110 REPORT—1 883. 
conjectural curve. If the gap is somewhat longer, several plans may be 
suggested, and judgment must be used as to which of them is to be 
adopted. 
If there is another station of observation in the neighbourhood, the 
values of 6h for that station may be inserted. 
The values of 6h for another part of the year, in which the moon’s 
and sun’s declinations are as nearly as may be the same as they were 
during the gap, may be used. 
It may be, however, that the hiatus is of considerable length, so that 
the preceding methods are inapplicable: as when in 1882 the tidal record 
for Vizagapatam is wanting for 67 days. The following method of treat- 
ment will then be applicable :-— 
We find approximate values of the tidal constituents of long period, 
and fill in the hiatus, so as to complete the 365 values, with the com- 
puted height of the tide during the hiatus. 
To find these approximate values we form  éh cos lt and Yéhsin lt 
for the days of observation ; next, in the ten final equations of Schedule 
P we neglect all the terms with small coefficients, and in the terms whose 
coefficients are approximately 182°5, we substitute a coefficient equal to 
182-5 diminished by half the number of days of hiatus. For example, 
for Vizagapatam in 1882 we have 1825—}x67=149, and, eg., 
XCéh cos (c—az) t = 149 A approximately. After the approximate values 
of A, B, C, D, &., have been found, it is easy to find the approximate 
height of tide for the days of the hiatus. This plan will also apply where 
the hiatus is of short duration. 
It may be pursued whether or not we are working with cleared 
daily means; for if the daily means are uncleared, as will hence- 
forth be the case, we import with tne numbers by which the hiatus is 
filled exactly those fictitious tides of long period which are cleared away 
by the use of the “clearance coefficients,” in preparing the ten final 
equations for solution. 
Other methods of treating a stoppage of the record may be devised. 
If the stoppage be near the beginning of the year, or near the end, we 
may neglect the observations before or after the gap, and compute afresh 
the 100 coefficients of Schedule P, and the clearance coefficients of 
Schedule Q for the number of days remaining. If the gap is in the 
middle we might compute the values of the coefficients of Schedules P 
and Q as though the days of hiatus were days of observation, bearing 
in mind that the formule are to be altered by the consideration that time 
is to be measured from the initial 11" 30™ of the year, instead of from 
the initial 11> 30™ of the days of hiatus. 
The so computed coefficients are then to be subtracted from the 
values given in Schedules P and Q, and the amended final eqnations and 
amended clearance coefficients to be used. 
It must remain a matter of judgment as to which of these various 
methods is to be adopted in each case. 
§ 11. Method of Equivalent Multipliers for the Harmonic Analysis for the 
Tides of Long Period. 
Up to the present time the harmonic analysis for these tides has been 
conducted on a plan which seems to involve a great deal of unnecessary 
labour. If 7 be the speed of any one of the five tides for which the 
