HAEMONIC AISTALYSIS AND PREDICTION OF TIDES. 



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into 12 equal groups and the mean of the hourly heights for each 

 group taken, these means would represent the approximate height of 

 the combined annual and semiannual components for the middle of 

 each group, and the middle of the first group would be the initial 

 point from which the zeta (0 as obtained by the usual process would 

 be referred. As each group would represent 30° of motion for the 

 annual component, or 60° for the semiannual component, to refer 

 this r to the actual beginning of the series of observations it would 

 be necessary to apply a correction of 15° for the annual component 

 or 30° for the semiannual component. 



In obtaining the monthly means by the usual process of including 

 29 days only, the year is divided only approximately into 12 equal 

 groups. The following table shows the comparison of the middle of 

 each group actually used in the summation and the middle of each 

 corresponding group obtained by dividing a Julian year beginning 

 January 1, hour, into 12 equal parts. In the summing for mean 

 sea level each group extends from hour on the 1st day of the month 

 to the 23d hour on the 29th day, making the group from first to last 

 observation exactly 28 days and 23 hours long. The middle of each 

 group will therefore be 14.48 days later than the first observation of 

 the group. 



From the above table it is evident that in the summation for the 

 monthly means for a calendar year the middle of each group of a 

 common year is on an average 1.62° earlier than the middle of the 

 corresponding group when the Julian year is equally subdivided, 

 and the middle of each group of a leap year is on an average 0.80° 

 earlier. Subtracting these values from 15°, the interval between the 

 beginning of the observations and the middle of the first group of an 

 equal subdivision, we have 13.38° and 14.20°, for common and leap 

 years, respectively, as a correction to be applied to the f of Sa as 



