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Friction.-The Angle of Repose.

enter into each other; hence the friction is greater between such than between different substances having dissimilar grain.

The friction of one piece of iron, wood, brick, stone, &c., on another piece of the same substance, is measured by using the second piece as an inclined plane, and then gradually lifting one end of it until the upper mass begins to slide-the inclination of the plane, just before the sliding commences, being called the angle of repose. This angle, different for different substances, is found to be, for metals, generally such as to mark that the force required to overcome the friction between small pieces of them is equal to about a fourth of the weight of the moving piece; for woods, it is about a half. But for large pieces or for great pressures, the friction is proportionally less.

269. The adjoining fig. 62 exhibits to the eye the different angles

of repose for different materials, giving the extreme values of the angle as determined from a large number of experimental observations.

It is this angle in the substances concerned which determines the degrees of acclivity, or the slope which becomes permanent in the sides of hills composed of sand, gravel, earth, &c., and

in the banks of canals, rivers, water reservoirs, &c.

If the thread of a screw winds round the spindle with an angle less than this, the screw can never recoil, or slide back, from force acting against its point.

270. But for friction, men walking on the ground or pavement would always be as if walking on ice; and our rivers, that now flow so calmly, would all be rapid torrents. It is friction which retains all loose objects on earth in the situations in which for convenience men choose to place them-the furniture of a house, the contents of libraries, museums, &c. Friction is therefore essential to our existence.

Friction it is which enables men, out of the comparatively short fibres of cotton, flax, or hemp, to form lengthened threads, cordage, webs, &c.; for friction alone, consequent upon the mutual pressure

of the interwoven and twisted fibres and threads, keeps the material of all these fabrics together.

The Mechanical Laws of Friction.

271. There are three principles that govern the amount of friction between two plane surfaces, one being fixed and the other sliding over it. They have been confirmed by innumerable experiments. First, the friction is exactly proportional to the pressure between the sliding surfaces.

Thus, if we have a number of similar bricks, and it take a certain force to slide a single brick over any surface, that force will have to be doubled or tripled to overcome the friction, when we lay a second or a third brick on the top of the first.

Second, the friction is independent of the extent of surfaces in sliding contact.

Thus, to take the case of the brick, the same force will be required to overcome the friction of a single brick, whether we lay it on its broad face, or on its side, or on its edge.

This law is contrary to what we might be inclined at first sight to allow.

Third, the friction is independent of the relative velocity of the sliding surfaces.

The frictional resistance to be overcome in moving a railway train or a sledge is quite the same, whether the motion be swift or slow; being dependent solely on the nature of the surfaces in contact and the load which presses them together.

272. It is to be remembered, however, that the friction to be overcome in first moving one surface over another, is much greater than when the motion is once begun. After surfaces have been some time in contact, the increase of frictional resistance may be very considerable, and is very uncertain.

Vibrations of surfaces in contact also diminish the frictional adhesion. Thus the carpenter, by a single blow on the end of his plane, loosens the wedge which keeps the cutting-iron firmly in its place.

Wheel carriages, in travelling over rough roads or pavements, are apt to have their nuts loosened by the lessening of the frictional adhesion between the nuts and the surfaces on which they are screwed down.

Hence in carriages, and in all machinery which is subject to con

152

Anti-friction Expedients.

siderable vibration, this slipping of the nut has to be prevented by adding another nut, screwed hard down upon the first.

273. But friction, which is so essential to our existence and to the construction of a piece of machinery, is also a serious cause of waste of Energy in its transmission through any machine. In practice the relation between the Energy applied as the power to a machine and the Energy recovered as work, differs considerably from what is deduced by the theoretical considerations such as we have given for the lever, the pulley, &c.; and the practical man knows the allowance to make for frictional waste of Energy in each case. However perfectly a machine may be constructed, this waste is always a very appreciable fraction-sometimes as much as a fourth, or a third, or a half, or even more-of the Energy applied; and the efficiency of a machine depends, therefore, on the means employed to avoid this useless waste.

274. The following means are employed to diminish friction between rubbing surfaces, and are used singly or in combination, according to circumstances.

1. Making the rubbing surfaces smooth.

2. Interposing some lubricating substance between the rubbing parts; as oils for the metals; soap, greasc, black-lead, &c., for the woods.

3. Letting the substances which are to rub on each other be of different kinds. Axles are made of steel, for instance, and the parts on which they bear are made of gun-metal or brass: in small machines, as time-keepers, the steel axles often play in agate or diamond. The swiftness of a skater depends much on the great dissimilarity between steel and ice.

