These experiments and many others show us that we must regard the surface of a liquid as covered with an invisible film, which is in a state of stretch, or which resists stretching. If we imagine a jam-pot closed with a cover of thin sheet indiarubber pulled tightly over it, it is clear that any attempt to make puckers, pleats, or wrinkles in it would involve stretching the indiarubber. It is exactly the same with water. If very _small_ wrinkles or pleats, as waves, are made on its surface, the resistance which is brought into play is that due to the surface tension, and not merely the resistance of the surface to being made unlevel. Wavelets so made, or due to the above cause, are called _ripples_. It can be shown by mathematical reasoning[11] that on the free surface of a liquid, like water, what are called _capillary ripples_ can be made by agitations or movements of a certain kind, and the characteristic of these surface-tension waves or capillary ripples, as compared with gravitation waves, is that the velocity of propagation of the capillary ripple is _less_ the greater the wave-length, whereas the velocity of gravitation on ordinary surface waves is _greater_ the greater the wave-length. It follows from this that for any liquid, such as water, there is a certain length of wave which travels most slowly. This slowest wave is the dividing line between what are properly called ripples, and those that are properly called waves. In the case of water this slowest wave has a wave-length of about two-thirds of an inch (0·68 inch), and a speed of travel approximately of 9 inches (0·78 foot) per second. More strictly speaking, the matter should be explained as follows: Sir George Stokes showed, as far back as 1848, that the surface tension of a liquid should be taken into account in finding the pressure at the free surface of a liquid. It was not, however, until 1871 that Lord Kelvin discussed the bearing of this fact on the formation of waves, and gave a mathematical expression for the velocity of a wave of oscillatory type on a liquid surface, in which the wave-length, surface tension, density, and the acceleration of gravity were taken into account. The result was to show that when waves are very short, viz. a small fraction of an inch, they are principally due to surface tension, and when long are entirely due to gravity. It can easily be seen that ripples run faster the smaller their wave-length. If we take a thin wire and hold it perpendicularly in water, and then move it quickly parallel to itself, we shall see a stationary pattern of ripples round the wire which moves with it. These ripples are smaller and closer together the faster the wire is moved.