On Mean Sea Level and its Fluctuations. 7 



approximate, not to 55 in., but to 84/16 =5"25 in. And this is almost 

 precisely what wo actually find, both in the above random example and 

 in others which 1 have worked out. It would seem, in short, that 

 we should lose very little indeed were we to save ovu'selves the trouble 

 of adding up the odd inches in all these multitudinous observations ! 

 This, however, has not been done. 



I. The Annual and Semi-Annual Tides. 



In the annexed Tables (I.-III. pp. 37, 38) are shown the monthly 

 means for Dundee, of high water (II.), of low water (III.), and of mean 

 sea level (I.) as above defined, that is to say, the mid-height between 

 the two foregoing values ; and these results are further reduced to 

 annual means, and to the monthly means for the whole period of 

 sixteen years. In Tables IV.-VI. (pp. 39-41) the same data are given 

 for the still longer and more important records, covering no less than 

 fifty-two years, which I have received from Aberdeen. The phenomena 

 at the two ports are very similar, and the mean results are set forth 

 and compared in the following epitomised table : — 



Table A. — Departures from the Annual Mean of the Monthly Mean 

 Values of Mean Sea Level, Mean High Water, and Mean Low 

 Water, at Aberdeen (1862-1913) and Dundee (1867-1912), in 

 feet : — 



Mean Sea Level. 



Dundee . 

 Aberdeen . 

 Difference 



Dundee 

 A berdeen 

 Difference 



Dundee 

 Aberdeeu 

 Difference 



M. 8. L. 

 M. H. W. 

 M. L. W. 



Mean High Water. 



Mean Low Wate): 



The Differetices srnoollicd. 



•45 

 •36 

 •09 



•66 

 •50 

 •16 



•06 

 •01 

 •13 



We now see that, in each of our three factors, mean sea level, 

 mean high water, and mean low water, a definite annual wave is 

 apparent. In the case of Mean Sea Level (Fig. 1), this annual wave 

 has its minimum about the month of May, and its maximum in 

 December. The wave is similar but not identical, in phase and ampli- 

 tude, for high water and for low (Figs. 2, 3). 



