If we then consider the wedge to leap forward and repeat the process, two more inclined waves will be formed in front of the first; and again we may suppose the process repeated, and a third pair of waves formed. The different positions of the ship’s bows are shown in the diagram at 1, 2, and 3 in Fig. 35; and _c_, _e_, and _f_ are the three corresponding sets of echeloned waves. For the sake of simplicity, the waves are shown on one side only. If, then, we imagine the ship to move uniformly forwards, its bows are always producing new inclined waves, which move with it, and it is always, so to speak, leaving the old ones behind. All these echelon waves produced by the bow of the ship are included within two sloping lines which each make with the direction of the ship’s line of movement, an angle of 19° 28´.[16] This angle can be thus set off: Draw a circle (see Fig. 36), and produce the diameter BC of this circle for a distance, CA, equal to its own length. From the end A of the produced diameter draw a pair of lines, AD, AD′, called tangents, to touch the circle. Then each of these lines will make an angle of 19° 28´ with the diameter. If we suppose a ship-to be placed at the point marked A in the diagram (see Fig. 36), all the echelon waves it makes will be included within these lines AD, AD′. [Illustration: FIG. 35.] Moreover, the angle of the lines will not alter, whether the ship goes fast or slow. This is easily seen in the case of a duck swimming on a lake. Throw bits of bread to a duck so as to induce it to swim faster or slower, and notice the system of inclined or echelon ripples made by the duck’s body as it swims. It will be seen that the angle at which the two lines, including both the trains of echelon ripples meet each other is not altered as the duck changes its speed. [Illustration: FIG. 36.] This echelon system of inclined waves is really only a part of a system of waves which is completed by a transverse group in the rear of the vessel. A drawing has been given by Lord Kelvin, in his lecture on “Ship Waves,” of the complete system of these waves, part of which is as represented by the firm lines in Fig. 37. This complete system is difficult to see in the case of a real ship moving over the water. The inclined rear system of waves can sometimes be well seen from the deck of a lake steamer, such as those on the large Swiss or Italian lakes, and may sometimes be photographed in a snap-shot taken of a boy’s yacht skimming along on a pond. [Illustration: FIG. 37.]