86 THE FRESH-WATER LOCHS OF SCOTLAND 
of phase, but the binodal limnograph showed a well-marked vibration 
whose period was 1*35™, while the best-marked period of the em- 
broidery on the statolimnogram was "44™ to •47"\^ 
2. The vibrations might be transversal seiches of the lake. In my 
memoir on the Hydrodynamical Theory of Seiches I expressed some 
doubt whether seiches of this kind could be stable in an elongated 
lake. But in a paper already mentioned Dr Endros has stated that 
he has, by means of phase observations, definitely established the 
existence of a transversal seiche of period 1*56™ 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 already referred to. 
There remain, however, two difficulties as regards Loch Earn. I 
have calculated by means of a parabolic approximation the periods of 
the cross seiches for various breadths of Loch Earn, and find values 
which averao-e 1 -85"^ the smallest beina; 1 •83"\ the greatest 2-30™. 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™ 
or more, Avhich exceeds any of the periods observed in the embroidery 
by more than any likely error, either of observation or calculation. 
Then there is the further fact, already mentioned, that no cor- 
respondence 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 progressive 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 travellino; down the wind. The heio-ht and also the 
length of these waves depends 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 established, and the range and 
1 See fig. 33, where the statolimnograms in question are reproduced. 
2 Petermanu's Mitt., Heft ii., 1908. 
