HARMONIC ANALYSIS OF TIDAL OBSERVATIONS. 103 
accurate if we took ,'; of the sum of the 25 consecutive values, if it is 
found that the division of every 24th hourly value into two halves mate- 
rially increases the labour of computing the daily means. The three 
plans for finding the daily mean are then 
ar(hoth, +... #+hy3) ct @) 
se(Shothy + «~~. +ho3+tho,) ee (il) - (64) 
sis(hothyt . ~~» +hozgthos) ... s+» (ll) | 
And they will be denoted as methods (i), (ii), (iii) respectively. It 
does not, however, seem very desirable to use the third method. Major 
Baird considers that the use of method (i) is most convenient for the 
computers. 
The formation of a daily mean does not obliterate the tidal oscillations 
of short period, because none of the tides, excepting those of the prin- 
cipal solar series, have commensurable periods in mean solar time. 
A correction, or ‘clearance of the daily mean,’ has therefore to be 
applied for all the important tides of short period, excepting for the solar 
tides. 
Let Reos (nt—Z) be the expression for one of the tides of short 
period as evaluated by the harmonic analysis for the same year, and let 
a be the value of nt— at any noon. Then the 25 consecutive hourly 
heights of water, beginning with that noon, are— 
R cos a, R cos (n+), Reos (2n+a)... 
R cos (23n+a), R cos (24n +a). 
In the method (i.) of taking the daily mean it is obvions that the 
‘clearance’ is 
sin 127 
1 
gzR 
cos (a+ 11}n) | 
sin 32 
In the method (ii) it is easily proved to be 
oa: sin 12n 
aS er 3 
cos (a+12n) at tet yarl as) ct oe ae 
and in method (iii) it is 
nN 22 
L Ron yn 
a ao: 
cos (a+12n) 
sin $n 
The clearance, as written here, is additive. 
It was found practically in the computation for these tides that only 
three tides of short period exercise an appreciable effect, so that clearances 
for them have to be applied. These tides are the M,, N, U tides. It was 
usual to compute these three clearances for every day in the year, and to 
correct the daily values accordingly.!_ But in following this plan a great 
‘ In 1882 a mistake was noticed in the Tidal Report for 1872 in the instructions 
for reducing the tides of long period. It was supposed both by Mr. Roberts and by 
Major Baird (then in England) that this mistake had been acted on. Accordingly a 
