body is projected downwards throughout its trajectory; motion is imparted to it, in virtue of the grasp that its base had of it, by adhesion or otherwise; and the velocity of projection impressed, or that which, of the total velocity of the wave at its moment of maximum, is effective in projection, is the difference, between the maximum velocity of the wave, and that which is destroyed by adhesion, or other equivalent resistances. The larger the mass the greater is the proportion of the total velocity effective.
Were there no adhesion or equivalent resistance (as in the case of a ball balanced on the top of a staff), the body would drop plumb or nearly so, and might be struck by the base (the wall in Fig. 2) in the second semiphase of the wave; or if the velocity of the wave were infinite or extremely great in relation to , the body might, whether adherent or not, be displaced and replaced, without projection. These, however, do not occur. The relation in nature between and is such, that bodies are projected from buildings, &c., in both semiphases of the wave, and the adhesion of the base is most generally of such a nature as to impart a movement of rotation to the body thrown, which is sufficient to turn it over, more or less (usually from the forms found either through 90° or 180° during its descent, notwithstanding its high vertical velocity downwards.
Let the axis of (Fig. 105), be measured downwards vertically, and that of horizontally from the origin, at the centre of gravity of the body projected, the trajectory described is
| (XXXVII.) |
, being the height, due to the velocity of projection.
