ON THE SEICHES OF LOCH EABN. 493 



establish either coincidence or opposition of phases. We also made observations with 

 the statolimnograph at a point opposite the limnograph near the eastern binode, while 

 the latter was running at high speed (2*96 mm. per minute). Not only were there no 

 apparent coincidences of phase, but the binodal limnograph showed a well-marked 

 vibration whose period was l'35 m , while the best-marked period of the embroidery on 

 the statolimnogram was "44 m to -47 m . # 



2. The vibrations might be transversal seiches of the lake. In a former memoir 1 

 expressed some doubt whether seiches of this kind could be stable in an elongated lake. 

 In an elaborate and most interesting review of our present knowledge of the seiche 

 periods of lakes in general, recently published, t Dr Endros has stated that he has, by 

 means of phase observations, definitely established the existence of a transversal 

 seiche of period l'56 m in the Tachinger See, and shown that both it and the seiche 

 between Morges and Evian, observed by Forel and suspected by him to be 

 transversal, as well as certain other cases of the same phenomenon, agree very well 

 with the hydrodynamical theory. My doubt on this matter must therefore be 

 abandoned. Dr Endros' view is that only part of an elongated lake takes part in 

 the transversal oscillation, and that the establishment of a cross seiche is favoured 

 by the existence of bays on the two sides of the lake, the ends of which determine 

 the axis of the seiche. This view is strongly supported by the results of the Japanese 

 observers regarding secondary tidal oscillations in the bays of the coast of Japan, to 

 which we have already referred. 



There remain, however, two difficulties as regards Loch Earn. 1 have calculated by 

 means of the parabolic approximation the periods of the cross seiches for various breadths 

 of Earn, and find values which average l'85 m , the smallest being l - 83 m , the greatest 

 2 'SO" 1 . The section at the eastern binode, where the observations above referred to 

 were made with the statolimnograph and the Sarasin limnograph, is very nearly 

 parabolic in shape, and the period there would be 1 "9 m or more, which exceeds any of 

 the periods observed in the embroidery by more than any likely error, either of obser- 

 vation or calculation. 



Then there is the further fact, already mentioned, that no correspondence of phase 

 could be detected, although it was anxiously looked for, and indeed at first expected. 



3. Another cause of the embroidery of the limnogram may possibly be found in pro- 

 gressive surface waves and wave groups. 



Everyone is aware that the effect of a persistent wind, which has blown for some 

 time along a lake-surface, is to produce a progressive train of waves travelling down the 

 wind. The height and also the length of these waves depend on the " fetch," i.e. the 

 length of water over which the wind has blown, as well as on its velocity. The range 

 and the wave-length both increase as we go " down the wind," until at last the wave- 

 crests break and "white horses" are formed. Then a sort of dynamical equilibrium is 



* See fig. 19, where the statolimnograms in question are reproduced, 

 t Petermanns Geog. Mittheilungen, Heft ii., 1908. 



