324 



heport -1882. 



the schedule with an asterisk, and with the initial letter by which the 

 tide is denoted in the Tidal Reports. 



Table I. 



The fortnightly tide is free from the cumulative influence arising from 

 the method of diurnal means. But as Ave shall see below, the elliptic 

 monthly tide is sen.sibly altered by this cause. 



The synodic fortnightly is aflected in this way by the principal lunar 

 semidiurnal tide, and the semiannual by a much less important semi- 

 diurral tide. The annual tide may apparently be much influenced, since 

 all four speeds actually exist as sensible tides, but the numerical compu- 

 tation made below seems to show that the resulting influence is not 

 large. 



In the Report of 1872 it is stated that the only tides which are found 

 practically to have a sensible eflfect, so that the diurnal means have to be 

 purifled from their efi:'ects, are the semidiui-nal M or 2-y — 2o-, the semi- 

 diurnal N or 2y — 3(7 + -ra-, and the diurnal O or y — 2o-. I have there- 

 fore computed the following tables, giving superior limits to the undue 

 influence on the height of mean water for the year, and on the height of 

 the five long-period tides. In the case of the synodic fortnightly tide, 

 the cumulative influence arises which has just been discussed. 



The numerical values of the speeds are taken from the Tidal Reports, 

 and substituted in the forraulte given above. 



First, for the eSect on mean watermark, the superior limit is 

 B^^^ . sin 182.' cot i«. 



The following are the computed values of this coefficient of E :- 



Table II. 



From tide Jt 

 From tide N 

 From tide O 



■O0O.S92 

 -000188 

 -000834 



The following is a numerical example illustrative of the practical 

 result. At Liverpool in 1857-8, the values of R for the M, N, O tides 

 were respectively 9-6745, 1-8608, 0-4410 in British feet ; and for 1869-70 

 they were V)-l-i4S, 1897, 0-3314. 



