6 S. ]Sakaiiiiira and K. Honda : 



holes bored in both sides of the penholder. By this arrangement, 

 the pen could be displaced to any height and fixed there by means 

 of the screw S. 



a. TreatiiBeat of llie records. 



It is not an easy task to determine the periods of several 

 component oscillations from the limnograms. Even when there 

 are only two components with different periods, the general aspects 

 of the curve may differ considerably according to circumstances. 

 such as the relative magnitudes of their amplitudes and their 

 relative retardations. The pei'iods of several seiches existing in a 

 given lake do not stand in simple ratios as was formerl}^ thought 

 to be the case. In an interesting paper* entitled "On the 

 hydrodynamical theory of seiches," Chrystal has calculated 

 theoretically the periods and the positions of nodes for seiches in 

 lakes of various forms and has shown that the ratios of the periods 

 of several modes of oscillation may be an}^ whatever. In a 

 rectangular lake of uniform depth, indeed, the periods for uni- 

 nodal, binodal, and trinodal seiches stand in the simple ratios of 

 1:^:^. ..; but in other lakes they are quite complex, and their 

 ratios may be even imcommensurable. The amplitudes and 

 phases of the several components are quite independent of one 

 another. Thus when we have a limnogram before us and wish to 

 determine the periods and phases of the several components, at 

 first we are at a loss how best to proceed. In an expansion of a 

 function in Fourier's series, we know the periods a priori and the 

 values of the amplitudes and phases are sought for. Here we know 

 neither the periods, the amplitudes nor the phases. An analytical 

 method of finding the most probable values of the periods of 



* Trans. Eoy. Soc. Edinburgh XLT. part III, 10O5. pp. 599-(;49. 



