But it is also subject to another force, namely that of gravity, which acts on it vertically, and deflects it in a vertical direction exactly as much and as fast as a body would do if dropped from rest at the same instant as the bolt leaves the bow. But the cat is such a body. Hence, then, since by the electric arrangement they are both let go together, they will both drop simultaneously, and thus will always be on the same level, and when the bolt reaches the wooden wall and has fallen vertically from a to c, the cat will also have fallen vertically from a to c, and the bolt will pin him to the wall. It does not matter how far you take the bow from the wall, nor how strong the bow is, nor how heavy the bolt is, nor how heavy the cat is, nor whether a b is horizontal or pointing upwards or downwards.
Fig. 73.
In every case, if only the barrel is pointed directly at the cat, then the bolt and cat fall simultaneously and at the same rate, and the bolt will pin the cat to the wall.
In trying the experiment the bolt should be pretty heavy, say half a pound, and have a good spike; but if carefully done the experiment will succeed every time. It enables you also to measure the speed of flight of the bolt. For if the distance of the bow from the wall be thirty feet, and the cat have fallen three feet when it is struck, then the time of fall is T² = √((2S)/g) = √(6/g) = ·43 seconds. But the bolt in this time went thirty feet; hence its velocity was thirty feet in ·43 seconds, or seventy feet per second.
Of course if you make the bolt heavier the velocity of projection will become slower, the time longer, and hence the cat will fall further before it is transfixed by the bolt.
My task is now at a close. I have endeavoured not merely to give a description of clocks and various apparatus for measuring time, but to explain the fundamental principles of mechanics which lie at the root of the subject.
May I end with a word of advice to parents?
There is a certain number of boys, but only a certain number, who have a real love for mechanical science. Such boys should be encouraged in every way by the possession of tools and apparatus, but in the selection of this apparatus the following principles should be borne in mind:—
First, that almost everything a boy wants can be made with wood, and metal, and wire, and string, if he has someone to give him a little instruction how to do it. A bent bit of steel jammed in a vice makes an excellent tuning fork.