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4-inch wheels on, and a load of 40 lbs. the carriage described 89 feet in 5 seconds and 33 feet in 3 seconds; therefore the spaces described are very nearly as the squares of the times.

With 8-inch wheels and a load of 40 lbs. the carriage described 77 feet in 4 seconds.

We have shewn that W (sin. i — 1) is equal to the

force which accelerates a carriage down an inclined plane; and by Formula, Part I. page 83, the force which accelerates a body down an inclined plane

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In the first of the latter experiments, sin. i=039, 8 = 8.9 feet, and t = 5 seconds; if these be substituted in the above equation, we have

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The second trial, where s = 3.3 feet, and t3 seconds,

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In the last, s

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The ratio of the friction to the pressure, as deduced from these experiments, is the next subject to be considered; and since the diameter of the axis is 55, and the diameter of the wheel 4 inches, when the whole resistance

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From the experiments with the 8-inch wheels, we have fx .55

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or f

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The mean between these is nearly, and this will be about the friction in practical cases.

Mr. Grimshaw, of Sunderland, made a great many experiments on the friction of wheel-carriages. He laid a cast-iron railway down upon beams of wood, and placed upon this railway the carriages which he used in conveying coals down to the river. He then elevated those beams at one end until they formed different angles with the hori zon, and observed the time the carriages were in descending from one end to the other when the plane was elevated to different angles; and by comparing the spaces actually passed over by the carriage with the space which gravity would have caused the body to describe in the same time when descending freely, the amount of retardation caused by the friction was ascertained.

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Loaded carriage weighing altogether 8522 lbs. friction equal to 50 lbs. or the 11th part of its weight.

*

Empty carriage weighing 2586 lbs, friction 10 lbs. or th part of its weight.

Mr. Wood, of Killingworth colliery, has made a very extensive range of experiments, and with very great care and attention. They may, therefore, be relied on much better than those of any other writer on this subject. He states the friction to be th part of the weight; but, considering the improvements that have been made in carriages, he says it may, in practice, be taken at the part of the weight.

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The whole resistance is resolvable into two parts; that which acts upon the axles, and that which acts upon the rails.* Mr. Wood, by a great number of experiments,

* The friction at the rails is that of rolling; but the friction at the axles is that of rubbing, or attrition as it is sometimes called.

has determined the resistance of the rolling of the wheels to be th part of the whole weight. His experiments also shew that this ratio is not increased by an increase of the weight, and that it is nearly the same in velocities varying from 5.5 to 14-45 feet per second; so that the resist ance by the rolling of the wheels is a uniformly retarding force, both with respect to velocity and weight.

Now, supposing the resistance from the wheels to be Tooth part of the weight, and the whole amount of friction to be known, we can easily obtain that of the attrition at the axles; and the following table, which is taken from Mr. Wood's Treatise on Rail-roads, second edition, page 222, will give the results of his experiments :

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9 9408 8096 41-46 9.40 10 9408 8096 44-19 9.40| 34-79 232 11 3472 2160 12-73 3.47 12 9100 7840 39.

9.10 29.90 262 12-3621.2

From this table it appears that there is a very great difference in the amount of friction between the experiments of Mr. Tredgold and Mr. Wood, but, as we

32-06 252

11-6 217

11-620

9.26 233

11.6 20.

have observed before, the great number of experiments which Mr. Wood has made, their coincidence, and the care and judgment with which they were performed, are particular recommendations in their favour. Indeed, Mr. Tredgold observes that he did not take the greatest care in preparing his model, for he considered that this could not be kept up in larger carriages; but in this he appears to be mistaken.

ON LOCOMOTIVE ENGINES.

Since the opening of the Liverpool and Manchester Railway, the most astonishing improvements have been made in the principles of these engines. Previous to that time, they were hardly capable of effecting a greater speed than six miles, and very frequently not more than four or five miles an hour: but now we find their regular day's work averaging more than 15 miles an hour; and, as will hereafter be seen, the Rocket has traversed the space of seven miles at the prodigious rate of 30 miles per hour, but without any train or tender; and allowance being made for stoppages, the seven miles may be considered as performed at the rate of 35 miles per hour.

A very valuable experiment was made by Mr. Wood, of Killingworth colliery. He caused five loaded waggons, weighing each 9408 lbs. to descend an inclined plane railway, rising 134 inches in 388 yards, or of an inch to a yard nearly. He found that the waggons passed over this space in 2 minutes. He then attached an engine to these waggons, weighing 9 tons, making the whole weight 67,200 lbs. ; and he found that the time of the whole passing over the 388 yards was now 2 minutes. In this case, the moving force was the difference between the friction and the force of the weight down the plane. No steam was furnished from the boiler; and the force of the weight gave motion to the wheels of the engine, to the pistons, and all other parts connected with the same. By this

means, the friction of the wheels and all the other parts of the engine, as well as the friction of the five waggons, was employed to resist the force of the weight down the plane. This gives the friction of the five waggons,

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47040 lbs. H te)W, in which W =

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134,

1611, and t = 120 seconds.

1164

131600) × 47040 = 216 lbs.

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The resistance from the friction of the axles and the action of the wheels on the rails, being estimated at the 200th part of the weight, gives 100 lbs. which leaves 112 lbs. for the friction of the pistons, &c.

We will now give an account of the grand competition of locomotive engines at the Liverpool and Manchester Railway, selected from Mr. Wood's Treatise on Railroads and the Mechanic's Magazine.

Mr. Harrison, who was one of the directors, had been for some time of opinion that the excitement of a reward, publicly offered, would be the most likely mode of effecting their object; and in this opinion the other directors ultimately coincided. Accordingly, on the 20th of April, 1829, they resolved on offering a premium of £500 for the best locomotive engine, subjected to the following stipulations and conditions:

"Stipulations and Conditions on which the Directors of the Liverpool and Manchester Railway offer a Premium of £500 for the most improved Locomotive Engine. "1st, The said engine must 'effectually consume its own smoke,' according to the provisions of the Railway Act, 7 Geo. IV.

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