square of the velocity. Hence our steam-coach, when moving at 4 miles an hour in a still atmosphere, would encounter a resistance from the pressure of the air of 2 pounds; at 8 miles an hour the resistance would be 9 pounds; at 12 miles 20 pounds; at 16 miles 36 pounds; at 20 miles 57 pounds. The steam-waggon, presenting only half the surface in front, would experience only half the resis

tance.2

Let us assume, according to what we have already stated, that a power of 150 pounds would just put the steam-coach in motion; then if we allow an additional power of 33 pounds for acceleration-making 183 pounds altogether, we find that, if the air did not oppose its progress, it would move over 43 miles in one hour. Now, since it is propelled only by a force of 33 pounds, as soon as the resistance of the air pressed it back with a force of 33 pounds, the acceleration would cease, and the motion become uniform. This would take place within 12 or 15 minutes, and when the velocity had risen to 14 or 15 miles an hour. With the steam-waggon, presenting only half the front, the velocity would become uniform at 22 miles an hour. Hence we see, that if we had always a perfect calm in the atmosphere, we could impel 15 tons along a Railway with a velocity of 15 or 22 miles an hour (according to the extent of surface the vehicle presented) by a force of 183 pounds. We may now compare the resistance on a Railway with that in a Canal or arm of the sea, in a calm atmosphere.

Power required to move a Boat in water.-According to the table formerly given, the force required to impel a vessel weighing with her load 15 tons, through water, at different velocities, would be as follows:

Power required to move a Waggon on a Railway.—In this case,

'See Rouse's Table, No. 317, article Pneumatics, Encycl. Britann.-Also article Resistance, in the same work.

2 To affect minute accuracy in calculations of this kind is a mere deception. I have therefore generally rejected fractional quantities. In point of fict, the resistance increases rather faster than in the simple ratio of the surface, and the resistance of a sphere is less than the half of that of its great circle. On the other hand, the resistance increases in a ratio rather less than that of the square of the velocity. See Pneumatics, ubi supra, and Playfair's Outlines, I. 264.

supposing the waggon with its load to weigh 15 tons, we have merely to add to the power necessary to overcome the friction (150 pounds), a few pounds more to balance the resistance of the atmosphere at the velocity proposed. For the steam-coach with 30 feet of front, it would be as follows:

We may now combine the two tables into one, and exhibit the results in horse-power as well as pounds-reckoning one horsepower equal to 180 pounds.

We see from this table the astonishing superiority of the Railway over the Canal, for all velocities above four miles an hour. Nearly three times as much power would be required to move an equal mass at 6 miles an hour on a Canal as on a Railway; 5 times as much power would be required at 8 miles an hour; 10 times as much at 12 miles; 15 times as much at 16 miles; and 24 times as much at 20 miles an hour. It is evident, also, that an addition of power, too trifling to add anything material to the weight of the vehicle, would raise the terminal or uniform velocity from 4 miles an hour to 20; and that, speaking practically, it would cost no more to command a velocity of twenty miles an hour on a Railway, than a velocity of one. Except for the chances of injury to the railway or the vehicle, there would not be the smallest reason for conveying goods even of the coarsest kinds at 4 miles, rather than at 20 miles an hour!

But a perfect calm in the atmosphere is very rare, and vehicles intended for daily and constant use must be prepared to contend with the strongest winds. The power must therefore be increased

to such an extent as to enable the vehicle to travel at its wonted

pace in all weathers. Now, according to Mr. Smeaton, a “hard gale" is found to sweep along the surface of the earth at the rate of from 40 to 50 miles an hour. This velocity, which would be increased to 60 or 70 by that of the steam-coach when travelling at 20 miles an hour, would produce a resistance of 600 pounds on the 30 feet of front of the steam-coach, or 300 pounds on the front of the steam-waggon. With a speed of eight miles an hour, the coach and waggon would encounter a resistance about one-half less. The vehicles, however, should not be constructed entirely with a view to extreme cases; and except for the conveyance of mails, and some similar purposes, an average velocity of 20 miles an hour, for vehicles of the weight and description mentioned, would be secured by a power varying from 200 to 500 pounds-that is, from one-fifth to one-tenth of the power required to produce the same effect on water. We see, however, that the resistance of the air, which, in vulgar apprehension, passes for nothing, comes to be the greatest impediment to the motion of the vehicles, and may in some cases absorb five parts in six of the whole power. Let it be remembered, at the same time, that this aerial resistance rises into consequence solely because the high perfection of the machinerythe vehicle and the road-almost annihilates every other. The atmosphere equally opposes the progress of the stage-coach, the trackboat, and the steam-boat; but the motion of these vehicles is comparatively so slow, and the power of impulsion required to overcome the other impediments to their progress is so great, that the resistance of the air is disregarded.

