378 Prof. G. H. Darwin. On an Apparatus for [Dec. 15, 



The mean discrepancy in the case of the semi-diurnal tides is 

 0-0022 ft., and the greatest is +0-0068; in the case of the diurnal 

 tides the mean discrepancy is 0'0026 ft., and the greatest is 0'0089. 



In tidal work results derived from different years of observation 

 differ far more than do these two sets of results, and hence the ana- 

 lysis of 12 two-hourly values for diurnal and semi-diurnal tides gives 

 adequate results. 



I find that this abbreviation does not give satisfactory results for 

 quater-diurnal tides, and the sixth harmonic is not derivable from 12 

 values. Therefore, when these tides are to be evaluated the 24 

 hourly values must be used. 



It will still be necessary to write all the 24 hourly heights on each 

 computing strip, but when the strips are put into any one of the 

 arrangements, except where quater-diurnal tides are required, we 

 need only add up the columns 0, 2, 4, . . . . , 22, and may omit the 

 columns 1, 3, . . . . , 23. 



10. On a trial of the proposed method of reduction. 



As already mentioned, I have the tidal reductions for one year 

 (beginning April 19, 1880) for Port Blair, Andaman Islands. I am 

 thus able to make a comparison between the results of the old method 

 and of the new. The computation was, in large part, done for me by 

 Mr. Wright. 



It appeared sufficient to evaluate the tides of the S series and 

 those allied with them, the tides of the M series, and the tide Q ; also 

 the tides of long period MSf, Mf, Mm. 



The S series test the new process of harmonic analysis of monthly 

 harmonic components for annual and semi-annual inequalities. I 

 chose M because it is the most important tide, and Q because it puts 

 the proposed method of grouping to a severe test, and is very small in 

 amplitude. 



In the Q time scale the day is 26 h 52 m of mean solar time, from 

 which it follows that one of the 24 mean solar hourly observations 

 may fall as much as 2 h O m away from the exact Q hour to which it is 

 reputed to belong. Thus the hourly observations are arranged in 

 wide groups round the Q hours, and the hypothesis involved in the 

 method is put to a severe strain. 



Lastly, the results for tides of long period test my proposed 

 abridgment. 



It will be seen in the table on p. 379 that the two methods give 

 results in close agreement. There is, however, a sensible discrepancy 

 in the K 2 tide, but in this case I am inclined to accept the new value 

 as better than the old one. This tide is governed by sidereal time, 

 which differs but little from mean solar time. Hence, in the Indian 



