Tidal Phenomena at Inland Boreholes near Cradock. 
105 
APPENDIX^ 
As Chrystal's Eesiduation Method appears to be little known, and 
his original paper seems to be difficult of access in South Africa, I quote 
his description, which is as follows : — 
Methods of Eesiduation. — In practice on Loch Earn, more par- 
ticularly in our attempts to determine the positions of the nodes, we were 
compelled to work with short, large-scale limnograms ; and the seiches 
were rarely pure. In these cases we resorted very often to a certain way 
of treating the limnogram, which we came ultimately to call ' Eesiduation.' 
Consider a compound seiche, the equation of whose limnogram is — 
Construct a new curve by slipping the curve (18) a distance r backwards 
along the ^-axis, and from these two curves form a new one by adding the 
ordinates ; or, what comes to the same thing, derive from (18) a new 
curve by adding to the ordinate at each point the ordinate of the point 
whose abscissa is greater by r. 
The equation of the resulting curve is — 
... TTT . ^tt/^ 7-\ „ . rrr . ^tt/ t\ 
n = 2Ai cos rn- sin m U - + o J + ^A^ COS rrr sm rfrl ^ " + 9 ) + . 
The derived curve, or residual with respect to r, contains in general all 
the harmonic oscillations of the original. The phase of each component 
is retarded by the same time, ; and the amplitudes are altered in 
different proportions, viz. — 
Suppose, in particular, that we put r^-J-T^ ; then the first component 
disappears altogether, and we get a curve, whose equation is — 
This last curve we call the residual of the limnogram with respect to the 
seiche of period T^. 
To show how this may be used in practice, suppose we have a short, 
large-scale limnogram, the principal or only components in which are the 
uninodal seiche (Tj) and the binodal (T2). In general one, say the 
uninodal, will predominate ; the other may be scarcely perceptible at first 
= Aj sin '^-(t - (xj + A2 sin ^(^ - ^2) + . . . &c. 
(18) 
2 cos (7rr/T,) : 1, 2cos(7rr/T2): 1, &c. 
