384 PROFESSOR CHRYSTAL AND MR JAMES MURRAY 



figuration Period " of the limnogram. Thus, for example, taking the calculated values 

 of Tj and T 2 for Loch Earn, we have T,/T x = U'50/8'14 = 1781. If we convert 'L/% 

 into a continued fraction, we get 



% ~ + 1 + 3+ 1 + 1 + 2+ 1 + 12' 



the third convergent to which is 9/5 = 1*8 ; and this represents the value of T 2 /T l with an 

 absolute error of less than "02. Hence five uninodal oscillations of the lake occupy very 

 nearly the same time as nine binodal oscillations. Therefore a portion of the limnogram 

 consisting of five uninodal, or nine binodal, oscillations, will be observed to recur a 

 considerable number of times ; and would recur for ever if 9/5 were the exact value 

 of T 2 /T l5 and the dicrote seiche persisted indefinitely without decay or disturbance. 



Fig. 4 shows three such configurations in a dicrote seiche of Loch Earn, registered 

 at St Fillans on 6th September 1905. 



The existence of a well-marked configuration period gives us two great advantages. 

 By looking for points of symmetry we can determine very accurately when the two 

 seiches are both at a maximum, both at a minimum, or one at a maximum and the 

 other at a minimum ; also, when the time-length of the configuration period is known, and 

 also the period of one of the seiches of the dicrote, the other period can be calculated. 



By observing near a Binode or near the Uninode we eliminate the binodal and 

 uninodal seiches respectively. As the trinodal and higher seiches on Earn are in- 

 frequent, and nearly always of small range, we thus obtain curves which, apart from 

 non-seiche disturbances, are very nearly sinusoidal. Fig. 7 is an example. We secured 

 a considerable number of such series ; and, but for the defective working of our 

 Sarasin limnographs, would have got many more. These give good determinations of 

 T x and T 2 , on the assumption that the seiche has undergone no change of phase during 

 the series. Undoubtedly such changes do occur ; they are probably due to the inter- 

 mittent action of the cause which produces the seiche. In this way two seiches of 

 the same period are superposed, the apparent result being a change in phase, with or 

 without a change in amplitude. A sudden and considerable change of phase would, 

 of course, be noticeable ; but small or gradual changes of phase would certainly escape 

 notice. 



The observation on a large scale of short series of comparatively 'pure sinusoidal 

 undulations also give good period-determinations. For this purpose index limnographs 

 magnifying the range of the seiche fourfold, and limnograms having a time-scale of 

 "2 inch (5 mm.) per minute, were used; and occasionally the statolimnograph. By 

 bisecting lines drawn across the undulation parallel to the time-scale we can judge very 

 accurately of the symmetry of the particular part of the limnogram, and infer whether 

 the turning-point was or was not much disturbed by higher seiches or other dis- 

 turbances. When two turning-points are determined in this way, we get of course a 

 determination of the period, and the advantage of the method is that the result is not 

 so likely to be vitiated by change of phase. 



