40 
Tidal Computations and Predictions. 
A brief explanation of the method of analysing the figures 
obtained from the records and of making out predicted tide tables 
for any place will constitute a fitting conclusion to this paper. 
First of all from the remarks that have already been made when 
explaining the “Establishment of a Port,” it can be perhaps realised 
that it would be impossible to calculate a tide table for any port 
unless observations had been taken there beforehand. This is a 
point that is overlooked by many people and only goes to prove how 
inadequate all the theories of the tides really are. From the tide 
curve, which for preference should consist of a complete year start- 
ing from January 1, though this is not absolutely necessary, hourly 
readings of the heights are extracted and summed in various ways. 
The figures resulting from this summation are then analysed with the 
object of determining the actual semi-range of each tide and its 
1 base at some definite epoch. 
A brief digression must be made here to explain this last state- 
ment. Owing to the earth’s revolution round the sun, the earth’s 
rotation on its axis and the moon’s revolution round the earth, the 
two tide-generating bodies, the sun and moon, are continually occupy- 
ing different positions, not only with regard to the earth but also 
relatively to one another. And further, owing to the eccentricities 
of the orbits of the earth and moon, the moon moves at varying 
speeds round the earth, while the former travels at changing rates 
round the sun, or in other words the sun appears to do so. Realising 
what this means, some idea of the difficulties to be overcome in a 
solution of a tide table for any port may be better imagined than 
described. 
If the earth’s path round the sun were circular and the moon’s 
motion quite regular, then the prediction of tide tables would be a 
comparatively easy problem. 
And yet it was by applying this principle that Sir George 
Darwin overcame (he difficulty met with in Nature. He split up the 
sun and moon, as it were, into a number of small bodies and imagined 
each one to be travelling at a certain fixed rate round the earth. The 
problem then simply resolved itself into finding the tide produced 
by each of these imaginary bodies. And, therefore, keeping this 
1 oint in mind, the actual curve traced from day to day by the tide- 
gauge pencil may be considered to result from the combination of a 
number of separate curves drawn by pencils travelling along at 
different velocities and each one moving through different heights 
or amplitudes. The question is thus reduced to one of simple har- 
monic motion and a glance at Plate VIII., Fig. 2, will explain this. 
Let the point P move regularly round the circumference of a circle 
and let perpendiculars be continually dropped upon a fixed diameter 
1)1). Then as P moves round the cicle, M will move up and down with 
a speed varying from zero at either end of the diameter to a maxi- 
mum at the centre. This movement of M is called “Simple Harmonic 
