92 
Transactions of the Boyal Society of South Africa. 
long record of 1908 was the fact that arapUtudes of the water-level curve 
are regularly at a niaximuni at the time of full and new moon and at a 
minimum during the moon's first and third quarters. This fact implies 
that the two principal harmonics in the curve have their respective maxima 
synchronising twice in a lunar month or once in 14 days. It follows from 
this that 14 days must be the least common multiple of the periods of the 
two harmonics. 
The measurements already made on curve D have shown that its 
dominant harmonic period must be in the neighbourhood of 12 hrs. 27 min., 
or nearly of a fortnight. It now appears probable that it is exactly 
of a fortnight, or 12 hrs. 26 min., and that the remaining harmonic must 
either have a period of ^^-g of a fortnight, or 12 hours, or alternatively -^-^ 
of a fortnight. 
In order to test the reliability of this last probable hypothesis in a 
practical way, the curve D was residuated with respect to T = 12 hrs., and 
in this way was obtained a residual curve F. This curve was composed 
of waves of small amplitude amounting on the average to about -14 of an 
inch, and it was evident that in this residuation I was approaching the 
lower limits of accurate working. I determined 24 H.W. points and 
25 L.W. points in the curve, and measured each wave interval both from 
L.W. to H.W. and also from H.W. to H.W. 
In this way I found the average distance from H.W. to H.W. to be 
18"16 cm., and the average wave-length as measured from L.W. to L.W. 
to be 1815 cm. 
Taking the average clock rate as 41*06 minutes per centimeter, and 
converting these averages into time, we get the values : 12 hrs. 25f min., 
and 12 hrs. 25 min. This result, though not obtained by strict adherence 
to the Eesiduation process, at least shows that curve C is plausibly 
divisible into two harmonic components having periods of 12 hrs. 
26 min. and 12 hrs. respectively. The possibility of its being equally 
divisible into another pair of components is not quite excluded. 
Summary of the Besults of the foregoing Analysis. 
The record curve obtained at Tarka Bridge during the period June 4 
to June 18, 1905, has been dissected into two curves having as their 
main harmonic periods 
12 hrs. 27 min., 
and 23 hrs. 57 min. respectively, 
together with an anharmonic residuum which appears to correspond 
substantially to a vertical inversion of the barogram for the fortnight 
obtained on the farm. 
Further the curve of 12 hrs 27 min. periodicity has been shown 
