56 PROCEEDINGS OF SECTION A. 
each lunar day. Instead of this simple condition of things, 
however, the lunar tideS are complicated by the facts that 
the moon’s orbit is elliptical instead of circular; that the 
plane ot the orbit is inclined to the plane of the earth’s 
equator; that this inclmation is not constant; and that the 
sun disturbs the moon, producing evection and variation. 
These irregularities in the moon’s motion are all reflected in 
the lunar tide, but the combined effect is exactly equiva- 
lent to the superposition of a number of strictly periodic 
waves of simple type. So that the effect of the moon upon 
the oceans may be considered to be that it produces not one 
tidal wave, but a number of waves, some of which ‘are sem 
diurnal, others diurnal, two fortnightly. and one monthly, 
and that the actual result is duc to the compounding of all 
these separate constituents. In a similar way the tidal 
wave due to the sun may be split up into a number of com- 
ponent waves. Our actual tides are due to the combination 
of all the junar and solar components. For purposes of 
tidal calculation, we replace the actual sun and moon by 
a number of imagmary satellites, which would together pro- 
duce an equivalent tidal result, but such that each 
separately produces a simple sine wave. At first sight it 
may appear that there is no simplification in doing this, but 
that we are rather making,the problem more complex by the 
introduction of so many attractive forces. The simpifica- 
tion, however, consists in the fact that each of these satellites 
revolves in a circular orbit either in the plane of the equator 
or paraliel to it. So that if we could manage to separate 
out and measure the wave produced by one satellite. we 
could determine what the height and position of that wave 
would be at any subsequent time, because it recurs at 
regular fixed intervals. Theoretically, an infinite number 
of such satellites would be necessary to produce exactly 
equivalent effects to the actual sun and moon, but practic- 
ally only 20 of them produce a-measurable and observable 
effect; and in most places it is only necessary to take into 
account some nine or ten. The use of the fictitious satel- 
lites is not necessary, but is a great convenience. The 
diferent component waves we may divide into three types— 
the semi-diurnals. whose periods, or time from one high- 
water to the next, are about half a day; the diurnal, with 
periods of about one day; and the long-period tides, whose 
periods are a fortnight, month, half-year, and year. 
By means of a self-registering tide-gauge we may be 
placed in possession of a continuous record of the height of 
the water at a place. The irregular wavy curve so obtained 
