Position of the line of traction.

From these remarks, then, we may deduce the proper position of the line of traction. When the line of traction is horizontal, as AD, the lever of resistance is CF; but if this line is oblique to the horizon, as Ad, the lever of resistance is diminished to Cf, while the lever of the horse's weight remains the same. Hence it appears that inclined traces are much more advantageous than horizontal ones, as they uniformly diminish the resistance to be overDeparcieux, however, has investigated experimentally the most favourable angle of inclination, and found, that when the angle DAF, made by the trace Ad and a horizontal line, is 14 or 15 degrees, the horses pulled with the greatest facility and force. This value of the angle of draught will require the height of the spring-tree bar, to which the traces are attached in four-wheeled carriages, to be one-half of the height of that part of the horse's breast to which the fore end of the traces is connected."

come.

Notwithstanding the great utility of inclined traces, it will not be easy to derive complete advantage from them in twowheeled carriages without diminishing the size of the wheels. In all four-wheeled carriages, however, they may be easily employed; and in many other cases where wheels are not concerned, great advantage may be derived from the discovery of Deparcieux.

On the Position of the Centre of Gravity, and the manner of Disposing the Load.

Position of

From Mr. Ferguson's observations on the centre the centre of of gravity, (Vol. i, p. 11,) it must be evident, that if gravity. the axle-tree of a two-wheeled carriage passes through the centre of gravity of the load, the carriage will be in equilibrio in every position in which it can be placed with respect to the axle-tree, and in going up and down hill, the whole load will be sustained by the wheels, and will have no tendency either to press the horse to the ground or to raise him from it. But if the centre of gravity is far above the axle-tree, as it must necessarily be according to the present construction of appear to exert their strength, I was inclined to suspect its accuracy; but a circumstance occurred which removed every doubt from my mind. I observed a horse making continual efforts to raise a heavy load over an eminence. After many fruitless attempts, it raised its fore feet completely from the ground, pressed down its head and chest, and instantly surmounted the obstacle.

7 This height is about 4 feet 6 inches, and therefore the height of the spring-treebar should be only 2 feet 3 inches, whereas it is generally 3 feet.

wheel-carriages, a great part of the load will be thrown on the back of the horses from the wheels, when going down a steep road, and thus tend to accelerate the motion of the carriage, which the animal is striving to prevent; while in ascending steep roads a part of the load will be thrown behind the wheels, and tend to raise the horse from the ground, when there is the greatest necessity for some weight on his back, to enable him to fix his feet on the earth, and overcome the great resistance which is occasioned by the steepness of the road. On the contrary, if the centre of gravity is below the axle, the horse will be pressed to the ground in going up hill, and lifted from it when going down. In all these cases, therefore, where the centre of gravity is either in the axle-tree, or directly above or below it, the horse will bear no part of the load in level ground: In some situations the animal will be lifted from the ground when there is the greatest necessity for his being pressed to it, and he will sometimes bear a great proportion of the load when he should rather be relieved from it.

The only way of remedying these evils is to assign such a position to the centre of gravity, that the horse may bear some portion of the load when he must exert great force against it; that is, in level ground, and when he is ascending steep roads; for no animal can pull with its greatest effort, unless it is pressed to the ground. Now, this may, in some measure, be effected in the following manner. Let BCN (Plate VII, Fig. 20) be the wheel of a cart, AD one of the shafts, D that part of it where the cart is suspended on the back of the horse, and A the axle-tree; then, if the centre of gravity of the load is placed at m, a point equidistant from the two wheels, but below the line D A, and before the axle-tree, the horse will bear a certain weight on level ground, a greater weight when he is going up hill and has more occasion for it, and a less weight when he is going down hill and does not require to be pressed to the ground. All this will be evident from the figure, when we recollect, that if the shaft DA is horizontal, the centre of gravity will press more upon the point of suspension D the nearer it comes to it; or the pressure upon D, or the horse's back, will be proportional to the distance of the centre of gravity from A. If m, therefore, be the centre of gravity, b A will represent its pressure upon D, when the shaft DA is horizontal. When the cart is ascending a steep road, A H will

be the position of the shaft, the centre of gravity will be raised to a, and A a will be the pressure apon D. But if the cart is going down hill, AC will be the position of the shaft, the centre of gravity will be depressed to n, and c A will represent the pressure upon the horse's back. The weight sustained by the horse, therefore, is properly regulated, by placing the centre of gravity at m. We have still, however, to determine the proper length of b a and b m, the distance of the centre of gravity from the axle, and from the horizontal line DA; but as these depend upon the nature and inclination of the roads, upon the length of the shaft DA, which varies with the size of the horse, on the magnitude of the load, and on other variable circumstances, it would be impossible to fix their value. If the load along with the cart weighs 400 pounds, if the distance D A be 8 feet, and if the horse should bear 50 pounds of the weight, then bought to be 1 foot, which being of D A, will make the pressure upon D exactly 50 pounds. If the road slopes 4 inches in one foot, bm must be 4 inches, or the angle b4 m should be equal to the inclination of the road, for then the point m will rise to a when ascending such a road, and will press with its greatest force on the back of the horse.

