Upon a general view of the body of experimental researches which have been detailed in this Report, the following practical conclusions appear to be fully established :—

1. The resistance offered to the moving power by a railway train is not, as has been heretofore supposed, independent of the speed, but is augmented in a high proportion as the speed is increased.

2. If the carriages be unaltered in number, form, and magnitude, the resistance will be in the simple ratio of the load, the speed and other circumstances being the same.

3. If the train be increased by augmenting the number of carriages, the ratio of the resistance to the weight at the same speed, other things being the will be diminished.

same,

4. The practice hitherto adopted of expressing the resistance on railways as so many pounds per ton of the gross load ought to be discontinued, since the resistance is not proportional to the gross load, and therefore such expression may lead to erroneous conclusions.

5. The resistance of ordinary loads transported on railways at ordinary speeds, more especially of passenger trains, is very much greater than has been heretofore assumed, being with heavy loads at least double the common estimate, and with light loads threefold greater.

6. That a considerable amount of the resistance, more especially in the case of passenger trains, is due to the resistance of the air, and therefore expedients (such as wheels of increased magnitude) to diminish the amount of the mechanical resistances are not likely to be attended with adequate advantage.

7. That the resistance due to the air appears to proceed from the effect of the entire volume of the train, and not to depend in any sensible degree on the form of its foremost end. Expedients, therefore, for attaching a sharp front to the engine are ineffectual and useless.

8. That the mathematical formulæ given in the first part of this Report, consisting of two parts,-one proportional to the gross weight of the load but independent of the speed, and the other proportional to the square of the speed-have given results in all the cases to which they have been applied in accordance with the experiments. Such formula may therefore be taken to represent the facts until further and more extended and varied experience shall show the corrections of which they may be susceptible.

9. That the resistance produced to railway trains moving at ordinary speeds,

by curves of a mile radius, is inappreciable, and therefore curves of a much shorter radius may be safely laid down.

10. That the mean amount of resistance to railway trains being so much above the estimate heretofore adopted by engineers, and the resistance from curves being so much less than their estimate of it, the practical principles on which they have generally acted in laying out lines of railway will require serious modifications, all of which fortunately will have a tendency to diminish the expense and difficulty attending the construction and the working of railways.

In consequence of the low estimate of the resistance and the high estimate of the effect of curves, which engineers in general have heretofore adopted, great expense has been incurred and difficulties encountered to obtain flat gradients and straight lines. In some cases the gradients have been so levelled as not to exceed from four to six feet per mile, and the lines have been rendered so straight, that the curves nowhere have so short a radius as a mile. From what has been proved in the present Report, it is evident that such lines of railway will afford no practical advantage over those which have been laid down with gradients of sixteen, twenty, or even twenty-five feet per mile, and on which curves of a mile or less radius have been allowed.

The writer of this Report cannot conclude it without acknowledging the liberal assistance he has received from the Grand Junction Railway Company, who supplied engines, carriages, and waggons, without charge, for the experiments; also from the Liverpool and Manchester Railway Company, who allowed many of the experiments to be made on their line.

Mr. Hardman Earle of Liverpool, has also been of the greatest assistance in conducting the experiments, several of which were suggested by him.

Similar acknowledgements are also due to Mr. Edward Woods, engineer to the Liverpool and Manchester Railway Company. This gentleman superintended and directed many of the most important experiments, and subsequently reduced and tabulated them, when the writer of this Report was prevented by professional business from being present.

Report on Railway Constants. By EDWARD WOODS.

In the first Report, by Dr. Lardner, of the Committee appointed by the British Association to investigate the mean values of the resistance of trains moving upon railways, published in the eighth volume of the Transactions of the Association, the various modes proposed for ascertaining the amount of resistance to the tractive power were described, and their relative merits discussed.

The methods alluded to were

1. By the dynamometer.

2. By observing the motion of a load down an inclined plane, sufficiently steep to give accelerated motion.

3. By putting the load in motion on a straight and level line of railway, so as to impart to it a certain known velocity, and then observing the rate of its retardation.

4. By a combination of the two preceding methods, as resorted to by Le Comte de Pambour.

5. By a plan proposed by Dr. Lardner, viz. selecting two inclined planes of

different acclivities, and observing the maximum loads which an engine can draw up those planes whilst exerting an equal tractive power.

