Oil Mean Sea Level and Us Flueluationa. 3n 



of about 4o years, and a total ainplitu(l(> of about ()()8 ft., or '24 cm. ; 

 but even this is far from clear. 



Among other methocls, J have used one iiiveji l)y Pi'ofessor H. H. 

 1'urner.* By this method we may easil}^ carry the Fourier analysis 

 through a long series of numbers, for instance, our series of monthly 

 values of Mean Sea Level ; and in doing so, we may obtain, for each 

 consecutive, and overlapping, series of twelve months, the mean (Ao) 

 the amplitude (Aj), and the phase (s), of the annual fluctuation. 

 Now, if there happens to be a single well-marked ])eriodicity, and this 

 corresponds with the period selected (in this case twelve months), 

 then the values of A^ and g will remain nearly constant. If theie be 

 a single well-marked periodicity, but of a period greater or less than 

 12 months, then the values will increase or decrease steadily. 

 And lastly, if there be more than one periodicity, but all the periodi- 

 cities are of a permanent character, then there will be " interferences " 

 which will cause the values to follow a wavy, but more or less 

 I'egular, line. Now the last of these is very clearly what happens in 

 our case (Figs. 16, 17). All three values — mean, amplitude, and 

 phase — fluctuate in a recuiiing seiies of waves ; for two or three 

 consecutive waves we may seem to see an equality of period, but this 

 apparent equality disappears, giving place to waves of gradually 

 changing amplitude and period. This is a sme sign of the presence 

 of complicated interference phenomena. 



Now, whatever be the causes of our phenomenon, we may be quite 

 sure that, in the aggregate, they are very complex. Meteorological 

 influences, possibly rainfall and more certainly barometric gradient, 

 undoubtedly enter in ; changes in the great ocean currents (whatever 

 these changes may in tui'n be due to) in all probability play their part ; 

 the minute oscillations of the earth's axis produce a noticeable and 

 measurable effect ; and even the long-period astronomical tides, small 

 as is the magnitude of their influence^ must not be wholly left out of 

 account. But besides all these we must bear in mind two other 

 important conditions : (1) the existence of interference phenomena, 

 or " beats," resulting from the interference of ordinary well-known 

 tides of moderate period ; and (2) the possibility, or rather probability, 

 that a part of the apparent phenomenon is spurious, and due to our 

 selection of a certain artificial period (calendar month and calendar 

 year) for the determination of our means. It is obvious that in the 

 simplest harmonic series we should get an apparent slow change of 

 mean if we took our data from portions only of the wave ; and it is 

 equally obvious that in the complex tidal effect no single period that 

 we may choose for the determination of oiu* average values will keep 

 us clear of this more or less fallacious result. 



In short, what with the actual and little understood causes which 

 perturb the mean level of the sea, and what on the other hand witli 

 the difficulties which attend its determination even though nothing 

 more than the complex tidal wave were present to disturb it, it is 

 quite plain that the determination of !\Iean Sea Level is an extremely 

 difficult thing, and one which cannot by any possible means be achieved 

 in any brief period of time. I do not see how it is ever to be deter- 



* " On a simple method of detecting discontinuities in a .series of recorded 

 observations, with an application to Sunspots." Papers of the I.U.S.R. Com- 

 puting Bureau, No. XIII. IdUi. (Monthly Notices of the R.A.S., Dec. 11)13). 



