the whole strain would be determined by the bite of the wheels.

But it will very fairly be observed that the wheels themselves, if of longer radii, must be stouter, to be of equal strength. Let us calculate the quantity of additional weight on this account. It is evident that the strain on the wheels will be in the plane of the wheels, and, therefore, the vertical dimensions of them need not be increased. Now, it is well known, and might very easily be shown from the preceding arguments, if one of the dimensions of a bar remain constant, that when the strain is in the variable dimension to produce a lateral fracture, and applied at the end of the bar, that the cube of the thickness must be as the length, to support an equal pressure at the end. Therefore the cube, or third power of the weight will be as the fourth power of the length or radius.

Hence, for 50 per cent. increase in the radii of the wheels, the weight must be about 71 per cent. greater. In round numbers, therefore, by increasing the gage and radii of the wheels 50 per cent., we shall double the joint weight of the wheels and axles of the engine. The other parts need not be increased, unless the cranks are not increased as the radii of the wheels, or a greater tension of strain used.

Consequently, if the weight of the wheels and axle form a third part of the total weight of the engine (which is mere guess work), and the working-wheels are three-quarters of this, their weight, supposing the engine to be 12 tons, will be then 3, and the new weight 6. But, reckoning twentyeight times the insistent weight for the load drawn, these 3 additional tons on the working-wheels will meet power for 84 tons of additional load. On the principle of economy, therefore, and the power of overcoming inclines, this would pay well, supposing no advantage besides was gained.

I have not taken into account the greater weight of the axles and wheels (if thought advisable to make these greater) in the carriages, because my arguments have been directed chiefly to the engines, and I have not by me any account of the proportional weights of the parts. But the computation is easily made, and I do not augur that the total amount of increase of weight, particularly if the wheels be not enlarged, would be more than a small fraction of the weight of the whole train.

Another object the Great Western Company have in view, which in a commercial and agricultural sense is worth serious consideration. They expect, by increasing the

breadth of their lines, to be able to construct trucks lower, and more safe and convenient than they now are, for the transportation at once of loaded vehicles to distant places, without the trouble and expense of unloading, loading, and warehousing the articles; so that when they arrive at the nearest point there will be nothing to do but to put on fresh horses and take the goods, on the same waggons or carts they were first loaded on, to their destination. This, perhaps, some will say can now be done. So it may; but could any one prudentially place a top-heavy cart or waggon, whose wheels are 5 feet apart, on a truck, whose wheels are only 4ft. 8in., to be whirled along 20 or 25 miles an

hour?

On the Axle-tree Friction of Wheel Carriages.

While discoursing of the merits of Mr. Brunel's plan of increasing the breadth of the lines and height of the wheels, the other day, it was observed to me that increasing the dimensions of the wheels relatively to the axles was expected to reduce the axle friction considerably, which is an important element in the friction of trains. Not being able to see it in this light, I was induced to consider it in my return home, and the result in my mind was, that no advantage whatever would be gained in this respect, supposing our present principles of friction to be true. Finding so marked à difference between my own conclusions, on a subject apparently so simple, and those of the gentleman I allude to, I was induced to examine the different authors I have by me touching on the subject. As they all more or less sanction the opinion of the above gentleman, but either without giving any reasons or such as are perfectly absurd, I have thought it advisable to take this opportunity of bringing the matter formally before the scientific world, that it may have that full investigation experimentally, which, from its influence in our present mode of transit, it is entitled to. With this view I shall cite the opinions of the authors alluded to, and then give my own investigation.

Emerson, p. 110 of his "Mathematical Tracts," says: "It may be observed that great wheels and small axles have the least friction." An observation without a reason, which amounts to nothing.

Hutton, vol. ii., p. 601, " Mathematical Dictionary," observes: "If we consider wheels with regard to the friction on their axles, it is evident that small wheels, by turning

oftener round, and swifter about their axles than large ones, must have much more friction." Nothing surely can be more erroneous, if the principle now generally admitted and confirmed by all experimentalists is true, namely, that "friction is independent of velocity." This very law is given as the result of Vince's experiments in vol. i. of the same Dictionary, p. 557.

A third writer, who touches on friction, and indeed is always ready to retail the opinions of others, if likely to be profitable, but who very sensibly happens to be silent on this particular point, says, "the revolution of wheels on axles partakes of the nature of sliding and rolling friction, and holds a sort of intermediate place between the two." Unless the particles of grease or oil, by which the axles are generally lubricated be the rollers, I should be glad to know where there is any rolling between the axle and its box. To me nothing appears but a simple slipping friction.

These authorities evidently say nothing to the purpose. I shall, therefore, simply lay down the principle now generally received, draw my conclusions from it, and hope it will excite the attention of abler hands.

Principle." Friction between hard surfaces is proportional to the weight, but independent of velocity or the quantity of rubbing surfaces."

