PRESIDENTS ADDRESS.. 5& 
more rapidly than the forced tidal wave, we should have 
high-water under the moon and low-water in the guedra- 
tures. With this position of the wave the tidal forces are 
continually acting to retard it, and make it move mere 
slowly. . : 
5. With the first canal the effect of friction is to cause 
the high-water to reach any particular place earlier thau it 
would if the water were frictionless. 
4. With the second canai the effect of friction is to cause. 
the high-water to reach any particular place later than it 
would if the water were frictionless. 
After all, however, although the investigations of Airy 
into the behaviour of the tidal wave in canals, as those of 
Laplace upon the tidal oscillations of an ocean covering the 
whole earth, are of very great interest, they are of little 
value in enabling us to calculate the tidal effect at any par- 
ticular port. The depth of the sea is so irregular, and the 
disposition of land and water is so exceedingly complex, that 
the calculation of the height and time of the arrival of high- 
water at any particular spot on the earth’s surface from 
astronomical considerations alone, appears quite béyond ihe 
possibilities of mathematics. Laplace's dynamical theory 
as to the origin of the tidal wave is now generally accepted ; 
but, although it may enable us to calculate the height and 
progress of the tidal wave under certain very simple ideal 
dispositions of land and water, we cannot determine the pro- 
gress of the wave under the complex conditions which 
actually exist. 
In order, then, to be able to predict the tides at any port, 
we have to depend upon previous observations at that port ; 
but how to determine the order which we know must prevail 
in the apparent chao¢ which seems to exist at many ports is 
not a particularly smple:problem. It has been best. solved 
by the application to tidal records of the methods of Har- 
monic Analysis, as first suggested by Lord Kelvin. The 
systematic methods of procedure have been elaborated by 
Adams, and particularly by G. H. Darwin. ‘The basis of 
the method is due to Laplace, according to whose dynamical 
theory the height of the water at any place may be expressed 
as the sum of a certain number of simple harmonic functions 
of the time, the periods of these being known from astro- 
nomical considerations. If the moon were to move in a: 
circle round the earch in the plane of the earth’s equator, 
and at a constant distance from us, a semi-diurnal tide would 
be produced on the waters of the earth, which would be in 
the form of a regular simple wave exactly repeating itself 
