[3] The amplitude of disturbance of a particle of water at a depth equal to one wave-length is equal to 1/ϵ^{2π} of its amplitude at the surface. (See Lamb’s “Hydrodynamics,” p. 189.) [4] This can easily be shown to an audience by projecting the apparatus on a screen by the aid of an optical lantern. [5] See “The Splash of a Drop,” by Professor A. M. Worthington, F.R.S., Romance of Science Series, published by the Society for Promoting Christian Knowledge. [6] See Osborne Reynolds, _Nature_, vol. 16, 1877, p. 343, a paper read before the British Association at Plymouth; see also Appendix, Note A. [7] A very interesting article on “Kumatology, or the Science of Waves,” appeared in a number of _Pearson’s Magazine_ for July, 1901. In this article, by Mr. Marcus Tindal, many interesting facts about, and pictures of, sea waves are given. [8] Lord Kelvin (see lecture on “Ship Waves,” Popular Lectures, vol. iii. p. 468) says the wave-length must be at least fifty times the depth of the canal. [9] See article “Tides,” by G. H. Darwin, “Encyclopædia Britannica,” 9th edit., vol. 23, p. 353. [10] The progress of the Severn “bore” has been photographed and reproduced by a kinematograph by Dr. Vaughan Cornish. For a series of papers bearing on this sort of wave, by Lord Kelvin, see the _Philosophical Magazine_ for 1886 and 1887. [11] See Lord Kelvin, “Hydrokinetic Solutions and Observations,” _Philosophical Magazine_, November, 1871. [12] “On the Photography of Ripples,” by J. H. Vincent, _Philosophical Magazine_, vol. 43, 1897, p. 411, and also vol. 48, 1899. These photographs of ripples have been reproduced as lantern slides by Messrs. Newton and Co., of Fleet Street, London. [13] Some smokers can blow these smoke rings from their mouth, and they may sometimes be seen when a gun is fired with black old-fashioned gunpowder, or from engine-funnels. [14] For details and illustrations of these researches, the reader is referred to papers by Professor H. S. Hele-Shaw, entitled, “Investigation of the Nature of Surface-resistance of Water, and of Stream-line Motion under Experimental Conditions,” _Proceedings of the Institution of Naval Architects_, July, 1897, and March, 1898. A convenient apparatus for exhibiting these experiments in lectures has been designed by Professor Hele-Shaw, and is manufactured by the Imperial Engineering Company, Pembroke Place, Liverpool. [15] The French word _échelon_ means a step-ladder-like arrangement; but it is usually applied to an arrangement of rows of objects when each row extends a little beyond its neighbour. Soldiers are said to march in echelon when the ranks of men are so ordered. [16] See Lord Kelvin on “Ship Waves,” Popular Lectures, vol. iii. p. 482. [17] More accurately, as the 1·83 power of the speed.