50 
THE FRESH-WATER LOCHS OF SCOTLAND 
ing and measuring between two nearly symmetric minima, it is 
readily found that the longest period is about T-,^ = 14*5 min. On 
the limnogram is now superposed a tracing of itself, displaced to the 
left through a distance 14*50/2 = 7"25, and the two curves are com- 
pounded by taking at each point half the sum of their ordinates. In 
the resulting curve, A-U in fig. 17, the uninodal seiche is destroyed, 
or at least greatly reduced. It would be destroyed altogether if the 
value of T-^ obtained were quite accurate. The other component 
seiches are altered in a known way as regards phase and amplitude, 
but the periods are unaltered. The result is a curve still impure, but 
with a well-marked period of T2 — 8*11 min. Eliminating this com- 
ponent as before, we get the uppermost curve, which gives a period 
of T3 = 6*02 min. These are good approximations to the first three 
periods of Loch Earn. The approximation may be refined by now 
residuating out (as we got into the habit of calling this process) the 
binodal and trinodal, and redetermining T^ from the purified curve ; 
then residuating out T;^ and improving the value of Tg ; and so on. 
This kind of analysis differs essentially from the application of 
Harmonic Analysis, which is quite useless — indeed, often very mislead- 
ing — unless the periods are given beforehand, and only the amplitudes 
and phases of the components have to be determined. 
Functions of the Well and Access Tube 
The analysis of limnograms by the process of residuation naturally 
leads me to mention a method by means of which a lake may be 
made in some degree to analyse or purify its own limnograms. 
The first purpose for which the well or closed cylinder enclosing 
the float of a limnograph was introduced was no doubt to shield the 
float from wind, breaking waves, and the meddlesome fingers of the 
passers-by. But it can be utilised for a further purpose. Suppose, 
to begin with, that the cylinder is altogether closed from the lake ; 
then, of course, the float will not be affected by any disturbance of 
the lake-level. Next suppose that an access tube of very small bore 
is fitted. Then, owing to the smallness of the bore, the fluid friction, 
and the smallness of the differences of pressure at its two ends due to 
the denivellation of the lake, a considerable time is required before 
a given small denivellation runs into the cylinder enough water to 
produce the full effect on the float. If the outside denivellation has 
a long period, this is of little consequence as regards the amplitude of 
the motion of the float, the only marked result being that the maxi- 
mum height of the float lags behind the maximum height of the out- 
side disturbance. If, however, the period of the outside denivellation 
is very short, it has passed away before the flow through the access 
tube has had time to exert any sensible influence on the float, and the 
