(87.) A body falling from the top of the mast when the vessel is in full sail, is an example of the composition of motion. It might be expected, that during the descent of the body, the vessel having sailed forward, would leave it behind, and that, therefore, it would fall in the water behind the stern, or at least on the deck, considerably behind the mast. On the other hand, it is found to fall at the foot of the mast, exactly as it would if the vessel were not in motion. To account for this, let A B, _fig. 17._, be the position of the mast when the body at the top is disengaged. The mast is moving onwards with the vessel in the direction A C, so that in the time which the body would take to fall to the deck, the top of the mast would move from A to C. But the body being on the mast at the moment it is disengaged, has this motion A C in common with the mast; and therefore in its descent it is affected by two motions, viz. that of the vessel expressed by A C, and its descending motion expressed by A B. Hence, by the composition of motion, it will be found at the opposite angle D of the parallelogram, at the end of the fall. During the fall, however, the mast has moved with the vessel, and has advanced to C D, so that the body falls at the foot of the mast. (88.) An instance of the composition of motion, which is worthy of some attention, as it affords a proof of the diurnal motion of the earth, is derived from observing the descent of a body from a very high tower. To render the explanation of this more simple, we shall suppose the tower to be on the equator of the earth. Let E P Q, _fig. 18._, be a section of the earth through the equator, and let P T be the tower. Let us suppose that the earth moves on its axis in the direction E P Q. The foot P of the tower will, therefore, in one day move over the circle E P Q, while the top T moves over the greater circle T T′ R. Hence it is evident, that the top of the tower moves with greater speed than the foot, and therefore in the same time moves through a greater space. Now suppose a body placed at the top; it participates in the motion which the top of the tower has in common with the earth. If it be disengaged, it also receives the descending motion T P. Let us suppose that the body would take five seconds to fall from T to P, and that in the same time the top T is moved by the rotation of the earth from T to T′, the foot being moved from P to P′. The falling body is therefore endued with two motions, one expressed by T T′, and the other by T P. The combined effect of these will be found in the usual way by the parallelogram. Take T _p_ equal to T T′; the body will move from T to _p_ in the time of the fall, and will meet the ground at _p_. But since T T′ is greater than P P′, it follows that the point _p_ must be at a distance from P′ equal to the excess of T T′ above P P′. Hence the body will not fall exactly at the foot of the tower, but at a certain distance from it, in the