98 REPORT—1883. 
We may here remark that there does not seem to be any advantage in 
the choice of 369° 5" as the period, excepting in the analysis for the 
M-series and S-series. At the same time there is no harm in that choice, 
and therefore the computation forras may be used as they exist. The 
choice of a special period for the diurnal tides J and Q also appears to be 
useless, and therefore they may be safely used for the period of 370% 5® 
based on erroneous arithmetic. It may perhaps be worth while to cut off 
the last entry in the Land N forms, and thus bring the pericd to its 
correct value. 
Let us now return to our general notation, and consider the 24 mean 
values, each pertaining to the 24 T-hours. We suppose that all the tides 
excepting the 7'-tide are adequately eliminated, and, in fact, a computation 
of the necessary corrections for the absence of complete elimination, which 
is given in the Tidal Report of 1872, shows that this is the case. 
It is obvious that any one of the 24 values does not give the true 
height of the T-tide at that T-hour, but gives the average height of the 
water, as due to the T-tide, estimated over half a T-hour before and half 
a T-hour after that hour. We must now consider the correction necessary 
on this account. 
Suppose we have a function 
h=A, cos 0+B, sin 64+ A, cos 20+B, sin204+ .. 
+A,cos79+B,sin76+ .... 
Then we see by integration that the function 
h'=A,' cos 04+B,’ sin 0+ A,’ cos 294+ B,' sin 29+ ... 
+A,’ cos r#+B,’ sin r9+ ...., 
where 
A,’_B‘_ smn, A,’ By’ sin 420 | A, UB, sutra 
= = ee Sa 5 ee 
Aj, Bb, ze Ay by 22 A, B, tra 
is derivable from h by substituting for the h, corresponding to any value 
of 0, the mean value of h estimated over the interval from 6+ 44 to 
6—ta. 
Thus when harmonic analysis is applied to the 24 T-hourly values, 
the coefficients which express that oscillation which goes through its 
period v times in the 24 T-hours must be augmented by the factor 
sra/sin ra. Thus we get the following expressions for the augmenting 
factors for the diurnal, semi-diurnal, ter-diurna! oscillations, &c., viz. :— 
Le, Laie Saige pe et 
om /sin 7° 80! ; 29% /sin 15°; LO" /sin 22° 30', &e. . (63) 
Computing from these we find the following augmenting factors. 
[M.] 
Augmenting Factors. 
For A,, B, , : . 1:00286 
Ay, By : . . 101152 
As, Bg 2 4 . 1:02617 
Ay, By é ; . 1:04720 
A,, Bs t : Ped Ore 
ewes Sg RY, 21-29990 
