A story is recorded of the great artist Turner, that he once spent a morning throwing stones into a pond. A friend reproved him for his idleness. “No,” said the painter, “I have not been idle; I have learnt how to paint a ripple.” If the artist’s eye has to be carefully trained to notice all that there is to see when a stone is hurled into a pond, it is not strange that a careless observer cannot grasp at once what really happens to the water in this ordinary occurrence. [Illustration: FIG. 11.—Ripples on a lake (Sierre), produced by throwing in a stone.] The photograph in Fig. 11 will, however, show one stage in the event. As soon as the first wave-crest, the origin of which we have already explained, is formed, it begins to move outwards in a circular form, and as it moves it gives rise to a _wave-train_, that is, it multiplies itself into a series of concentric ripples, or waves, which move outwards, multiplying in number, but getting smaller as they move. Thus if a large stone is thrown far out into a deep, still lake, after the first splash we shall see a circular wave spreading out from the place where the commotion was made in the water. As we look at this wave we shall see it growing in size and multiplying itself. At first there is but a single wave, then two, four, seven, ten, or more concentric ripples are seen, each circular wave expanding and getting feebler, but seeming to give birth to others as it moves. Moreover, a very careful examination will show us that the whole group of waves, or the wave-train, has an outward motion with a less speed than any individual wave. This observation will serve to initiate the conceptions of a _wave-train_ and of a _wave-group velocity_. At first it is difficult to understand that a _group of waves_ may move more slowly than the individual waves which compose it. If, however, we cast a stone into a pond, and look very carefully at what takes place, we shall see that the circular expanding band of ripples has an ill-defined but visible inner and outer edge, and that wavelets or ripples which compose it are being continually brought into existence on its inner edge, and dying away on its outer edge. Waves, so to speak, pass through the ripple band with a greater speed than that at which the whole band of waves moves forward. This rather difficult, but important, idea of the distinction between the velocity of a group of waves and that of an individual wave was first suggested by Sir George Stokes, who set a question in a Cambridge Examination on the subject in 1876, and subsequently it was elucidated by Professor Osborne Reynolds[6] and Lord Rayleigh.