273. The calculated values of the powers are shown by this table to agree extremely well with the observed values, the greatest difference being only O·3 lb. Hence there can be no doubt that the principles on which the formula has been calculated are correct. This table may therefore be regarded as verifying both the law of friction, and the rule laid down for the relation between the power and the load in the inclined plane.

274. The inclined plane is properly styled a mechanical power. For let the weight be 30 lbs., we calculate by the formula that 17·4 lbs. would be sufficient to raise it, so that, notwithstanding the loss by friction, we have here a smaller force overcoming a larger one, which is the essential feature of a mechanical power. The mechanical efficiency is 30 ÷ 17·4 = 1·72.

275. The velocity ratio in the inclined plane is the ratio of the distance through which the power moves to the height through which the weight is raised, that is 1 ÷ 0·296 = 3·38. To raise 30 lbs. one foot, a force of 17·4 lbs. must therefore be exerted through 3·38 feet. The number of units of work expended is thus 17·4 × 3·38 = 58·8. Of this 30 units, equivalent to 51 per cent., are utilized. The remaining 28·8 units, or 49 per cent., are absorbed by friction.

276. We have pointed out in [Art. 222] that a machine in which less than half the energy is lost by friction will permit the load to run down when free: this is the case in the present instance; hence the weight will run down the plane unless specially restrained. That it should do so agrees with [Art. 147], for it was there shown that at about 13°·4, and still more at any greater inclination, the slide would descend when started.

THE SCREW.

277. The inclined plane as a mechanical power is often used in the form of a wedge or in the still more disguised form of a screw. A wedge is an inclined plane which is forced under the load; it is usually moved by means of a hammer, so that the efficiency of the wedge is augmented by the dynamical effect of a blow.

278. The screw is one of the most useful mechanical powers which we possess. Its form may be traced by wrapping a wedge-shaped piece of paper around a cylinder, and then cutting a groove in the cylinder along the spiral line indicated by the margin of the paper. Such a groove is a screw. In order that the screw may be used it must revolve in a nut which is made from a hollow cylinder, the internal diameter of which is equal to that of the cylinder from which the screw is cut. The nut contains a spiral ridge, which fits into the corresponding thread in the screw; when the nut is turned round, it moves backwards or forwards according to the direction of the rotation. Large screws of the better class, such as those upon which we shall first make experiments, are always turned in a lathe, and are thus formed with extreme accuracy. Small screws are made in a simpler manner by means of dies and other contrivances.

279. A characteristic feature of a screw is the inclination of the thread to the axis. This is most conveniently described by the number of complete turns which the thread makes in a specified length of the screw, usually an inch. For example: a screw is said to have ten threads to the inch when it requires 10 revolutions of the nut in order to move it one inch. The shape of the thread itself varies with the purposes for which the screw is intended; the section may be square or triangular, or, as is generally the case in small screws, of a rounded form.

280. There is so much friction in the screw that experiments are necessary for the determination of the law connecting the power and the load.

281. We shall commence with an examination of the screw by the apparatus shown in [Fig. 43].