At the time of the publication of their first Report the Committee had made a number of experiments in accordance with the second method,—that of observing the motion of trains down inclined planes of different degrees of acclivity, noting whether the motion were accelerated, uniform, or retarded. Although these preliminary experiments were limited in number, and tried under rather disadvantageous circumstances as respected the weather, the fact that resistance increased in a heretofore unsuspected degree, in proportion as the speed of the train increased, was satisfactorily established. In what ratio the increment took place, whether as the square or some other function of the velocity, could not be determined, the results presenting some trifling apparent discordances, in consequence of the varying effect of the wind which prevailed at the time of the experiments. In pursuing their inquiries at a subsequent period, the Committee have been more fully convinced of the soundness of the principle which guided them in the selection of the method they at first adopted, and they have accordingly continued to conduct their experiments in a similar manner, repeating them with various sizes of trains, at various velocities, on the Sutton incline of 1 in 89 on the Liverpool and Manchester Railway, and on the inclines of 1 in 177, 1 in 265, and 1 in 330, on the Grand Junction Railway.

It is to be regretted that the weather was not on all occasions perfectly favourable. In some instances, however, there was not a breath of wind to disturb the results, especially when engaged at the Sutton incline plane. Such results deserve great confidence, and are particularly valuable for determining the amount of friction, properly so called.

A few remarks are necessary on the principle of analysis, adopted with regard to the observations which appear in a tabular form at the end of this Report. The data given there or elsewhere in the Report are,

1. The coefficient of gravity on the inclination of the plane.

2. The initial velocity of the train at some determinate point on that plane. This may be either zero, as when the train starts from a state of rest, or some positive quantity.

3. The terminal velocity at some other determinate point on the same plane. 4. The time elapsed in traversing the space intervening between those two points.

5. The space intervening.

6. The force of gravitation, which in this latitude is known to be represented by 324, the velocity in feet per second acquired by a body falling freely in vacuo, at the end of the first second.

7. The weight or mass of the train, exclusive of the wheels and axles. 8. The weight or mass of the train subject to rolling motion, viz. the wheels and axles.

9. The radius of the wheels.

10. The distance from the centre of the wheel to the centre of oscillation. From these data, when accurately obtained, the resistance of the train can be determined with absolute precision, the method turning altogether upon a comparison between a certain fixed and standard force, the force of gravitation, and the observed force by which the train is impelled in its descent. If a body move down an inclined plane without encountering resistance, its velocity at any given depth below the level of the point where its motion first commences will be always equal to the velocity it would have acquired by a free vertical descent, through the same height. If, then, this standard velocity be compared with the observed velocity of a body which has moved down a

similar inclined plane to the same point, but which does meet with resistance in its passage, we at once obtain the means of assigning what amount of resistance it has suffered.

Some persons have objected to this method, on the ground that the results hitherto obtained by it have not always been consistent with each other. Such inconsistencies, however, may be satisfactorily explained, either on the supposition of the data not having been correct, or, what is more probable, from the fact of the existence of unobserved causes of irregularity, such as the influence of favouring or adverse winds, and differences of friction of the carriages. It will hereafter be shown what a remarkable correspondence the motions of the same train exhibit when permitted to descend along the same plane from the same point of elevation, provided the atmosphere be perfectly calm. Such correspondence could only exist under the uniform operation of the same producing cause, and the absence of accidental causes; and we therefore conceive that no surer test can be applied to determine the mean resistance experienced by a train in moving from one point to another down an uniform inclination, than a comparison between the observed time of its passage and the time it would have occupied if resistance had been altogether removed.

There are three cases of the motion to which the same formula is equally applicable:

1. When the motion is accelerated.

2. When the motion is uniform.

3. When the motion is retarded.

In the first case the coefficient (determined by the inclination of the plane) of gravity is greater than the coefficient of resistance, and therefore the quantity which must be added to the coefficient of gravity to represent the coefficient resistance is negative.

In the second case the coefficient of gravity is equal to the coefficient of resistance, and no correction is required.

