SECT. 5] LONG-TERM VARIATIONS IN SEA -LEVEL 603 



w = 19 the standard error of R will be 13 mm and that of ^ will be 75° (assuming 

 the theoretical value of R to be 10 mm). In order to reduce the standard error 

 of gr to the order of 20°, it is necessary to have the standard deviation of the sea- 

 level data reduced to 1 1 mm ; the standard error of R will then be about 4 mm. 



It was shown earlier that carefully maintained gauge records, accurately 

 reduced, could provide annual means to an accuracy of the order of 1 or 2 mm, 

 so that we may ignore the contributions from random observational errors and 

 slightly imperfect elimination of the shorter-period tides. To make further 

 progress we must either increase n by taking consecutive spans of 19 years, or 

 first eliminate, as far as possible, the term /{Bt, x) in equation (4). As n 

 appears within a square root sign in the expressions for the standard errors, ^ 

 the more effective of these two approaches is the latter ; it is certainly the more 

 instructive, and has been attempted for the stations listed, by determining the 

 coefficients Ur in equation (1). 



For the stations 10 and 11 in the North Sea the pressure data for the triangle 

 De Bilt-Stornoway-Bergen were used, and for stations 1 to 9 the triangle 

 Warsaw-Bergen-Haparanda was combined with them ; for Newlyn the 

 triangle De Bilt-Sciilies-Stornoway sufficed. Substituting the computed 

 values of ttr into equation (1) for each station enables /(^r, x) to be calculated, 

 and some examples of Z and the residuals Z —/{Bt, x) are given in Fig. 2. The 

 standard deviations of the residuals are shown in Table III, and these are 

 more nearly uniform over the region than were those for Z, being of the order 

 of 20 mm. The high correlation from station to station between the original 

 means is clearly shown, arguing regional meteorological influences modified, 

 at some stations (e.g. Esbjerg), by local conditions. 



An extension of the method to include the effects of Atlantic weather, by 

 using pressures at Reykjavik, Sable Island (Canada) and Lisbon, has produced 

 no detectable decrease in the residuals at any station. We must, therefore, look 

 to other causes for an explanation of these residuals. 



Table III contains the values of secular variation and nodal tide computed 

 in the same fashion as before, but this time using the residuals of sea-level. In 

 all cases the secular variations are appreciably altered, in some cases being 

 reversed in sign. The amplitudes of the nodal tide have been greatly reduced, 

 and are closer to the equilibrium values ; the phase lags, however, are still far 

 removed from zero degrees. The differences between the results obtained 

 before and after removing /{Bt, x) are, of course, direct results of the effect 

 of pressure distribution. The question remains as to whether these differences 

 arise from corresponding real effects in the pressures, or from random varia- 

 tions. So far as the writer is aware, there is little reason to expect a secular 

 variation in atmospheric pressure, and even less to suggest a measurable nodal 

 tide ; it seems more reasonable to suppose that the figures given at the foot of 

 Table III are contributions from random variations. 



The equilibrium form of the nodal tide is neither disproved nor confirmed by 



1 To reduce the values of standard deviations from a to ^a would require n to be 171 

 years. 



