44 J. Waterhouse — An Account of the Tidal [No. 1, 



synthesis of Ltiplace. Thus a number of fictitious stars are assumed to 

 move, each uniformly in the plane of the earth's equator, with angular 

 velocities which are small in comparison with that of the earth's rotation, 

 so that the period of each star is something not very different from 24 

 mean solar hours, and ranges between a minimum of 23 hours and a max- 

 imum of 27. Each star is supposed to produce a primary tide in its quasi- 

 diurnal period, and also various sub-tides which run through their periods 

 ill i? "3 J 4 01* some other aliquot part of the primary period ; but of these 

 sub-tides it may here be observed that some are considerably larger than their 

 so-called primaries, as for instance, the lunar semidiurnal tide, the mag- 

 nitude of which is enormously greater than that of the lunar diurnal. The 

 primary is simply the tide of which the period is nearest to 24 mean solar 

 hours. 



Thus the momentarily varying level of the surface of the ocean is 

 supposed to be the resultant of a large number of tides, each of which is 

 perfectly independent of all the others, and has its own amplitude and 

 period of revolution, which remain ever constant throughout all time. 

 Occasionally several of the most important tides are in conjunction, and 

 then the range between high and low-water is a maximum, as at spring 

 tides ; at other times some tides are in opposition to others, and then the 

 tidal range is a minimum, as occurs at neap tides. 



Every tide may be represented by a circle of known diameter ; and i£ 

 we suj^pose a point to move uniformly right round the circumference of this 

 circle so as to make a complete revolution in the time which is the tide's 

 period, then the height of the point above or below the horizontal diameter 

 of the circle at any moment, represents the height of the tide at that moment. 



By the synthesis of Laplace w^e are able to find, from continuous obser- 

 vations of the varying level of the sea, the amplitude and the ej^och (as 

 they are called) of each of the several tides of which the height of the sea- 

 level at any moment is the resultant. The amplitude is the radius of the 

 representative circle, the epoch enables us to ascertain the point which the 

 tide has reached at any given moment during its movement over the 

 circumference of the circle. Thus when w^e know the amplitudes, the 

 epochs and the velocities of rotation of any number of constituent tides, 

 we are in a position to be able to compute and predict the height of the 

 sea-level, at any future moment, at the station where the observations on 

 which our calculations are based were taken. 



The velocity of rotation of a tide rests piimarily on certain combi- 

 nations of the angular velocities of the earth's rotation round its axis, the 

 moon's rotation round the earth, the earth's round the sun, and the progres- 

 sion of the moon's perigee, which are decided on a priori from theoretical 

 considerations. These preliminary angular velocities are the arguments 

 of the several fictitious stars of Laplace's method. 