In the third case the coefficient of gravity is less than the coefficient of resistance, and the addition to the coefficient of gravity is a positive one.

In all cases therefore the coefficient of resistance may be found, by adding to the coefficient of gravity a quantity (determined by considerations alluded to in the former Report) which is either negative, or equal to zero, or positive.

This quantity may be thus obtained :-Multiply the initial velocity (2) in feet per second by the time in seconds (4). From this product subtract the space (in feet) passed over (5), and divide the difference by 16 times the square of the time occupied (4). The quotient thus found must be subjected. to a slight correction, owing to the rotation of part of the moving mass, which correction may be determined by reference to data Nos. 7, 8, 9, and 10.

The initial velocity multiplied by the time represents the space which the train would describe were that velocity to remain constant. In the case of uniform motion, the velocity does remain constant, and the product of the two numbers equals the space traversed. Their difference, and consequently the whole quantity dependent upon it, vanishes, and the coefficient of gravity becomes also the coefficient of resistance.

In accelerated motion the product of the numbers is less than the space traversed, and the quantity to be added to the coefficient of gravity is negative, indicating the amount by which the force of gravity exceeds that of the resistance. On the other hand, when the motion is retarded, the reverse takes place, and the quantity to be added is positive.

Under the condition of uniform motion we are enabled positively to pronounce what is the mean resistance for that particular velocity. When, how

ever, the velocity is accelerated or retarded between the two points of observation, although the mean resistance is known, we cannot state whether that mean resistance is due to the mean velocity, or to some other velocity intermediate between the limits of the initial and terminal velocities, because experience has not yet assigned the law of the corresponding increments of resistance and speed. It will be sufficient for all practical, and even theoretical purposes, to assume the mean resistance as applying to the mean velocity, remarking that the calculations are chiefly made from observations where the initial and final velocities do not widely differ, thus reducing, as far as possible, the limits of error. A more considerable source of error arises from the difficulty of obtaining with precision the initial velocity, owing to our inability to measure the time of passing from stake to stake accurately to a small fraction of a second. To obviate this, a mean has been taken from the observed times of traversing one or two spaces, preceding and succeeding the post at which the actual velocity is required. The errors are thus diffused over a larger space, and rendered less sensible.

The carriages employed belonged either to the Grand Junction, or to the Liverpool and Manchester Company. The former were first class, the latter second class, but both kinds were closed at the top and sides, presented the same transverse section, were loaded to nearly the same gross weights, and in other respects were identical. It is next to impossible to obtain two carriages even of similar make, whose friction shall be exactly the same, and accordingly a slight difference was observed, and it was found on the whole that the mean friction of the Grand Junction carriages exceeded the mean friction of the Liverpool and Manchester carriages, a fact which may be accounted for by the latter having been in use for a longer period.

We shall now consider the results afforded by the tables under the following heads:

1. The Evaluation of Friction proper.

2. The additional resistance produced by increase of speed in trains of different sizes.

3. The effect of modifying the, form of frontage, and of otherwise altering the nature of the exterior surface of the train, as for instance, by closing up the spaces between the carriages, ascertaining also the effect of the engine (as regards its external configuration in diminishing the resistance).

1. The Evaluation of Friction, properly so called.-On the 23rd of August 1839, the weather being perfectly fine and calm, three Liverpool and Manchester first class carriages, weighing gross 14.8 tons, were allowed to descend the Sutton inclined plane from a state of rest, starting from a post numbered 0, and urged only by the force of gravitation. The experiment was repeated four times, and the train descended the plane from 0 to 22 post, a distance of 2420 yards, in the following times respectively:

1st. 4 m 28 s. 2nd. 4 m 25 s. 3rd. 4 m 23 s. 4th. 4 m 22 s.

These results coincide so closely, that we may fairly consider the sum of the resistances to have been the same in all cases, or at any rate to have decreased in only a very slight ratio, in proportion as the axles became better lubricated by continued running.

The fourth experiment is chosen as the subject of calculation, to determine the resistance of the said carriages at very slow velocities. Five separate computations are made from observations of the times of descent from No. 0 to No. 1, No. 0 to No. 2, No. 0 to No. 3, No. 0 to No. 4, and No. 0 to No. 5 posts respectively.