The experiment with the ball rolling down a slope is an instructive one to make, because it brings clearly before the mind what is meant by saying, in scientific language, that one thing “varies as the square root” of another. We meet with so many instances of this mode of variation in the study of physics, that the reader, especially the young reader, should not be content until the idea conveyed by these words has become quite clear to him or her. Thus, for instance, the time of vibration of a simple clock pendulum “varies as the square root of the length;” the velocity of a canal wave “varies as the square root of the depth of the canal;” and the velocity or speed acquired by a falling ball “varies as the square root of the distance fallen through.” These phrases mean that if we have pendulums whose lengths are in the ratio of 1 to 4 to 9, then the respective times of their vibration are in the ratio of 1 to 2 to 3. Also a similar relation connects the canal-depth and wave-velocity, or the ball-velocity and height of fall. Returning again to canal waves, it should be pointed out that the real path of a particle of water in the canal, when long waves are passing along it, is a very flat oval curve called an ellipse. In the extreme cases, when the canal is very wide and deep, this ellipse will become nearly a circle; and, on the other hand, when narrow and shallow, it will be nearly a straight line. Hence, if long waves are created in a canal which is shallow compared with the length of the wave, the water-particles simply oscillate to and fro in a horizontal line. There is, however, one important fact connected with wave-propagation in a canal, which has a great bearing on the mode of formation of what is called a “bore.” As a wave travels along a canal, it can be shown, both experimentally and theoretically, that the crest of the wave travels faster than the hollow, and as a consequence the wave tends to become steeper on its front side, and its shape then resembles a saw-tooth.