Friction of pine upon pine; the mean values of the
friction given in Table II. (corrected for the
friction of the pulley) compared with the formula
_F_ = 1·44 + 0·252 _R_.
+-----------+----------+-------------+----------+-------------+
| | | | |Discrepancies|
| Number of | R. | Corrected | F. | between the |
|Experiment.|Total load| mean |Calculated|observed and |
| | on slide | value of | value of | calculated |
| | in lbs. | friction. | friction.| frictions. |
+-----------+----------+-------------+----------+-------------+
| 1 | 14 | 4·7 | 5·0 | +0·3 |
| 2 | 28 | 8·2 | 8·5 | +0·3 |
| 3 | 42 | 12·2 | 12·0 | -0·2 |
| 4 | 56 | 15·8 | 15·6 | -0·2 |
| 5 | 70 | 19·4 | 19·1 | -0·3 |
| 6 | 84 | 23·0 | 22·6 | -0·4 |
| 7 | 98 | 25·8 | 26·1 | +0·3 |
| 8 | 112 | 29·3 | 29·7 | +0·4 |
+-----------+----------+-------------+----------+-------------+
The fourth column contains the calculated values: thus, for example,
in experiment 4, where the load is 56 lbs., the calculated value is
1·44 + 0·252 × 56 = 15·6; the difference 0·2 between this and the
observed value 15·8 is shown in the last column.
138. It will be noticed that the greatest discrepancy in this column
is 0·4 lbs., and that therefore the formula represents the experiments
with considerable accuracy. It is undoubtedly nearer the truth than the
former law (Art. 132); in fact, the differences are now such as might
really belong to errors unavoidable in making the experiments.
139. This formula may be used for calculating the friction for any load
between 14 lbs. and 112 lbs. Thus, if the load be 63 lbs., the friction
is 1·44 + 0·252 × 63 = 17·3 lbs., which does not differ much from 17·0
lbs., the value found by the more ordinary law. We must, however, be
cautious not to apply this formula to weights which do not lie between
the limits of the greatest and least weight used in those experiments
by which the numerical values in the formula have been determined;
for example, to take an extreme case, if _R_ = 0, the formula would
indicate that the friction was 1·44, which is evidently absurd; here
the formula errs in excess, while if the load were very large it is
certain the formula would err in defect.