756 DR E. M. WEDDERBURN AND MR A. W. YOUNG ON 



A considerable oscillation with a period of about 18 hours appears to have been 

 in progress when the observations were commenced, and to have been damped out by 

 the east wind which sprang up on the evening of the 14th. 



The most noticeable point about the oscillation is that the isotherms fall very 

 rapidly and rise gradually. This is more noticeable in the observations at No. 1 

 than at No. 2 station. The bottom line in fig. 8 represents the difference in level 

 between the two isotherms at the two stations, and from this diagram it is seen that 

 while the rapid descent is first felt at No. 2 station, the fall at No. 1 station very 

 soon exceeds it. To a considerable extent, as will be shown later, the rapid fall of 

 the isotherms is due to the combination of oscillations of different nodality, but if 

 this were all there would not have been so much difference between the curves for 

 the two stations. 



The theory of seiches in lakes (both ordinary seiches and temperature seiches) 

 assumes that the amplitude of the oscillation is small compared with the depth of the 

 lake. This is no longer true in the case of temperature oscillations. The oscillation 

 under discussion has an amplitude of about 16 metres, and the maximum depth of 

 the lake below the discontinuity is only about 80 metres. Towards the end of the 

 lake, where it is much shallower, the ratio between amplitude and depth is by no 

 means small. 



It will be sufficient to consider the case of an ordinary seiche where this ratio is 

 not small, though it may still be assumed that the vertical acceleration of particles is 

 small and negligible ; for we have seen that the same process may be applied to the 

 discussion of temperature oscillations as to ordinary seiches. 



Using the notation of Chrystal's Memoirs, but assuming for the sake of simplicity 

 that the lake is of rectangular cross-section and uniform breadth, the depth at any 

 point being h, the method described in Lamb's Hydrodynamics, 3rd ed., p. 245, 

 gives for the seiche equation 



dxj 



Since this equation is not linear a simple harmonic type of oscillation is not 

 possible, and as the oscillation progresses there will be a change of type. In the 

 deeper parts of the loch the ratio between amplitude and depth is smaller, and a 

 change of type will be the more easily averted by a slight adjustment of the velocities 

 of the water particles. Towards the ends of the loch, however, when the amplitude 

 is large, considerable distortion of the wave surface may be expected. The water 

 at station 2 was much deeper than at station 1, and it is to be expected that there 

 should be considerable and irregular difference between the level of the isotherms 

 at these two points. The suddenness of the fall of the isotherms which has been 

 noted is also probably largely due to the change in type of the wave in shallow 

 water. Where the amplitude of the oscillations is large, it is probable that the 

 isotherms will move very rapidly indeed, and possibly the wave may break, just as 



