^{page 455 note *} Trans. R.S.E., vol. xlv., p. 362, hereafter quoted as I.S.E.

^{page 456 note *} I.S.E., p. 382.

^{page 462 note *} H.T.S., p. 622.

^{page 462 note †} H.T.S., p. 638.

^{page 462 note ‡} Le Léman, t. ii., p. 122.

^{page 462 note §} “Periodische Seespiegelschwankungen beobachtet am Starnberger See,” Sitz. Ber. kgl. bayer. Akad. d. Wiss, Bd. xxx. (1900), p. 453.

^{page 462 note ¶} “Stehende Seespiegelschwankungen im Madüsee in Pommern,” Zeitschrift für Gewässerkunde, Bd. vi., p. 95.

^{page 463 note *} Trans. R.S.E., vol. xli., p. 850.

^{page 463 note †} Henceforth referred to as “C.”

^{page 464 note *} See my paper, “On the Theory of the Leaking Microbarograph, etc.,” Proc. B.S.E., vol. xxxviii., p. 454 (1908).

^{page 464 note †} I.e. whole range of seiche less than 2 mm.

^{page 465 note *} For brevity, in what follows we shall denote such a seiche by “UB-dicrote.” Similarly, “UBT-tricrote” would mean a tricrote seiche with uninodal, binodal, and trinodal components; and we shall occasionally denote the amplitudes (half ranges) of these components by U, B, T respectively.

^{page 466 note *} The following method of roughly analysing a dicrote seiche which is tolerably pure and shows the 5/9 configuration may be mentioned here. If y ₀ be the minimum minimonim of the ordinates of the limnogram, y₁, y₂, y₃ the ordinates at distances , and from y ₀, and if A be the ordinate of mean level, U and B the amplitudes (semi-ranges) of the uninodal and binodal components, then , .

^{page 468 note *} A separate account of the observations with the microbarographs has been published in the Proceedings of the Society, vol. xxviii., p. 437 (1908).

^{page 468 note †} Except in very large lakes, such as Erie. See Endrös, , Petermanns Geogr. Mittheilungen, 1908, Heft ii., p. 16.Google Scholar

^{page 468 note ‡} Quart. Jour. Geol. Soc., lxiii., p. 366 (1907).

^{page 471 note *} See Part V., p. 513.

^{page 476 note *} See Hann, , Lehrbuch der Meteorologie (1906), pp. 270, 275.Google Scholar

^{page 476 †} Seeschwankungen beobachtet am Chiemsee (1903), p. 103.

^{page 478 note *} I.e. 1·7 times the amplitude at the binodal limnograph.

^{page 478 note †} For further details, see my paper, Proc. R.S.E., vol. xxviii., p. 457.

^{page 487 note *} See Part V., p. 514.

^{page 489 note *} See Proc. Boy. Inst., Friday, May 17, 1907. t Proc. B.S.E., vol. xxvi., p. 146 (1906).

^{page 490 note *} Endrös, however, has given examples in point, in some cases of constricted lakes, where a seiche in one part forces a seiche of the same period in another part.

^{page 490 note †} “Secondary Undulations of Oceanic Tides,” by Honda, , Terada, , Yoshida, , and Isitani, , Journ. of the College of Science, Imperial University, Tokio, vol. xxiv., p. 1 (1908).Google Scholar

^{page 491 note *} See Trans. R.S.E., vol. xlv., pp. 366, 369, 370, 380, and 383.

^{page 492 note *} See my memoir on the “Hydrodynamical Theory of Seiches,” Trans. R.S.E., vol. xli., p. 639 (1905).

^{page 493 note *} See fig. 19, where the statolimnograms in question are reproduced.

^{page 493 note †} Petermanns Geog. Mittheilungen, Heft ii., 1908.

^{page 494 note *} The velocity of a “long wave” in which would be about 20 (ft./sec.).

^{page 496 note} It is much to be desired that further observations should be made on the period, wave-length, and velocity of propagation of single waves and wave groups, in lakes, on sea-coasts, and in the open sea. Sailors have many opportunities for such observations; and physicists might devote some attention to the matter, when they take an openair vacation from the ardent pursuit of the electron.

It is curious how ignorant we still are regarding some of the most important hydrodynamical phenomena, not withstanding something like a century and a half of continued researches, both mathematical and experimental. We know very little, for example, regarding the action by which the wind increases the range and the length of the waves as we pass to windward.

We are told, and it is easy to understand, that a wind whose velocity is greater than the velocity of progression of a train of waves must increase their range; but what is the explanation of the increase of wave-length? Observations, some of which are mentioned below, have strongly suggested the following as the modus operandi:—The dynamic instability of the surface after the wind has reached a certain velocity leads to the generation of wave trains of slightly varying length and phase. These trains interfere and produce wave maxima The wind, so long as it travels faster than the wave maxima, will increase the range of the waves near the maxima more than elsewhere. Thus the periodically occurring wave maxima will be elevated into independent wave trains no longer resolvable into the previous harmonic components. Thus a new train of progressive waves will be formed of considerably greater mean range and mean wave-length than before, but of slightly differing ranges and wave-lengths. These again will interfere, and through the action of the wind generate other trains of still greater mean range and mean wavelength; and so on, until the process is stopped by the breaking of the wave crests. This is merely a speculation, without sufficient basis, either theoretical or experimental; but the subject seems to call for investigation, and its practical importance is undeniable.

^{page 495 note †} Annalen der Hydrographie und maritimen Meteorologie, Heft i., Jan. 1890.

^{page 495 note 1} See Lamb's, Hydrodynamics, p. 669 (1906).Google Scholar

^{page 497 note *} Trans. B.S.E., vol. xlv., p. 368 (1906).

^{page 497 note †} Another is given in Part I. of this report, Trans. R.S.E., vol. xlv., p. 370, fig. 12 (1906).

^{page 499 note *} Theory of Sound, vol. i., § 87 (1877).

^{page 499 note †} Trans. B.S.E., vol. xli. (1905).

^{page 499 note ‡} Ibid., p. 660 (1905).

^{page 501 note *} It follows, of course, that which may be readily verified independently

^{page 504 note *} See Whittaker's, Modern Analysis, ch, x., § 128.Google Scholar

^{page 512 note *} See Lamb's, Hydrodynamics, 3rd ed. (1906), p. 9.Google Scholar

^{page 514 note *} This result may seem at first sight to be in contradiction with the ordinary theory of forced vibration; but it is not really so. In the ordinary theory we consider a practically infinite number of oscillations, and take into account the viscosity of the system. In the present case we consider only one oscillation, and neglect the viscosity. It is obvious that this latter supposition is nearer tlie truth in the case of lake oscillations, because the disturbances of pressure are always transient, and usually periodic only for a very few oscillations.