DETERMINATION OF THE LONGITUDINAL SEICHES OF LAKE GENEVA. 633 
curve. It will be seen that a large number of peaks exist, and it was necessary, 
therefore, to provide a very smooth curve in order to avoid excessive numerical 
errors due to the use of integration formulae. This was obtained by plotting from 
the original data, and the nominal accuracy of the interpolated values was 
increased by redrawing on a greater scale. Great care was taken in smoothing the 
curve. For the small values of x , in both systems, the graph of x/p(x ) was used in 
this smoothing process. 
6. Computation of I„(0, x) and V n (0,x). 
Let w(x) and e{x) denote the reciprocal of 10 ~ 15 u 3 p(x) in the w-system and 
e-system respectively ; these were calculated at intervals of 0 ‘01 in x. We now have 
to apply formula (ll) and (12). The integration was performed by means of the 
well-known Simpson formula 
3 j o ydx = % 0 + 4y h + y i7l ] .... (24) 
where A = 0'01 in the present instance. 
Successive application of this formula gives the values of three times the integral 
for x = 0, 2 h, 4 h , and, by a second series of calculations, for x = h, 3 h, 5 h, 
The odd and even series are thus calculated independently, and a check on the end 
values is practically sufficient ; this check was performed by means of the inter- 
polation formula 
1 6 y 3h = - y 0 + 9 y A + 9 y th - y rh . . . . (25) 
Thus any term in the odd series can be calculated by interpolation from the even 
series and compared with the value obtained from the Simpson integration. 
In the actual calculations powers of three were retained and powers of ten 
ignored until all the integrations were completed. 
Since l 0 (0,cc)=:r, the first procedure was to evaluate xw(x), and the accuracy of 
