On Mean Sea Level and its Fluctuations. 



and September, while the depaiturc from tlie mean has a maximum 

 in November or December, and a neoative maximum in May, in favour 

 of Dundee. In the case of Mean Hiyh Watei', the differences are of 

 less ma.uiiitude, and they aj^proximate to a double, oi- semi-annual 

 sine cm've, with positive maxima a])out May and November, and 

 neuative maxima about Febiuaiy aiul Auuiist. 



The harmonic analyses of our data elucidate these r(m<ih pre- 

 liminary results : — 



Table B. — Harmonic Formida? foi- the Mean Annual Variation in 

 Mean Sea Level, Mean Hij-h Water, and Mean Low Water, at 

 Dundee and Aberdeen {Efoch : mid-January). 



.A[. S. L. 



M H. W. 

 M. L. W. 



f Dundeo A + -31) cos (t +50") + -OG cos (2t +51°) 



\ Aberdeen A +-28 cos (t+58°) + -07 cos (21+41°) 



f Dundee A + -2() cos (t+()l°)+-05 cos (2t+53°) 



\ Aberdeen A+ -25 cos (t+r)8°) + -05 cos (2t + 78°) 



( Dundee A + ^G cos (t+4.'5°)+ -Ki cos (2t+48°) 



(^ Aberdeen A + -32 cos (t +4(5°) + -14 cos (2t +.54°) 



We see at once from these formulae that there is an important 

 difference between the two stations in the amplitudes of the annual 

 wave in the case of Mean Sea Level and Mean Low Water, and, on 

 the other hand, a considerable difference in the phase of the semi- 

 annual wave in the case of Mean High Water. But as regards this 

 last, it must be remembered that, owing to the very small amplitude 

 of the semi-annual wave, we cannot expect, with the means at our 

 disposal, to have determined its phase with very gTeat accuracy. 



In individual years, the characters of these waves are maintained 

 with very considerable constancy. In the case of Mean Sea Level, 

 I have set forth in an epitomised Table (Table C) the average dis- 

 crepancies between the individual monthly means and the corre- 

 sponding aggregate monthly means for the entire period. 



Table C— Mean Sea Level at Dundee (1897-1912) and Aberdeen 

 (1862-1913). Mean of the Discrepancies (in feet, irrespective 

 of sign), in individual months, from the Monthly Means for the 

 entire period. 



In spite of the fact that, as will be presently shown, the mean level 

 varies as a whole from year to year, and that no correction has been 

 applied here for this variation, yet the aforesaid discrepancies never 

 in Dundee, and only four times in the whole period of 624 months at 

 Aberdeen, exceed -5 ft. One quarter of them lie between and -04 

 ft. at Dundee, and between and -06 ft. at Aberdeen ; 75 per cent, 

 lie between and -19 ft. at Dundee between and -22 ft. at Aberdeen/ 

 h 



