638 MR E. M. WEDDERBURN AND MR A. M. WILLIAMS. 



AVhere y>l/3 tlie formula is accurate to within 1 per cent. This suggested as 



a formula for the calculation of the temperature seiche where the temperature normal 

 curve is parabolic the following equation : — 



2g(p-p) 



~p --^ • ■ • (6) 



+ 



where 



I , , ir// l . Ttti 



- tanli — - tank 



_ vl Jp'R + pH' ^\ 



y/2g{p- P ')B..R' 



H = - tanh — - and H' = - tanli — - . 

 it I -n I 



This is the formula which was used in calculating the periods of the oscillations given 

 below. If - is small, the period equation is the same as is given by the theory of § 18, 



t 



for then — tanh -r- = h. 



Apparatus and Methods. 



§ 41. In lakes the difference in density between the surface and bottom layers is due 

 to difference of temperature, but, for laboratory experiments it is more convenient, and 

 equally instructive, to represent the temperature distribution in a lake by two liquids 

 of different density, which do not mix, superimposed one on the other. In the following 

 experiments the liquids used were paraffin and water. 



§ 42. Some experiments were made in the trough which was used by White and 

 Watson * in their experiments on the period of ordinary seiches. This trough is 

 152 cm. long, 10*5 cm. broad, and 14 cm. deep. It was fitted with a parabolic bottom, 

 which, however, did not fit the trough very closely. The trough was partially filled 

 with water and then a layer of paraffin was added. Accurate results were not obtainable 

 with this trough because of the ill-fitting of the parabolic bottom. The gaps between 

 the sides of the trough and the blocks of wood which formed the bottom must have 

 considerably affected the period of slow oscillations due to difference in density between 

 the water and the paraffin. Moreover, the surface tension effect at the end of the 

 surface of separation of the two liquids was very great. The paraffin soaked into the 

 wood of which the bottom was made and thus thoroughly wetted it and formed a large 

 meniscus. No allowance was made for this in our calculations, and we took as the length 

 of the surface of separation the length it would have had if there had been no surface 

 tension effects. The long trough had the advantage that the depth was long compared 

 with the wave-length of the oscillations, and so the long wave theory was more strictly 

 applicable. Two sets of observations were made, first, simply with the trough fitted 



* Proc. Roy. Soc. Edin., vol. xxvi., 1905-6, p. 143. 



