102 REPORT— 1883. 
The A’s aud B’s having been thus deduced, we have R=/ (A?+B?). 
R must then be multiplied by the augmenting factors which we have 
already evaluated (Schedule [M]). We thus have the augmented R. 
Next the angle whose tangent is B/A gives ¢. The addition to ¢ of the 
appropriate V’,+z (see Schedule [I]) gives «x, and the multiplication of 
R by the appropriate 1/f (see Schedule [I]) gives H. The reduction is 
then complete. 
The following is a sample of the form used. 
[O.] 
Form for Evaluation of ¢, R, «, H. 
A form similar to [O] serves for the same purpose in the treatment 
of the tides of long period, to the consideration of which we now pass; 
it will be seen, however, that for these tides there is no augmenting 
factor, and that the increase of » for 114 hours has to be added to &. 
§ 10. On the Harmonic Analysis for the Tides of Long Period. 
For the purpose of determining these tides we have to eliminate the 
oscillations of water-level arising from the tides of short period. As the 
quickest of these tides has a period of many days, the height of mean 
water at one instant for each day gives sufficient data. Thus there will 
in a year’s observations be 365 heights to be submitted to harmonic 
analysis. In leap-years the last day’s observation must be dropped, 
because the treatment is adapted for analysing 365 values. 
- To find the daily mean for any day it has hitherto been usual to take 
the arithmetic mean of 24 consecutive hourly values, beginning with the 
height at noon. This height will then apply to the middle instant of 
the period from 0" to 23": that is to say, to 11" 30™ at night. We 
shall propose some new modes of treating the observations, and in the 
first of them it will probably be more convenient that the mean for the 
day should apply to midnight instead of to 115 30™, For finding a 
mean applicable to midnight we take the 25 consecutive heights for 0" to 
24h, and add the half of the first value to the 23 intermediate and to the 
half of the last and divide by 24. It would probably be sufficiently 
