departing from the conditions will be to show a fictitiously low co-efficient for the longer of the planes employed.
If the width of the planes in proportion to their fore and aft length were sufficiently great, this effect would be negligible, as under these circumstances the sectional area of the fluid affected would vary substantially with the width itself; we will provisionally assume this to have been the case, and treat the fore and aft length as the l of the dimensional equation, at the same time bearing in mind the direction in which error is to be expected.
The first three series of experiments are as follows, the figure quoted being in each case the mean resistance per square foot taken over the whole area at a velocity of 10 feet per second:—
| Nature of surface. | Length of Surface (Fore and Aft Dimension). | ||
| 2 feet. | 8 feet. | 20 feet. | |
| Varnish | .41 | .325 | .278 |
| Paraffin | .38 | .314 | .271 |
| Tinfoil | .30 | .278 | .262 |
The values of the index calculated from the above observations, on the basis of the dimensional equation, are given in columns 1 and 2 of the Table that follows.
The observed index, that is to say the index calculated from observations made at different velocities is (taking the mean of all observations) given in column 3.
| Observation at 2 feet in relation to Observation |
|||
| At 8 feet. | At 20 feet. | ||
| (1) | (2) | (3) | |
| Varnish | 1.825 | 1.z832 | 1.88 |
| Paraffin | 1.86 | 1.854 | 1.94 |
| Tinfoil | 1.94 | 1.940 | 1.97 |
We here find the theory receives confirmation, inasmuch as, firstly, the order in which the indices arrange themselves is the
63