Method of disposing the load.

When carts are not constructed in this manner, we may, in some degree, obtain the same end, by judiciously disposing the load. Let us suppose that the centre of gravity is at O, when the cart is loaded with homogeneous materials, such as sand, lime, &c. ; then if the load is to consist of heterogeneous substances, or bodies of different weights, we should place the heaviest at the bottom and nearest the front, which will not only lower the point O, but will bring it forward, and nearer the proper position m. Part of the load, too, might be suspended below the fore part of the carriage in dry weather, and the centre of gravity would approach still nearer the point m. When the point m is thus depressed, the weight on the horse is not only judiciously regulated, but the cart will be prevented from overturning, and in rugged roads the weight sustained by each wheel will be in a great degree equalized.

In loading four-wheeled carriages, great care should be taken not to throw much of the load upon the fore-wheels, as they would otherwise be forced deep into the ground, and require

8

great force to pull them forward. In some modern carriages this is very little attended to. The coachman's seat is sometimes enlarged so as to hold two persons, and all the baggage is generally placed in the front, directly above the fore-wheels. By this means, the greatest part of the load is upon the small wheels, and the draught becomes doubly severe for the poor animals, who must thus unnecessarily suffer for the ignorance and folly of man.

CHAPTER VIII.

ON THE FORCES OF ELASTICITY AND TORSION.

ELASTICITY is that property of bodies, in virtue of which their particles return to their original state, when their equili brium has been disturbed by any external force. When we bend a long stripe of glass, it will resume exactly the same shape which it had before it was bent; but if we subject a plate of steel to the same force, it will not resume its original form. In the first case, the elasticity is said to be perfect, and in the second imperfect.

It would be unsuitable to the character of this work, to enter into those theoretical discussions into which such a subject tends to lead us. It will be sufficient to describe the apparatus which has been employed for determining the elasticity of bodies, and to give a popular abstract of the most prominent results which philosophers have obtained on this subject.

The vast importance of these experiments, in a practical point of view, and the extensive utility of the force of torsion in physical inquiries, will justify us in devoting a few pages to their illustration.

The earliest and most correct experiments on the elasticities of bodies were made by S'Gravesende, with an apparatus shewn in Plate VIII, Fig. 1. It consists of a frame A B C D, which carries the pincers or vices M, N, between which is fastened the wire or rod of steel, or any other substance MN, whose elasticity is to be tried. A scale S, carrying weights, is fixed to

8 Dr. Young remarks, that the centre of gravity in four-wheeled carriages should divide the distance between the fore and hind wheels in the ratio of the cubes of the diameters. If the diameters of the wheels are as 4 to 5, the centre of gravity should be twice as near the hind as the fore wheels. Lectures, Vol. II, p. 201.

a piece of metal P Q, perforated at Q, so as to permit the wire or rod to pass through it. To the upper end of this piece is fixed a silk thread QR, passing over the pulley R, and suspending a weight W, exactly equal to the weight of the piece P Q. The axis of this pulley carries the index V, which points to the divisions of a dial-plate. If we now put different weights into the scale S, the elastic body M N will be bent by the weight, the middle point Q will descend, drawing after it the thread Q R, and consequently turning the index TV from right to left. In order to know the exact space through which the point Q has descended, or the degree of flexure of the body M N, we must determine by direct experiment the relation between the divisions on the dial-plate and the descent of any point of the thread QR. By this apparatus, S'Gravesende determined the degree of flexure, or the descent of the middle points of wires and plates produced by various weights placed in the scale S. The wire which he used was metallic, and such as are employed in musical instruments. Its length was 34 inches, and its weight 24 grains. Having given it a certain degree of tension by means of one of the screws, he measured the degree of flexion, or the descent of the middle point, produced by two different weights. He then gave the wire a second, and even a third degree of tension, and ascertained the flexion as before. The results

which he thus obtained are given in the following table:

From these experiments S'Gravesende concludes

1. That when the string almost returns to its primitive condition, the elongations which it receives from different weights or forces are proportional to these weights or forces.

2. That as the elongations of similar strings of different lengths must be as their lengths, the elongations of similar strings of the same thickness must be in the compound ratio of the lengths of the strings, and the weights or forces which elongate them.

3. That the weights or forces which elongate strings of the