SKCT. 5] LONG-TERM VARIATIONS IN SEA-LEVEL 599 



that tlie resultant friction is such as to leave only the forced long -period tide, 

 which must be of the (corrected) equilibrium form. The requisite amount of 

 friction depends upon the period of the constituent, and Proudman has further 

 deduced that, for the validity of the law, the period of the constituent must be 

 long compared with 27r/A;, where k is a parameter of friction. For shallow water, 

 2nlk has its lower limit (4.6 days) and for oceanic waters its upper limit (5.1 

 years), making it appear certain that the nodal tide will obey the law. It is less 

 certain that the solar annual tide (So) and the solar semi-annual tide (Ssa) will 

 do so. 



The theoretical amplitudes of the equilibrium tide must be corrected for the 

 influence of a yielding earth. The earth tides (or body tides, to distinguish 

 them from the loading tides referred to in the next paragraph) are generated 

 by the gravitational attractions of sun and moon, and since they too are of 

 equilibrium form they reduce the water tide by a factor ^ ; ^ is dependent upon 

 the rigidity of the earth. This deformation of the earth is responsible for a 

 secondary effect, however, since it exerts an attractive force on the water bulge 

 and thus augments it by a factor k; k is dependent upon the distribution of 

 density within the earth. The two pure numbers h and k are the well known 

 Love numbers. These considerations lead to the relationship 



Observed tide = (l+k — h) Equilibrium tide. 



Tomaschek (1957) has given a comprehensive account of the various methods 

 used to estimate the quantity l+k — h. It is of interest to note that, despite 

 the uncertainty surrounding the existence in nature of the equilibrium forms 

 of Mm and Mf , observations of these tides give estimates for l+k — h which are 

 in reasonable accord with the figure deduced (0.7) from methods independent 

 of tidal theory. It should be mentioned here that in general the fortnightly tide 

 Msf cannot be used for these determinations as it may contain a sizeable 

 contribution from the interaction, in shallow water, of the principal lunar and 

 solar semidiurnal tides M2 and S2. Nor can the Ssa and Sa constituents be used, 

 as the results of harmonic analyses of tidal data at ports all over the world 

 reveal that they are dominated by the seasonal variations of meteorological 

 and oceanographical origin discussed in sections A and B. A fuller treatment 

 of these last two variations is given in Pattullo, Vol. 2. 



One further contribution is made to the observed long-period tides (and to 

 any other species of tide) by the yielding earth, known as the loading tide. The 

 effect of the tidal distribution of water in tilting the earth's surface has been 

 shown, principally from earth-tide measurements, to extend a remarkable 

 distance inland from continental coastlines. 



Before leaving the subject of the long-period astronomical tides, it is desirable 

 to comment upon the tidal cycle having a period of 18.6 years, that of the 

 revolution of the moon's nodes ; the tide associated with this period is possibly 

 the most quoted and the least known of all the tidal constituents. The theo- 

 retical existence of this tide is frequently used as an argument for taking 19- 

 yearly means, or taking a 19-year span of observations when examining data 



