ON THE HARMONIC ANALYSIS OF TIDAL OBSERVATIONS. 37 
For Mn, 
poses sin’ TF __}-0000—-1299 cos. N+ 0013 cos 2N. 
~(—$sin?w) (—$ sin? i) 
Even if all the terms in 2N were omitted, the approximations might be 
good enough for all practical purposes. 
TII. On tHe Periops cHOsEN FoR Harmonic ANALYSIS IN THE 
Comeutation Forms. 
Before proceeding to the subject of this section, it may be remarked 
that it is unfortunate that the days of the year in the computation forms 
should have been numbered from unity upwards, instead of from zero, as 
in the case of the hours. It would have been preferable that the first 
entry should have been numbered Day 0, Hour 0, instead of Day 1, 
Hour 0. This may be rectified with advantage if ever a new issue of the 
forms is required, but the existing notation is adhered to in this section. 
The computation form for each tide consists of pages for entry of the 
hourly tide-heights, in which the entries are grouped according to rules 
appropriate to that tide. The forms terminate with a broken number of 
hours. This, as we shall now show, is erroneous, although this error may 
not be of much practical importance. 
In §9 of the Report for 1883 the following passage occurs :— 
‘The elimination of the effects of the other tides may be improved by 
choosing the period for analysis not exactly equal to one year. For 
suppose that the expression for the height of water is 
A, cos n,¢+B, sin n,t+A, cos not +B, sinn gt. . . (61) 
‘where n, is nearly equal to m,, and that we wish to eliminate the 
Mo-tide, so as to be left only with the 1-tide. 
‘Now, this expression is equal to 
{A, +A, cos (n,;—n,)t—By sin (n,—72)t} cos sal (62) 
+ {B, +A, sin (7 —n,)t+B, cos (n, —N)t} sin nyt . 
‘That is to say, we may regard the tide as oscillating with a speed ,, 
but with slowly varying range.’ 
Although this is thus far correct, yet the subsequent justification of 
the plan according to which the computation forms have been compiled 
is wrong. 
In the column appertaining to any hour in the form we have nt a 
Pe of 15°, if m, be a diurnal, and of 30°, if n, be a semidiurnal 
tide. 
Consider the column headed ‘p-hours’; then n,;{=15° p for diurnals, 
and 30° p for semidiurnals. 
Hence (62), quoted above, shows us that, for diurnal tides, the sum of 
all the entries (of which suppose there are qg) in the column numbered 
p-hours, is 
