Manual is considerably more laborious than the other, and it was highly desirable that the Abacus should 

 be used if it could be trusted for a short series of observations. I therefore asked Mr. WRIGHT, who 

 carried out the reductions and was familiar with the use of the Abacus, to reduce the first month in 

 duplicate by the two methods. Curves were drawn through ordinates representing the mean height of 

 water at the 24 hours of mean lunar time, as derived in the two ways. Although the whole range of 

 lie 24 mean lunar hours was only about six inches, the two curves showed a substantial 

 agreement. The same process was then applied with 0-time, when the range was found to be about 

 15 inches, and the agreement of the two curves was very close. The method of the Manual showed 

 several sharp peaks or irregularities in the curves which were nearly smoothed out by the use of the 

 Abacus. Such peaks would not affect the values of semi-diurnal or of diurnal components to a sensible 

 amount, and as they are clearly accidental I concluded that the use of the Abacus was quite satisfactory, 

 and accordingly that method was adopted throughout. 



In the use of harmonic analysis it is necessary that the month under discussion should differ a little in 

 length according to the tide which is being evaluated. For finding the M 2 -tide months of 30 days or of 

 29 days would be almost equally advantageous, but as 30 days gives us one more day of observation that 

 period was adopted. Similarly 30 days is appropriate for the Sj-tide. For a short period of observation 

 it is necessary to regard this tide as compounded of the 83 and K 2 -tides, and we must also suppose its 

 range to vary with the sun's parallax. The separation of these two tides from one another depends on 

 theoretical considerations, which appear to be well founded. 



Similarly, in a short series of observations the K! and P-tides must be treated as fused together in a 

 single tide, and they are separable by theoretical considerations only. For these two tides a month of 

 27 days is appropriate. Lastly the analysis for the 0-tide demands the use of a month of 28 days.* 



I determined, then, to separate the months in such a way that the shortest months (27 days) should 

 follow one another as closely as possible, while the longer months should overlap slightly. Whenever any 

 event occurred whereby it seemed likely that the observations might be vitiated, the months were chosen 

 so as to omit the time of possible or actual abnormality. 



It was clearly desirable that the largest possible number of independent or nearly independent months 

 should be discussed. This consideration led in one case to an overlap of as much as six days ; thus the 

 fifth month of 27 days ended on October 19, while the sixth month began on October 13. 



In the few cases where hourly observations were missing, the defects were made good by interpolation. 

 Although the observations- began in April, 1902, the first satisfactory continuous period began on May 12. 

 It will be well to state the epochs for the succession of twelve months which it was possible to obtain, and 

 to add a few comments on the observations. 



First month. This begins with O h May 12, 1902. The observations really begin at 2 h , but extrapolated 

 values were used for O h and l h . 



Second month. This begins with O h June 5, 1902. 



On the afternoon of July 5 the wire attached to the sinker parted and the observations ceased. The 

 apparatus was only reinstalled at 5 p.m. on July 23. 



Third month. This begins with O h July 24, 1902. 



Fourth month. This begins with O h August 23, 1902. 



Fifth month. This begins with O h September 23, 1902. The height for 6 h on October 20 was 

 interpolated. 



On October 1 it was found that the ship had shifted so as to affect the readings by one inch. The date 

 at which the shift had occurred was unknown, and, moreover, so small a change could not affect the results 

 sensibly. 



Sixth month. This begins with O h October 13, 1902. On November 9, the four hourly values, l h to 4 h 

 inclusive, were missing and were supplied by interpolation. 



As already remarked, this month considerably overlaps the one before it. This was necessary if a 



* This use of months of various lengths necessitates some small arithmetical changes in the method as explained in the 

 paper on the Apparatus referred to above. 



