ON THE SEICHES OF LOCH EARN. 495 



embroidery may therefore be due to wave groups ; but more observations are required 

 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," t Professor Borgen has suggested that the secondary tidal oscillations and 

 waves of unusually long periods occasionally observed on open coasts, where the circum- 

 stances 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 superposition of small motions), after the analogy of the difference 

 and summation tones of Helmholtz. It is quite possible that some such explanation 

 may apply in part to lake vibrations ; but we have no evidence to produce for or against 

 such a hypothesis. 



5. Towards the end of our survey of Loch Earn, we made some observations with 

 the statolimnograph (unfortunately we had time to make only a few) which point to 

 yet another explanation of some part, especially the more irregular part, of the embroidery 

 on the limnograph. 



In fig. 19 are placed together two statolimnograms, which were taken in close 

 succession at two stations near to each other on the northern shore of Loch Earn, during 

 a moderate westerly breeze [mean velocity 12 to 16 (mile/hour), extreme velocity 

 occasionally 24 (mile/hour)]. The upper one was taken in a sheltered bay to leeward 

 of the delta of the Glentarken Burn, the lower about 100 yards farther west, to wind- 

 ward of the delta. The bay was comparatively calm, disturbed only by the swell 

 propagated into it from the wind waves rolling outside. The difference between the 

 two limnograms is very striking. The maximum range of the embroidery to windward 

 is much greater, and the pattern is much more irregular and complicated. What 



* 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 oppor- 

 tunities 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 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, 1 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 ? Observa- 

 tions, 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 wave- 

 length ; and so on, until the process is stopped by the breaking of the wave crests. This is merely a speculation, with- 

 out sufficient basis, either theoretical or experimental ; but the subject seems to call for investigation, and its practical 

 importance is undeniable. 



t Annalen der Hydrographie und maritimen Meteorologie, Heft i., Jan. 1890. 



i See Lamb's Hydrodynamics, p. 6C9 (1906). 



TRANS. ROY. SOC. EDIN., VOL. XLVI. PART III. (NO. 20). 75 



