42 REPORT — 1886. . 



by which, we find how many rows to take to minimise the efiect of the 

 S2 tide on the Mj tide is there shown to be 



l°-01589582=14°-4920521r. 



If r=l, 2=14-26 ; and if r=2, q=28-5. 



From a reason similar to that given in 1885 we conclude that, in 

 analysing about a fortnight of observation we must have 14 rows of 

 values on the M sheet, and for a month's observation 29 rows of values. 



Similarly, to minimise the efiect of the Mj tide on the S2 tide the 

 equation is 



l°-01589582=15°r. 



If r=l, 2=14-76; and if r=2, 2=29-5. 



Whence we must have 15 , rows of values on the S sheet for a fort- 

 night's observation, and 30 rows of values for a month's observation. 



These two rules are simply a statement that on the M and S sheets we 

 are to take a period equal to the interval from spring-tide to spring-tide, 

 or twice that period. 



Similarly, to minimise the effect of the K, tide on the tide, the 

 equation is 



l°-09803302=13°-9430356r. 



Ifr=l, 2=12-69; andifr=2, 2=25-38. 



Whence we mast have 13 rows of values on the O sheet for a fort- 

 night's observation, and 25 rows for a month's observation. 



Lastly, to miniinise the effect of the O tide on the Kj tide, the equa- 

 tion is 



l°-09803302=15°-0410686r. 



If r=l, 2=13-70 ; and if r=2, 2=26-4. 



Hence, in using the numbers on the S sheet for determining the 

 diurnal tides, we must use 14 rows of values for a fortnight's observation, 

 and 26 rows for a month's observation. 



Thus, on the S sheet we use more rows for the semidiurnal tides than 

 for the diurnal — namely, one more for a fortnight and three more for a 

 month. 



The rules for drawing up the computation forms then specify, in 

 accordance with the above results, where the entries are to stop on the 

 three sheets, and give directions for the dual use of the S sheet, according 

 as it is for finding semidiurnal or diurnal tides. 



When the entries have been made, the twenty-four columns on each 

 sheet are summed, and each is divided by the number of entries in the 

 column. On the S sheet there are two sets of sums and divisions, one 

 with and the other without the additional row or rows. 



The three sheets thus provide us with four sets of twenty-four mean 

 hourly values ; the M sheet corresponds with mean lunar time, the hour 

 being 15 -=-14-49 of a mean solar hour ; both the means on the S sheet corre- 

 spond with mean solar time ; and the O sheet corresponds with a special 

 time, in which the hour is 15-=-13-94 of a mean solar hour. 



The four sets of means are then submitted to harmonic analysis : the 

 semidiurnal components are only evaluated on the M sheet ; the diurnal 

 components are evaluated from the shorter series on S, and the semi- 

 diurnal from the longer series ; and the diurnal components from the O 

 sheet. We may also evaluate the quaterdiurnal components from the 

 M and S sheets. 



