ON MEAN SEA LEVEL AND ITS FLUCTUATIONS. 



By D'ARCY went worth THOMPSON. 



Few data are more often referred to than " sea level," and few 

 physical constants are so little known and so inaccurately determined. 



The mean between two consecutive tides, high and low, is our 

 first approximation to the mean level of the sea ; and it becomes 

 a better and better approximation when we take these means for a 

 more and more lengthened period. In certain cases this method is apt 

 to fail us. For it may happen, for instance, that at certain places 

 the tide stands for a comparatively long period in the neighbourhood 

 of high water, and makes a more abrupt lise and fall when near the 

 ebb ; where, in other words, the tide-gauge records an unsymmetrical 

 wave. In such a case as this the mid-height between high and low 

 water is obviously not the mean level of the sea, and this mean level 

 must be determined by integrating, or determining the area of, the 

 recorded curve. In ordinary cases, however, and wherever, as is the 

 case on the East Coast of Scotland, the record of the tide-gauge gives 

 us a fairly simple and regular wave, the " mean-tide-level " or the 

 mean height between high water and low water, is a fair approxima- 

 tion to the mean level of the sea. 



But it is well known that if this mean level be determined month 

 by month, and year by year, the values so determined will show 

 marked and even large fluctuations. The mean for one year is not 

 identical with that for the next, and, within a single year, the mean 

 monthly values group themselves into a more or less regular, and 

 annually recurrent, periodic series. There exist, in short, certain 

 " tides of long period," the chief of which are the annual and semi- 

 annual tides ; and over and above these, there are fluctuations from 

 year to year, of which we know very little, and in which no regular 

 periodicity has yet been traced. 



The study of mean sea level and its fluctuations is interesting 

 from several points of view. Firstly, it is of practical importance to 

 determine what mean sea level is, inasmuch as it is, or is supposed 

 to be, the datum to which all heights are referred in our national 

 survey. As a matter of fact, this datura is an arbitrary one. The 

 actual mean sea level has never been determined with accm-acy ; 

 and it would seem, from the conditions of the case, that all we can do 

 is to approach slowly, during a long course of years, to an approximate 

 determination. 



Secondly, while the annual and semi-annual tides {Sa and Ssa) 

 are well known, and have been determined for a number of ports, 

 and are taken careful account of in tide-prediction, their origin and 

 nature are still very little understood. They are known to be of 

 greater magnitude than can be accounted for by astronomical condi- 

 tions : they are described as " meteorological " tides, and are generally 



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