88 THE FKESH- WATER LOCHS OF SCOTLAND 
It'is obvious that the single waves could not cause the ordinary 
and most prominent periods in the embroidery, which run from about 
•5"^ to 1 '5'" ; but there is no doubt that they cause the thickening or 
bkuTing of the limnogram which usually appears when the wind is high. 
On the other hand, the periods of the wave groups are nearly coincident 
with some of the more prominent periods of the embroidery. Part of 
this embroidery may therefore be due to wave groups, but more observa- 
tions are require*d to settle the matter beyond doubt.^ 
4. In a paper " On the Relation between the Velocity of the 
Wind and the Dimension of Oceanic Waves, with an Explanation of 
the Waves of Longer Period on Open Coasts,"' ^ Professor Borgen has 
suggested that the secondary tidal oscillations and waves of un- 
usually long periods occasionally observed on open coasts, where the 
circumstances do not seem to justify the assumption of a seiche, may 
be due to difference and summation waves (whose theoretical existence 
arises from the non-applicability of the theory of the linear super- 
position of small motions). Such waves would be analogous to 
the difference and summation tones of Helmholtz. It is quite 
possible that an explanation of this kind may apply in part to lake 
1 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 open-air vacation from the ardent pursuit of the electron. It is 
curious how ignorant we still are regarding some of the most important hydro- 
dynamical phenomena, notwithstanding 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 wa\'es as we pass to windward. 
We are told (see Lamb's Hydrodynamics, p. 569, 1906), and it is easy to under- 
stand, 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 ojperandi : — The dynamic instability of the 
surface after the wind has readied a certain velocity leads to the generation of 
wave trains of slightly varying length and phase. These trains interfere and pro- 
duce wave maxima. The wind, so long as it travels fastet 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 wave-length ; 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. 
2 Amialen der Hydrographie und maritimsn Meteorologie, Heft i., 1890. 
