| Cohesion, in pounds per square foot. | Angle of rupture with the horizontal, | Coefficient normal component of the thrust | ||||
|---|---|---|---|---|---|---|
| Theory. | Experiment. | Theory. | Experiment. | |||
| +⅓ | 0 | 0 | 50° 12′ | 0.060 | ||
| 1 | 51° | 51° 30′ | 0.042 | 0.043 | ||
| 2 | 52° 30′ | 0.026 | ||||
| +⅓ | ⅔ | 0 | 33° 41′ | 0.182 | ||
| 1 | 44° | 47° | 0.084 | 0.091 | ||
| 2 | 49° | 0.043 | ||||
| 0 | 0 | 0 | 56° 36′ | 0.111 | ||
| 1 | 57° | 56° 30′ | 0.093 | 0.090 | ||
| 2 | 58° | 0.077 | ||||
| 3 | 58° 30′ | 0.062 | ||||
| 0 | ½ | 0 | 47° 30′ | 0.178 | ||
| 1 | 50° | 51° | 0.148 | 0.141 | ||
| 2 | 53° | 0.121 | ||||
| 3 | 55° | 0.098 | ||||
| 0 | ⅔ | 0 | 33° 41′ | 0.345 | ||
| 1 | 44° | 49° | 0.205 | 0.195 | ||
| 2 | 46° 30′ | 0.150 | ||||
| 3 | 50° | 0.111 | ||||
| –⅓ | 0 | 0 | 60° 21′ | 0.185 | ||
| 1 | 63° | 61° | 0.171 | 0.179 | ||
| 2 | 63° | 0.155 | ||||
| –⅓ | ⅔ | 0 | 33° 41′ | 0.660 | ||
| 1 | 57° | 57° | 0.267 | 0.387 | ||
| 2 | 50° | 0.236 | ||||
The results in [Table 3] are remarkable, and explain quite satisfactorily how Leygue, Darwin, and others found, by experiments on small models, results differing so much from the ordinary theory, where cohesion is neglected.
It should be remarked that the values of
given in [Table 3] under “Experiment,” are not exactly those given by Leygue in his tables, but are the averages obtained from the two sets of drawings given by him in the plates, and represent the inclinations of the chords of the really curved surfaces of rupture. His experiments with the spring apparatus are not considered, as the results are open to doubt, because the prism of rupture, in descending, could not slide down freely, but as it advanced would rub over the floor, thus lessening the thrust there considerably.
From [Table 3], the results given by experiment are seen to differ widely from the ordinary theory in which
.
The discrepancies are largely, or almost entirely, due to the very small models used, as will be evident from the following considerations: Suppose the height,