Permit me, now, to illustrate the most essential of the points that I have just adduced, by means of a few rough drawings taken from older and less perfect photographs. In the sketch of Figure 57 you see the projectile, which has just left the barrel of the rifle, touch a wire and disengage the illuminating spark. At the apex of the projectile you already see the beginnings of a powerful head-wave, and in front of the wave a transparent fungiform cluster. This latter is the air which has been forced out of the barrel by the projectile. Circular sound-waves, noise-waves, which are soon overtaken by the projectile, also issue from the barrel. But behind the projectile opaque puffs of powder-gas rush forth. It is scarcely necessary to add that many other questions in ballistics may be studied by this method, as, for example, the movement of the gun-carriage. [Illustration: Fig. 57.] A distinguished French artillerist, M. Gossot, has applied the views of the head-wave here given in quite a different manner. The practice in measuring the velocity of projectiles is to cause the projectile to pass through wire screens placed at different points in its path, and by the tearing of these screens to give rise to electro-magnetic time-signals on falling slabs or rotating drums. Gossot caused these signals to be made directly by the impact of the head-wave, did away thus with the wire screens, and carried the method so far as to be able to measure the velocities of projectiles travelling in high altitudes, where the use of wire screens was quite out of the question. The laws of the resistance of fluids and of air to bodies travelling in them form an extremely complicated problem, which can be reasoned out very simply and prettily as a matter of pure philosophy but practice offers not a few difficulties. The same body having the velocity 2, 3, 4 ... displaces in the same interval 2, 3, 4 ... times the same mass of air, or the same mass of fluid, and imparts to it _in addition_ 2, 3, 4 ... times the same velocity. But for this, plainly, 4, 9, 16 ... times the original force is required. Hence, the resistance, it is said, increases with the square of the velocity. This is all very pretty and simple and obvious. But practice and theory are at daggers' points here. Practice tells us that when we increase the velocity, the law of the resistance changes. For every portion of the velocity the law is different. The studies of the talented English naval architect, Froude, have thrown light upon this question. Froude has shown that the resistance is conditioned by a combination of the most multifarious phenomena. A ship in motion is subjected to the friction of the water. It causes eddies and it generates in addition waves which radiate outward from it. Every one of these phenomena are dependent upon the velocity in some different manner, and it is consequently not astonishing that the law of the resistance should be a complicated one.