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



also 



e-W-^mnntf-r) . . . . (15') 



Z'^ 2A ' W *m»M-T) (16') 



a 



but 



and therefore 



and we oet the relation 



A=A', 



&{z) = ?h'. 



§ 31. The motions of water particles are shown on fig. 4, the light line representing 

 the motion of the upper layer particles and the heavy line that of the lower layer. 

 The surface of separation is a plane which oscillates about the uninode. 



PART III. 



Computation of the Period of the Madusee. 



§ 32. The calculation of the period of the ordinary seiche according to Chrystal's 

 method is sufficiently laborious, but the calculation of the period of the temperature 

 seiche is considerably more so, until the normal curve has been constructed. There- 

 after the process of approximating to the normal curve is exactly the same. In fig. 5 

 the heavy line shows the temperature normal curve for the Madusee, i.e. the curve 



whose ordinates are b(x)l<-r£- + — ^— I and whose abscissas are dxb(x). The broken 



line shows the ordinary seiche normal curve (the scales being different for this curve). 

 It will be seen that the curve is not one which can be approximately replaced by any 

 simple curve. The faint line on the diagram shows what I judged to be the best 

 approximation, taking into account the fact that the wave velocity varies as the square 

 root of the depth. It would have been very laborious and rather purposeless to obtain 

 an approximation by piecing together a number of parabolee and straight lines, for it is 

 probable that some of the assumptions which have been made introduce as large an 

 error as will the approximation by a single parabola. 



§ 33. The equation to the approximation curve for the Madusee was 



2(w) = H( 1 

 where 



H = 24-4x 10 12 C.G.S. units 

 a = 10-43xl0 10 



i.e. half the area enclosed by the L 5-metre depth contour, that being the depth at 

 which, it was thought, the discontinuity occurred. The temperature of the upper layer 

 was assumed to be uniformly 17° C. (p = -9988), and of the lower layer 8° C. (p = -9999). 



