﻿H sin K for each month and have taken the mean of each as giving the mean values of H cos k and H sin k. 

 It is easy to compute from these the proper mean vahies of H and k for each tide. The results are given 

 in the following table : — 



Mean Values of Tidal Constants. 



The sum of the semi-ranges of the three diurnal tides is 21 • 6 inches and of the three semidiurnal tides 

 is only 3'4 inches. This result corresponds with the fact that little trace of the semidiurnal tide is to be 

 discovered from mere inspection of the tide curve. 



When tidal observations have been reduced it is always important to verify that the constants found do 

 really represent the tidal oscillation, for, in computations of such complexity, it is always possible that 

 some gross mistake of principle may have slipped in unnoticed. Such a verification is especially important 

 in a case where the tides are found to be very abnormal, as here, and where the results from month to 

 month are not closely consistent. I accordingly asked Mr. Glazebrook to run off curves for two periods 

 with the Indian tide-predicter at the National Physical Laboratory. The constants used were the means 

 for the tides evaluated. It is jirobable that a better result might be attained if a number of other tides, 

 with constants assigned by theoretical considerations from analogy with the constants actually evaluated, 

 had also been introduced, but I did not think it was worth while to do so. Evidence will be given 

 hereafter to show that the smaller elliptic diurnal tides must exercise an apprecialile influence. 



The periods chosen for the compariison were about three weeks, beginning on May 12, 1902, and nearly 

 the same time in November. It does not seem worth while to reproduce the whole of the observed and 

 computed curves for these periods. The observed tide curve has frequently sharp irregularities, presumably 

 produced by weather or by unperceived shifts of the ship, and the maxima are sometimes sharp peaks 

 instead of flowing curves. However, on the whole, the computed and observed curves follow one another 

 very well, at least throughout all those portions where the diurnal tide is pronounced. Where the diurnal 

 inequality is nearly evanescent, and the semidiurnal tide becomes perceptible, the discordance is sometimes 

 considerable, although, even in these cases, every rise and fall of the water is traceable in the computed 

 curve. Such discordance was inevitable, for at this part of the curve all those tidal oscillations which 

 have any importance have disappeared, and only those tides remain which are very small ; moreover, most 

 of these tides are avowedly omitted from the computed curve. 



I give two figures. The first shows the two curves where the diurnal tide is large, viz., from 0'' to 24'^ 

 November 18; it is a rather favourable example of the general agreement referred to above. The second 

 figure, from 12'' May 29 to 12'' May 30, is selected because it exhibits by far the worst discordance which 

 occurred in the six weeks under comparison. 



I conclude that the reductions are quite as good as could be expected from tide-curves which present as 

 much irregularity as these do. It would not be possible to make a very good tide-table from the 

 constants, but no one wants a tide-table for Eoss Island. We only need sufficient accuracy to obtain an 

 insight into the nature of the Antarctic tides, and the constants are quite sufficient for that end. 



When the mean heights of water at the 24 hours of mean lunar time were plotted in curves for each 

 month, it became obvious that a pure semidiurnal inequality did not represent the facts very closely, and 

 that there remained also a sensible diurnal inequality. Such an inequality is given by the tide Mi, and if 

 we neglect the minute portion of the tide Mi, which depends on the terms in the tide-generating potential, 

 which vary as the fourth power of the moon's parallax, such an inequality is found to depend on the 



