We must first transform a speed of 27 miles per hour into its equivalent in feet per second. Since one mile is 5280 feet, 27 miles per hour is equal to 2376 feet per minute. Accordingly, it is easy to see that the wave-frequency must be 7·92, or nearly 8, because 7·92 times 300 is 2376. The answer to the question is, then, that the floating object will rise and fall eight times a minute. This rule may be embodied in a compact form, which it is desirable to hold firmly in the memory, viz.— _Wave-velocity_ = _wave-length_ × _wave-frequency_. This relation, which we shall have frequent occasion to recall, may be stated in another manner. We call the _period_ of a wave the time taken to make one complete movement. The periodic time is therefore inversely proportional to the frequency. Hence we can say that the _wave-length_, divided by the _periodic time_, gives us the _wave-velocity_. In the case of water waves and ripples, the wave-velocity is determined by the wave-length. This is not the case, as we shall see, with waves in air or waves in æther. In these latter cases, as far as we know, waves of all wave-lengths travel at the same rate. Long sea waves, however, on deep water travel faster than short ones. A formal and exact proof of the law connecting speed and wave-length for deep-sea waves requires mathematical reasoning of an advanced character; but its results may be expressed in a very simple statement, by saying that, in the case of waves on deep water, the speed with which the waves travel, reckoned in miles per hour, is equal to the square root of 2¹⁄₄ times the wave-length measured in feet. Thus, for instance, if we notice waves on a deep sea which are 100 feet from crest to crest, then the speed with which those waves are travelling, reckoned in miles per hour, is a number obtained by taking the square root of 2¹⁄₄ times 100, viz. 225. Since 15 is the square root of 225 (because 15 times 15 is 225), the speed of these waves is therefore 15 miles an hour. In the same way it can be found that Atlantic waves 300 feet long would travel at the rate of 26 miles an hour, or as fast as a slow railway train, and much faster than any ordinary ship.[1] The above rule for the speed of deep-sea waves, viz. _wave-velocity_ = _square root of 2¹⁄₄ times the wave-length_, combined with the general rule, _wave-velocity_ = _wave-length multiplied by frequency_, provides us with a useful practical method of finding the speed of deep-sea waves which are passing any fixed point. Suppose that a good way out at sea there is a fixed buoy or rock, and we notice waves racing past it, and desire to know their speed, we may do it as follows: Count the number of waves which pass the fixed point per minute, and divide the number into 198; the quotient is the speed of the waves in miles per hour. Thus, if ten waves per minute race past a fixed buoy, their velocity is very nearly 20 miles an hour.[2]