272. The calculated values are found to agree tolerably well with the observed values, but the presence of the large differences in No. 1 and No. 4 leads us to inquire whether by employing the more accurate law of friction ([Art. 141]) a better result may not be obtained.
In [Table VI]. we have shown that the friction for weights not exceeding 56 lbs. is expressed by the formula F = 0·9 + 0·266 × pressure, but the pressure is in this case = 0·955 R, and hence the friction is
0·9 + 0·254 R.
To this must be added 0·296 R, the component of the force of gravity which must be overcome, and hence the total force necessary is
0·9 + 0·55 R.
The powers calculated from this expression are compared with those actually observed in Table XV.
Smooth plane of pine 72"× 11"; angle of inclination 17°·2; slide of pine, grain crosswise; slide started; formula P = 0·9 + 0·55 R.
| Number of Experiment. | R. Total load on slide in lbs. | Power in lbs. which just draws up slide. | P. Calculated value of the power. | Differences of the observed and calculated powers. |
|---|---|---|---|---|
| 1 | 7 | 4·6 | 4·7 | +0·1 |
| 2 | 14 | 8·3 | 8·6 | +0·3 |
| 3 | 21 | 12·3 | 12·5 | +0·2 |
| 4 | 28 | 16·5 | 16·3 | -0·2 |
| 5 | 35 | 20·0 | 20·1 | +0·1 |
| 6 | 42 | 24·2 | 24·0 | -0·2 |
| 7 | 49 | 28·0 | 27·8 | -0·2 |
| 8 | 56 | 31·8 | 31·7 | -0·1 |
For example: in experiment 5, a load of 35 lbs. is found to be raised by a power of 20·0 lbs., while the calculated power is 0·9 + 0·55 × 35 = 20·1 lbs.