Vince it is known considered that the quantity of rubbing surfaces had something to do in the matter, and that between hard surfaces the less the abrading surfaces, the less the friction. Reason, however, and the experiments of Coulomb, Ximenes, &c., are against him, and it is now generally admitted they are right. Mr. Perkins assures me he has found the contrary to Vince's assertions between steel surfaces.

Now, on the received principle, it is the insistent weight, not the size of the axle, or the velocity with which the wheel revolves, that measures the amount of friction. The friction is also the same whether the axle is fixed and the wheel revolves on it with a given pressure, or whether the wheel rolls on the ground and is pressed by the axle with that pressure. In the case of the wheel revolving on a fixed axle, if F be the value of the friction, W the weight acting at the circumference of the wheel in its plane and perpendicularly to the radius which would just balance the friction, R the radius of the wheel, and r that of the axle, the wellR known principle of the lever will give us F=W; and if p

r

be the resistance on the centre of the axle of an imaginary

lever, W+p=F. Therefore, R and F being constant, W must increase in the same ratio as r does, and p diminish by the same increment that W increases; that is, the pressure on the centre of the axle must be less as the axle is greater. This would be strictly the case, if the wheel revolved on the axle. Reversing it, and the pressure on the centre of the axle, ought, on the principle of leverage, to be the force of traction, which would be less as the axle relatively to the wheel is greater, and would leave the remaining part of the friction to be compensated by a twisting of the axle, or a pressure in the line of traction directly downwards; but if, instead of having recourse to this imaginary leverage, the point of traction be fixed at the bottom of the axle, the whole force to be overcome is obviously the friction, which, by the above principle, is the same whatever be the size of the pressing surfaces, or the size of the axle, other things being alike.

Since writing the above, Mr. Perkins has informed me that he has found, by experience, a marked difference in favour of larger axles, which he very justly attributes to the solid bearings being more easily kept asunder by the lubricating medium. If then we reflect that the friction of the axles in railway trains constitutes, as I am informed, a very large portion of their whole friction, it is evident that the increased gage contemplated by the Great Western Company, by compelling them to have larger axles, will also reduce the friction and consequently the expense of transit. Hence it is plain that-in whatever point of view we regard it-an increased gage is desirable. In the three grand desiderata-wear and tear, reduction of friction, and safety in high velocities-there can be no doubt. The only question is the extent to which it will be proper to carry the increase. If we go beyond 7 feet in the gage, the subordinate parts of the engine, that is, the wheels and axles, will be obliged to be made disproportionably heavy, and power must be spent when it will make no adequate return; for what we are most in want of is a better supply of steam. On the contrary, if we do make an alteration, 6 feet seems to be the minimum to which, with our warm anticipations of improvement in engines, we should confine it. I do not know Mr. Brunel's views, but, taking all the circumstances into consideration, I should be more inclined to fix on 6 feet as a standard, than upon any other.

For want of space I must defer discussing another very important matter before alluded to, connected with this subject, and bearing strongly on it.-EDITOR.

PASSED

CAPITAL, COST, LENGTH, REVENUE, EXPENSES,
PROFIT, &c. &c., OF RAILWAYS,
DURING THE SESSION OF 1836.

BY JOHN THOMPSON, Esq.

To the Editor of the Railway Magazine.

Harwich Railway Office, 26, Austin Friars,
Oct. 20, 1836.

DEAR SIR, THE accompanying statement relative to the Railways, for which Acts have been obtained during the late Session of Parliament, I have been at some trouble in compiling, from the Reports of the Committee of the House of Commons upon the respective Bills. If you think it worth the space it will occupy in your Magazine, I shall be glad if you will insert it in the next number. Some of the results are curious, and as a piece of statistical information it may be valuable.

I am, dear Sir, your obedient Servant, JOHN THOMPSON. Railways for which Acts have been obtained during the Session of 1836, showing their respective lengths and estimated cost; the number of Tunnels and their lengths; the length of the Planes and their gradients; the number of Curves and their radii; the estimated revenue to be derived both from Passengers and Goods; and the Profit per cent. upon the Capital employed.

ARBROATH AND FORFAR.-Capital, 70,000l. Estimated cost, 69,4601. Length of line, 15 miles, 2 furlongs, 38 yards. Cost per mile, 4,548. Estimated revenue from passengers, 2,6007. Estimated revenue, from goods, 6,1797. Annual expenses, 2,900. Annual expenses per mile, 1901. Profit per cent. on capital, 8.-There are no planes to be worked by assistant engines. The steepest gradients are 1 in 200; 1 in 261; 1 in 232. The curves are favourable. The smallest radius is upward of one mile.

AYLESBURY.-Capital, 50,000l. Estimated cost, 45,2421. Length of line, 6 miles, 7 furlongs, 66 yards. Cost per mile, 6,5457. Estimated revenue from passengers, 3,3687. Estimated revenue from goods, 3,3601. Annual expenses, 3,000l. Annual expenses per mile, 4321. Profit per cent. on capital, 7.-There are no planes to be worked by assistantengines. The gradients are favourable; the steepest is