Seiches in Some Lakes of Japan. 65 



This assumption is not satisfied in the Hakoné lake owing to 



the great constriction in the middle, and the experiment with the 



model shows this point very clearly. (See PL IX, Fig 1.) But 



this is not of course sufficient to explain the great discrepancy of 



our calculations. The assumption that the normal curve consists 



of four inclined straight lines must be responsible for it. 



In our numerical calculations, we used the tables for Jo and Ji 



given in the appendix of the treatise on Bessel functions by Gray 



and Mathews, and the small tables for Yo and Yi of Smith given in 



the Messenger of Mathematics vol. 26. As the observed period is 



15.38 minutes, we took first T=800 and 1000 seconds, hoping to 



get residuals of opposite signs in the equation (5). The result was 



however that the residuals w^ere both positive. Hence we tried 



T=]200 seconds, and found it to be still positive, and proceeded 



to T = 1400 seconds when we got a negative residual. From this 

 we obtained 



We have said above that the great discrepancy between the 

 observed and the calculated periods may have been due to the 

 assumption that the normal curve consists of four inclined straight 

 lines. In order to examine this point, we applied the method of 

 calculation adopted under (8) according to Du Boys' s formula to 

 the reduced lake given in Table 30, considering it as a lake of 

 uniform breadth but of variable depth a. According to (8), the 

 required period is 



where I is the distance between two consecutive transverse sections, 

 with depths <^' and '^". In the former case, I was constant, but in 