Common roads may be considered as railways of a less perfect kind, and as to which nearly the same laws are applicable. But the friction is much greater, first, on account of the inequalities of the surface; and secondly, because the shocks the vehicle is subjected to in its motion over these inequalities, renders a heavier and clumsier construction necessary. But when the road is either covered with a small moveable gravel, or with a stratum of soft mud, these approximate to the nature of a fluid body, and the resistance from the rolling motion will probably rather increase with the velocity. The friction in this case cannot easily be reduced to any rule; but that it must be great is evident from an experiment made by M1. Palmer, who found, that by simply covering a tram-railroad with fine dust, the weight required to move a loaded waggon on it was increased from 36 pounds to 43, or one-fifth.

Mr. Stevenson, civil engineer, has recommended Railways of a cheaper and ruder kind for common roads and the streets of cities, which will probably be found extremely useful. These consist of wheel-tracks of smooth wrought stone, accurately joined. He employs for this purpose, stones measuring six or eight inches in the

lengthway of the road, twelve inches broad in the other direction, and twelve inches deep; the intervals between the tracks being laid with common ruble causeway. Two double tracks might be sufficient for a highway, one for going and one for returning; but the streets of a city should have as many as their breadth would admit. To give the work stability, the stones are made two or three inches broader at the bottom than the top, and they rest on a foundation of gravel or chips laid in mortar. Mr. Stevenson finds that the lineal yard of the double track would cost, in this quarter, about 9s. (13s. 6d. per square yard of laid surface), and in ordinary circumstances it might last 15 years.-Ruble causeway, or that formed of unequal stones, costs about 2s. 4d. per square yard, and aisler causeway formed of square stones, 4s. 8d. M'Adam-roads cost here about 1s. 6d. per square yard; but in great thoroughfares they are found to waste so fast as to require an entire renewal every three years, and on this account, besides having the disadvantage of being always partially under repair, they are actually more expensive than aisler causeway. There is every reason to believe that the stone-tracks will be less expensive than either common causeways or gravelled roads, and they will certainly save much in the wear and tear of carriages. They will besides connect most advantageously with the iron-railway system, by enabling the waggons used on the latter to travel through every part of a town. Mr. Menteath of Closeburn, who has paid much attention to the subject, is satisfied, that if smooth wheel-tracks were laid at all the acclivities, a good horse would be able to draw two tons on our present roads.

A hasty view of the subject led me at first to think that a smaller force of traction sufficed to move a carriage at a high than at a low velocity. This is true if we take the time into account, but not otherwise. The correct inference from the laws of friction is, that the force of traction, if measured by the dynamometer—or the pressure in pounds weight on the horse's shoulder, is the same, whether he travels over a given road in two hours or in four. When he travels quick, he continues the same pressure for a shorter time, and may in this sense be said to exert a smaller force. But from the greater power expended in moving his own body, and the necessary limits of animal strength, the smaller force, accompanied with a higher speed, requires a greater effort on the part of the

horse.

Returning now to our table, it will be observed, that though the same amount of horse-power which drags 1 ton on a good road, will drag 30 tons on a canal, at 2 miles an hour ; yet when we raise the velocity to 8 miles an hour, the resistance in water in

creases so much, that two horses on a road will do as much as one on a canal.

In the estimate respecting railways, I have not taken into account the time lost in overcoming the inertia of the waggon where a small power is applied, because, in point of fact, the casual resistance of the wind would render it necessary to provide double or triple the power above stated: but if necessary, the time lost by the slow motion at first might be saved. Suppose there are a certain number of places where the steam-coach or waggon was to stop, to take in or put out passengers or goods; and farther, that the waggon, by travelling a few miles, has acquired a uniform velocity of 20 miles an hour. Then if it is made to ascend an inclined plane of 10 feet perpendicular height, this velocity will be extinguished, and the vehicle will stop at the head of the plane. When it is to proceed again on its journey, its descent along an inclined plane of the same height on the other side, will enable it to recommence its career in a few seconds with the full velocity of 20 miles an hour. By raised platforms of this kind, at the two extremities of the journey, and at the intermediate stages, the velocity, once generated, might be treasured up for permanent use. The platforms should be of different heights, corresponding to the various velocities of the vehicles plying on the Railway. But, in point of fact, the terminal velocity is attained so soon from a state of rest, that this contrivance would probably be found unnecessary.

Where locks or lifts occur, the stationary steam-engine should drag up the vehicle (supposing it to be along an inclined plane), not simply from the one level to the other, but to a platform some feet above the higher level, that the vehicle, by its descent, might recover the lost velocity. It is plain, however, that when the difference of level did not exceed eight or ten feet, the momentum of the vehicle would carry it up without any assistance from a stationary engine, and with merely a small temporary loss of velocity.

Some persons imagine erroneously that teethed-wheels and rackwork would be necessary where the Railway was not perfectly level. But the friction of iron on iron being 25 per cent. of the weight, if the whole load was on the wheels to which the moving power was applied, and if the quantity of power was sufficient, the waggon would ascend without slipping, though the plane rose 1 foot in 4-while even cart-roads scarcely ever rise more than 1 foot in 18 or 20. If four-fifths of the load, however, were placed on separate cars, and only one-tenth of the whole pressure, for instance, was on the axle to which the moving force was applied,