140 THE ROYAL SOCIETY OF CANADA 



movements known as tidal streams, are left out of account. The 

 analysis deals exclusively with the form of the undulation, where it 

 passes any given point in the estuary; as represented by a curve with 

 time and height for its co-ordinates. The form of the curve can be 

 obtained automatically with great precision, by means of a registering 

 tide gauge. 



If a series of such tide gauges are established in the estuary, the 

 curve at the mouth will be practically symmetrical; but the gauges 

 farther up will give a curve which becomes steeper on the rise and 

 flatter and longer on the fall ; the summit being rounder and the trough 

 sharper. The variation in amplitude along the estuary will depend 

 upon its geographical shape; but usually the amplitude will increase 

 as the estuary becomes narrower, and will then decrease as it is cut 

 ofif by the river slope and the opposing forces already referred to. 

 The chief harbour in an estuary is usually situated where the tidal 

 amplitude reaches its maximum; and the analysis for tide tables has 

 thus to deal with the curve of maximum amplitude. 



The Present Harmonic Analysis. In the harmonic analysis, the 

 tide curve of an open coast is represented by a series of sinusoids 

 which have periods related to the movements of the sun and moon; 

 and the recompounding of these sinusoids gives the actual tide curve 

 as observed or recorded by a registering instrument. The periods 

 involved are the lengths of the solar and lunar day and half day, the 

 half lunar month, the periods of the variation in the distance of the 

 moon and sun, and of their variation in declination. All these are 

 natural periods, astronomical in character; and in addition to these 

 terms, a few others are introduced which represent lines of attraction 

 along the resultant direction of the moon and sun combined, all of 

 which have a direct physical interpretation, that is to say they are 

 not merely empirical constants of an arbitrary character. 



We need only mention six of the harmonic constants, as they are 

 required for comparison later. In the notation, M stands for moon 

 and S for sun; and we thus have M2 for the lunar semi-diurnal com- 

 ponent of the tide, and S2 for the solar semi-diurnal; and, similarly, 

 Ml for the lunar diurnal and Si for the solar diurnal. These do not 

 make up the whole, however; as there are two components which 

 represent their combined influence in the direction of their resultant 

 attraction ; for which K2 is the semi-diurnal and Ki the diurnal term. 



To represent the special or unequal form of the tide curve in an 

 estuary, a series of components are introduced which are termed 

 "overtides." This name is taken because the- terms are similar to 

 those representing the "overtones" in the analysis of musical sounds. 



