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amplitude of Mj is small ; it is also very small for the 6th month with phase 70°. The mean of all the 

 other phases is such that k is pretty small, and this agrees with what is to be expected, because k for the 

 tide is small. It thus appears probable that there has been a sensible disturbance from the Mj tide of 

 the values of the mean heights of water as arranged in mean lunar time. It should be noted that the 

 whole amplitude of oscillation is so small that it is really surprising that this eti'ect should be traceable 

 at all. 



There is one feature in the results which is so singular that it is well to refer to it. If we look at the 

 heights and phases of the Mo it will be observed that there is a progressive change both in amplitude and 

 phase as the season of 1902 advances, and this change is repeated in 1903. 



Mere inspection does not convince one of the degree of regularity, and I have, therefore, prepared a 

 figure which exhibits the march of H cos k and of H sin k. The values for each month may be taken to 

 appertain to the middle of the month, and the points surrounded by rings in fig. 6 give the values for the 

 season of 1902, while those marked with crosses give the values for 1903. The broken line shows 

 conjectural curves which appear to satisfy the observations. The conjectural curves are such that (in 

 inches) 



HcosK = 1-65 - 0-75 cos (i// + 2°), 



Hi 



= 0-23 + 0-53 cos (vi! + 79°), 



where >; is 360° per annum and t is expressed in months. 



There would thus be an annual inequality in II cos k and H sin k, and their mean values, viz., 1 •65 and 

 0'23 inches, would show that the mean lunar semidiurnal tide is expressed by H = 1| inches, k = 8°. 



The mean given previously as derived only from the observations was H = 2 inches, k = 10°. 



It will be noticed that the greatest retardation occurs about midsummer, and at the same season there is 

 a considerable decrease of amplitude. It is almost impossible to believe that the thawing of the sea could 

 decrease the amplitude of the tide, although it might possibly increase it. 



Dec I JanI 



Fig. 6. 



It would be strange if this result, depending as it does on 12 independent observations, should arise 

 from mere chance. Yet there is no astronomical tide which can give an annual inequality in the lunar 

 semidiurnal tide. I note that if the observations of 1903 were pushed backward one month the whole of 

 the observations would fall into a more perfect curve. Hence, an inequality of 13 months would satisfy 



