88 
Transactions of the Royal Society of South Africa. 
which is the equation for the curve assumed by Chrystal in his mathe- 
matical theory of the Eesiduation Process. 
The method therefore is appUcable to every curve which is the expres- 
sion of a finite periodic function of a variable, and hence obviously to the 
Tarka Bridge records. 
The residuation method is essentially a means of eliminating from a 
curve one by one its various harmonic components. My actual mode of 
working may be described as follows. 
The curve to be residuated is traced on to another sheet, and then a 
second tracing of the same curve is superimposed on the same sheet but 
with the original curve moved along the time axis through a distance 
corresponding to half the period of the harmonic to be eliminated; Then 
a line is drawn so that it is everywhere half-way between the two tracings, 
and the intermediate curve thus obtained is the first residuum. It contains 
all the harmonic components of the original except one, with their periods 
unaltered but with their amplitudes considerably reduced. 
I have found the process somewhat laborious in practice, but the 
results are much better than I had expected. 
Besicluation Method applied to Tarka Bridge Curve. 
The same reasons already mentioned as leading to the selection of the 
record June 4 to June 18, 1905, for purposes of comparison with marine 
tide records held good in the consideration as to which of the Tarka 
Bridge records was most suitable for residuation analysis, and accordingly 
the record June 4 to June 18 was again selected. 
The daily records for that period were fitted together and traced as a 
continuous curve on tracing cloth. This continuous record was almost 
5 meters long. The tracing was made in the form of a smooth curve 
carried through a mean position in the seiche frills of the original. (This 
is the curve A at the top of the photo-reduced Diagram 9.) 
The times of the first and last turning-points were determined as 
follows : — 
First L.W. at 11.55 a.m., June 4, 
Last H.W. at 8-0 a.m., June 18, 
giving a period of 332 hrs. 5 min., comprising 53 half -waves of the 
dominant harmonic, or — 
= 332 hrs. 5 min., 
from which we deduce 12 hrs. 32 min. as a first approximation for the 
value of T^. 
