms a great check to the working, particularly in bad or wet weather, when there is the risk of the engine slipping, and the entire train sliding back into the station.

Long steep gradients not only necessitate increased motivepower for the ascending trains, but also require increased brakepower, and precautionary measures for the descending trains. Where passenger trains are fitted with continuous brakes, the risk of losing control is minimized; but with goods trains composed of waggons, having only the ordinary independent sidelever brake, it will be found absolutely necessary in many cases to have additional heavy brake-vans for descending the inclines, and these special vans, unfortunately, will form so much extra non-paying weight to be hauled up on the ascending trains. Of

course, it is quite possible—and, indeed, in many places it is customary-to pin down some of the side-lever brakes before commencing the descent, but once pinned down the brakes cannot be eased or taken off until the entire train is brought to a stand.

Every goods waggon should be fitted with a brake, and it would be of immense value if that brake could in all cases be applied and controlled when the train is in motion.

The American type of long goods waggon, with a four-wheel bogie-truck at each end, is fitted with a brake very similar to those adopted on the ordinary horse tram-cars. On the top of the waggon a horizontal iron hand-wheel, about 18 inches in diameter, is fixed on to a strong vertical iron rod, which works in brackets, and extends down below the underside of waggon framing. One end of a short length of chain is secured to the foot of the vertical rod, and the other end is connected by light iron rods to the series of levers which pull on the brake-blocks. By rotating the horizontal hand-wheel the chain is coiled round the lower end of the vertical rod, the brake-levers are pulled over, and brake-pressure applied to the wheels of the waggon. The brakesman is supplied with a convenient seat and footboard, and on the floor-level of the latter there is a pawl and ratchet attached to the vertical rod, which permits the brakes to be applied to the extent required. The pawl retains the brakes in position until the brakesman with his foot pushes the pawl out of the notch of the rachet and releases the brake gearing, which is at once pulled off quite clear by strong bow-strings attached to the framework of the bogies.

The type of hand-brake is, perhaps, the simplest that can be made. The brakesman has merely to put it on, the pawl and ratchet keep it on, and the bow springs take it off when no longer required. Each one of these long, loaded goods waggons becomes a very serviceable brake-van, and for ascending and descending steep inclines all that is necessary is to take on a few additional brakesmen to manage the brakes of as many suitable waggons. These incline brakesmen, after going down, can return to the summit by the next ascending train, their small weight being a mere nothing as compared with that of special or extra brake-vans.

On some European lines it is the custom to sprag some of the goods waggon wheels when going down exceptionally steep