386 PROFESSOR CHRYSTAL AND MR JAMES MURRAY 



Now resicluate with respect to T\. The result will be a curve in which the uninodal 



harmonic is very much reduced, and will show the binodal in predominance. From 



this determine an approximation to T 2 , say T' 2 . 



Now return to the original limnogram, and residuate with respect to T" 2 . The 



result will be a curve from which the binodal harmonic is nearly absent. Hence the 



turning-points of the uninodal will be much less disturbed than before ; and we can 



now get a better approximation to T l5 say T'^. 



Residuate now the original limnogram with respect to T ! \, and we get a curve in 



which the binodal is less disturbed than before. We can therefore make a closer 



approximation, say T" 2 , to T 2 ; and so on. 



The process can, if necessary, be repeated until the accumulated errors incidental 

 to the manipulation obliterate the essential features of the diagram with which we are 

 dealing. 



In this way the periods of two or even three seiches can be determined, one after 

 the other, from a comparatively short large-scale limnogram. We discovered in this 

 way seiches the existence of which had not been suspected ; and without this process we 

 should not have obtained a determination of the period of the trinodal seiche of Earn at 

 all, which never occurred pure, and had always a comparatively small range. The process 

 was also used in purifying compound limnograms with a view to determine nodes. 



Fig. 19 (scale |-) reproduces an actual application of the method of residuation. At 

 St Fillans, on the 10th July 1905, Mr James Murray made with an index limnograph* 

 one of the most remarkable seiche observations with which I am acquainted. He 

 observed every half-minute from 9.30 a.m. to 5.35 p.m. During the whole time the lake 

 was calm and the seiche steady. The limnogram presented very clearly to the eye the 

 configuration of a dicrote composed of the uninodal and binodal seiches of Earn, and 

 this was repeated four times during the observation. The lowest curve, A A in fig. 

 19, is rather less than the third part of the limnogram as plotted by Mr Murray. 

 Measuring from k to I, which are two nearly symmetric mimima on A A, we get 

 T / 1 =14'5 / . In second part of fig. 19, A A is as before, and A 'A' is the same curve 

 slid backwards a distance corresponding to 7'25 r . The third (thick black) curve, A — U, 

 bisects everywhere the vertical distance between A A and A'A', and is therefore the 

 residual curve as above defined with the scale of ordinates halved. It is at once 

 obvious that it is mainly a dicrote of the binodal and another seiche, the time-length 

 of the configuration period being three periods of the binodal. Measuring from c to d, 

 we get T' 2 = 8-02. 



After residuating in the ordinary way with respect to T' 2 , we get the curve A — U - B, 

 on measuring which from a to b we get T' 3 =6 '02'. We thus get, obviously, a close 

 approximation to the period of the trinodal seiche, the existence of which was not 

 suspected in the original limnogram. 



* It was mounted on friction wheels, and magnified the seiche about four and a half times. Time-scale of 

 limnogram, '2 inch per minute. 