4. Using wheels, as in wheel-carriages, instead of dragging a solid mass or sledge along the ground. This is a contrivance of very great antiquity. Castors on household furniture are miniature

wheels.

5. Placing the thing to be moved on rollers, as is commonly done when a log of wood or a heavy package is drawn along the ground upon smaller round pieces; or when a heavy cannon, with a flat circular base to its carriage, is turned round by rolling on loose cannon-balls having a hard level bed.

Fig 63.

6. Using what are called friction wheels, or rather anti-friction wheels; which still farther diminish the

Object of Wheels in Carriages.

153

friction even of a small axis, by allowing it to rest on their circumferences, which turn with it. In fig. 63, a represents the end of an axis, resting on the rims of two friction wheels, b and c.

Of all rubbing parts, the joints of animals, considering the strength, frequency, and rapidity of their movements, are those which have the least friction. The rubbing surfaces in these are covered, first, with a layer of elastic cartilage, and then with an exceedingly smooth membrane, over which there is constantly poured from surrounding glands a fluid called synovia, more emollient and lubricating than any oil, and which is renewed constantly as required. We study and admire the perfection of animal joints, without being able very closely to imitate them.

275. Wheel carriages illustrate many of the circumstances connected with friction. They have three advantages over the ancient sledges for which they are the substitutes :

1. The rubbing or friction, instead of being between an iron shoe and the stones and irregularities of the whole road, is between the axle and its surrounding bush, of which the surfaces are smoothed and fitted to each other, and well lubricated.

2. While the carriage moves forward, ten or fifteen feet, by one revolution of its wheel, the rubbing part, viz., the axle, slides over only a few inches of the internal surface of its smooth greased bush.

3. The wheel instead of butting against any abrupt obstacle on the road, surmounts it by the axle describing a gentle curve over it,— as shown in fig. 64, where a represents an obstacle, and where the curve from c, of which the beginning has the direction shown by the line ce, represents the

path of the axle in surmounting it. The wheel is as if rising on an inclined plane, and gives to the drawing animal the relief which such a plane would bring. The advantage is greater in a large than in a small wheel, for the smaller

a

Fig. 64.

wheel, in having to surmount more quickly the same size of obstacle, b, has to rise in the shorter and steeper curve beginning at d. Again, a small wheel will sink to the bottom of a hole or

depression in the road, where a larger one would rest on its edges as a bridge, and would sink less.

The fore-wheels of carriages are usually made small, to facilitate the turning, by their passing under the body of the carriage. It is not true, however, according to the popular prejudice, that the large hind-wheels of coaches and waggons help to push on the little wheels before them, as if the carriage were on an inclined plane; but there is the accidental advantage, that in ascending a hill, when the horses have to put forth their strength, the load rests chiefly on the large hind wheels, and in descending, when an increased resistance is desirable, the load falls chiefly on the smaller fore-wheels.

276. The wheel of a carriage, simple as, from our extreme familiarity with it, it now appears to us, is a thing of very nice workmanship, and has exercised much ingenuity. It possesses marvellous strength, somewhat of the nature of that of the arch, from what

a

is called its dished form, seen in the wheel c d (fig. 65), as contrasted with the flat wheel, e b. In a wheel of this form, the extremity of a spoke cannot be pressed or strained inwards, or towards the carriage, unless the rim of the wheel be diminished; and it cannot be displaced outwards, or Fig. 65. away from the carriage, unless the rim be cnlarged; now the rim being bound by a strong ring or tire of iron, cannot suffer either increase or diminution, and the strength of all the spokes is thus by it compelled to aid each individually. In a perfectly flat wheel a given degree of displacement outwards or inwards of the extremities of any one spoke, is not resisted by the strength of all the others. A dished wheel is stronger than a flat wheel, for the same reason that a watch-glass and a round piece of egg-shell are stronger than flat pieces of like thin substances.

277. The application of springs to carriages, which is an improvement of comparatively recent date, not only renders them softmoving vehicles on rough roads, but much lessens the pull to the horses. When there is no spring, the whole load must rise with every rising of the road, and if time be given, must sink with every depression, and the depression costs as much labour as the rising, because the wheel must be drawn up again from the bottom of it: but in a spring-carriage moving rapidly along, only the parts below the springs are moved in correspondence with the road-surface, while all above, by the inertia of the matter, have a comparatively