628 MR E. M. WEDDERBURN ON THE TEMPERATURE SEICHE. 



organised. They have demonstrated the existence of a temperature seiche the period 

 of which agrees with surprising accuracy with the computed period and which has an 

 amplitude of about 10 metres, i.e. about one-quarter of the depth of the lake. This 

 amplitude is relatively to depth about the same as that of the Loch Ness temperature 

 seiches, which had an amplitude of from 150 to 200 feet. Professor Birge thought that 

 sucli an amplitude was impossible without serious disturbances occurring at the surface, 

 but this is evidently due to a misconception of the nature of the motion of the water. 

 But the observations will, it is hoped, have a wider effect than the mere proving 

 the existence of temperature oscillations in the Madtisee. They should demonstrate to 

 other observers the necessity for more careful investigation of lake temperatures and 

 the futility of basing comparisons between lakes on observations made at one point and 

 at considerable intervals of time. With numerous observers and continuous observations 

 it may become possible to correlate quantitatively wind velocities and temperature 

 changes, and it is thought that physical research in lakes should now be directed to that 

 end. Another problem which invites investigation is the nature of the temperature 

 changes which occur within the discontinuity layer itself. Of these we know nothing, 

 except that they are frequently large and rapid. It is likely that progressive waves are 

 propagated in that layer, and they could be detected by simultaneous observations made 

 at close intervals along the lake. Apparent irregularities in the temperature seiche 

 oscillations can easily be explained on the assumption of the interference of progressive 

 waves, and from experimental observations which are being carried out, it is likely that 

 waves are propagated at the discontinuity whenever there is a change in the direction 

 or in the force of the wind. 



PART II. 



Theory of Temperature Oscillations. 



§ 18. The nature of oscillations at the surface of separation of two heavy liquids of 

 different density in canals of rectangular section and uniform depth is sufficiently known 

 and is dealt with in most text-books. # The velocity of propagation of these waves is 

 given by the equation 



c^l P^4 > • ■ • • ■ 0) 



k p coth kh + p coth kh' 



where p and h, p' and h' are respectively the densities and depths of the two liquids. 

 Where h is very small compared with A (as will be the case in most lakes), 



7T 1 



and A is the wave-length, since k = — , coth kh = — - and equation (l) simplifies to 



A kh 



2 P ~ P 



p,p_- • ■ ■ ■ {) 



h h' 



* Lamb, Hydrodynamics (1906 ed.), p. 353. 



