upon rollers, the velocity of the periphery on which the rope runs, being to the velocity of the circumference of the axle, or part exposed to rubbing, as 16:1; we reduce the friction in that proportion, and make it equal to the 59-20th part of the weight, or 12317: 208, as shown in columns five and six of the table. And, in like manner, the friction will always bear different proportions to the weight of the body, according to the diameter of the sheeves or rollers on which the rope or the weight is placed. When the diameter of the axle remains the same, column nine will then show the ratio which the friction bears to the weight, when it is not placed upon sheeves; and our reason for giving the ratio in this manner, was to express it in terms not variable with the size of the sheeves upon which it might be placed, but in constant terms which might be reduced to practice when the size of the sheeves was fixed upon. Column six shews the whole weight or pressure of the apparatus put in motion. when the carriages are descending, and comprehends the weight of the rollers, the rope wheels, the rope, and its pressure upon the wheel which it winds round; observing, that in the fixed engines, only one half the weight of the sheeves is reckoned, as the amount of their action is only one half of the whole. The resistance of the rope, it will be perceived, is greater in some of the self-acting planes than the fixed-engine planes, which most probably arises from the rope of the former having to bend round wheels of smaller diameter than the fixed engine rolls when the carriages are traversing the plane; while, in the latter, the rolls are not only of larger diameter, but the rope is only uncoiled off the roller, as the carriages drag it out from the engine.

In

§ 3.-Theoretical Conclusions on the Friction of Ropes. The maximum resistance in self-acting planes, is nearly the third, and the maximum as 1 : 3.77. practice, it will, however, be sufficiently accurate, and perhaps more advisable, to take the third. In the fixedengine plane, the same ratio should be taken; as the engine, in winding the rope upon the roll, will be subjected to the same amount of friction that occurs in the self-acting plane, from the bending of the rope. In calculating, however, upon a descent of plane, that will cause the carriages to drag the rope out from the engine, we may, under favourable circumstances, take the ratio at 3:1. Assuming, therefore, the ratio as one-third, by causing the rope to run upon rollers, the periphery of which, where the rope is supported, being twelve inches, and the diameter of the axle, on which the roller runs, one inch; then the friction will be diminished in that ratio, and become only the thirtysixth part of the weight, and in the same proportion with any other size of roller. And, in general, we can calculate, "à priori," the friction of the rope upon any plane, by taking the weight of the whole apparatus, inclined-wheel, sheeves, and rope; and the pressure of the latter upon the wheel, in winding round it, and also its extra pressure by any curves in the line of the road; then the friction will amount to one-third of the whole of that weight, if no rollers are employed. Knowing the diminution, by the size of sheeves fixed upon, the actual friction is found.

Thus let Rthe weight of the wheel, or rope roll.

R'

that of the sheeves.

R" the weight of the rope.

P = the pressure upon the wheel, or rope roll.

and r the ratio of difference between the diameter of the axle, and periphery of rope roll, or sheeves; diameter of

Having thus ascertained the ratio of the friction to the weight, it will be evident that the friction of ropes of different lengths will be in proportion to those lengths, or to the weight.

The preceding proportion, expressing the resistance of the rope, we trust may be depended upon as a datum of calculation in general; but, in applying it to practice, it must undergo some limitation. It has been ascertained, under favourable circumstances, the planes were not prepared for the purpose; but taken as in actual use, and as they had remained for some years: but, during the experiments, the weather was favourable, and this has considerable effect upon the resistance; we must, therefore, found our calculations upon data, which will hold good under every possible variation of weather, and this can only be done by appealing to practice.

In the selection of the planes which we have here given, there is one which we consider just adequate, with the number of carriages usually employed, to effect a regular and constant passage during all states of the weather, except under very extraordinary circumstances indeed, such as the rails being covered with snow. We shall, therefore, make that the foundation of our data for estimating the effects on other planes.— To effect the descent of any carriage or train of carriages down a plane by the action of gravity, we must give a certain excess of preponderance above the friction of the respective parts, to accomplish that descent in a given time; and this time will be entirely governed, and be in precise proportion to the excess of gravi

tating force employed, compared with the weight of the carriages.

The self-acting plane, Experiment I., Chap. VIII., is one which, when six loaded carriages are employed in dragging six empty carriages up by the rope there described, we can safely state, from a frequent opportunity of witnessing its action, has just sufficient preponderancy to produce the required effect; and we do not think it would be proper in any case to allow less.

The whole weight there moved, including the inertia of the wheels, rope, sheeves, &c. will be 86198 lbs., and the excess of preponderance, above the friction and resistance of the whole train G-g+F+f+ will be equal to 369 lbs. nearly.

Whence we have, if w denote the inertia of the whole mass in motion,

In

By Experiment I., Chap. VIII., when the moving force, and resistance were in a state of dynamical equilibrium, the time of descent was 200 seconds. practice, as above, we find that in order to effect the certain transit or passage, it is necessary the preponderance should be such as that, under the most favourable weather, the descent should be effected in 176 seconds; then the excess or preponderance of gravitating power to be given in practice above what is required to merely effect the descent in fine weather, or by taking the resistance as shewn in the table, must be in the ratio of 200 176, or, in even numbers, as

CHAPTER IX.

THEORY AND APPLICATION OF THE VARIOUS KINDS OF MOTIVE POWER EMPLOYED ON RAILROADS.

THIS chapter will comprehend practical illustrations, as well as theoretical applications, of the different species of motive power previously enumerated; deduced from the foregoing disquisitions, and from experiments made on their performances in actual use upon railroads.

Retaining the classification adopted when describing the different kinds of motive power, we shall divide them into the following order :

1. Horses.

2. Self-acting Planes.
3. Engine Planes.

4. Locomotive Engines.

§ 1.-Horses.

The power of a horse, or that part of his muscular exertion which, in travelling, he is capable of applying upon the load, has been variously stated by different authors. It is not the force he is capable of exerting at a dead pull, or for a short period, by which we are to judge of, or estimate his strength; it is what he can exert daily, and day after day for a long period, without injury to his physical powers, that we are to take as the criterion for practice.

A railroad is peculiarly adapted to show the power of a horse, as he is continually employed in overcoming the same resistance; and the inclination of the road, in general, has little effect upon the power required to overcome the gravity of his own weight.