125. If the power be too small, the load either does not continue moving after the start, or it stops irregularly. If the power be too great, the load is drawn with an accelerated velocity. The correct amount is easily recognised by the uniformity of the movement, and even when the slide is heavily laden, a few tenths of a pound on the power hook cause an appreciable difference of velocity.
126. The accuracy with which the friction can be measured may be appreciated by inspecting Table II.
Smooth horizontal surface of pine 72" × 11"; slide also of pine 9" × 9"; grain crosswise; slide started; force applied is sufficient to maintain uniform motion of the slide.
| Number of Experiment. | Load on slide in lbs., including weight of slide | Force necessary to maintain motion. 1st Series. | Force necessary to maintain motion. 2nd Series. | Mean values. |
|---|---|---|---|---|
| 1 | 14 | 4·9 | 4·9 | 4·9 |
| 2 | 28 | 8·5 | 8·6 | 8·5 |
| 3 | 42 | 12·6 | 12·4 | 12·5 |
| 4 | 56 | 16·3 | 16·2 | 16·2 |
| 5 | 70 | 19·7 | 20·0 | 19·8 |
| 6 | 84 | 23·7 | 23·0 | 23·4 |
| 7 | 98 | 26·5 | 26·1 | 26·3 |
| 8 | 112 | 29·7 | 29·9 | 29·8 |
127. Two series of experiments to determine the power necessary to maintain the motion have been recorded. Thus, in experiment 7, the load on the slide being 98 lbs., it was found that 26·5 lbs. was sufficient to sustain the motion, and a second trial being made independently, the power found was 26·1 lbs.: a mean of the two values, 26·3 lbs., is adopted as being near the truth. The greatest difference between the two series, amounting to 0·7 lb., is found in experiment 6; a third value was therefore obtained for the friction of 84 lbs.: this amounted to 23·5 lbs., which is intermediate between the two former results, and 23·4 lbs., a mean of the three, is adopted as the final result.
128. The close accordance of the experiments in this table shows that the means of the fifth column are probably very near the true values of the friction for the corresponding loads upon the slide.
129. The mean frictions must, however, be slightly diminished before we can assert that they represent only the friction of the wood upon the wood. The pulley over which the rope passes turns round its axle with a small amount of friction, which must also be overcome by the power. The mode of estimating this amount, which in these experiments never exceeds 0·5 lb., need not now be discussed. The corrected values of the friction are shown in the third column of [Table III.] Thus, for example, the 4·9 lbs. of friction in experiment 1 consists of 4·7, the true friction of the wood, and 0·2, which is the friction of the pulley; and 26·3 of experiment 7 is similarly composed of 25·8 and 0·5. It is the corrected frictions which will be employed in our subsequent calculations.
FRICTION IS PROPORTIONAL TO
THE PRESSURE.
130. Having ascertained the values of the force of friction for eight different weights, we proceed to inquire into the laws which may be founded on our results. It is evident that the friction increases with the load, of which it is always greater than a fourth, and less than a third. It is natural to surmise that the friction (F) is really a constant fraction of the load (R)—in other words, that F = kR, where k is a constant number.