41 
Motion’’ and, if the length of the diameter and the position of P, 
measured by the angle MOP, are known, then the distance of M 
from 0 can be computed. 
Now, applying this reasoning to the solution of any one of these 
simple tides: — The speed is known and therefore the rate at which 
P travels round the circle. For example, the main solar tide is 
caused by a sun moving uniformly round the equator at the rate of 
15° per hour, namely 360° or once round in one day; the main lunar 
by a moon moving in the equator at the rate of 14.4° per hour, 
namely 360° in 25 hours; while the rates of the other fictitious tides 
are given in the tables of constants. For each tide the semi-range 
is determined and therefore the diameter of the circle is known. The 
I base or angle MOP is worked out for a certain epoch — say January 
1st, Olirs. Then from the known speed the alteration of the angle 
MOP, after any interval, can be estimated and, knowing this angle, 
the height OM for any instant can be found for each tide. The 
algebraical sum of all the tides gives the resulting height of water. 
This same principle is elaborated in the construction of tide- 
predicting machines, except that the procedure is reversed. 
Analyses of the figures for 1908-12, Fremantle, and 1913, Port 
Hedland, were completed at the Observatory and appear in the 
following table: — 
