

1892.] facilitating the Reduction of Tidal Observations. 373 



It is easy to see that the influence of a disturbing tide is evanescent 

 when the means are taken over a period such that the excess of the 

 argument of the disturbed over that of the disturbing tide has in- 

 creased through a multiple of 360. As, however, we are working 

 with integral numbers of days, and as the speeds of tides are incom- 

 mensurable, this condition cannot be exactly satisfied. 



From this consideration it appears that to minimise the perturbation 

 of So, 2SM, p, by M 2 (and vice versa} we must stop at an exact multiple 

 of a semi-lunation. To minimise the effect of M 2 on "N and L, and of 

 KI on J and Q, we must stop at an exact multiple of a lunar anom- 

 alistic period. To minimise the effect of M 2 on v, we must stop at a 

 multiple of the period 27r/(a + T!r2r)). To minimise the effect of 

 KI on 0, we must stop at an exact multiple of a semi-lunar period. 



For the quater- diurnal tide, MS, it is immaterial where we stop, 

 and so it may as well be taken at a multiple of a semi-lunation. 



The following table (p. 374) gives the rules derived from these 

 considerations. 



8. On the tides of long period. 



The annual (Sa) and semi-annual (Ssa) tides are evaluated in the 

 course of the work by which other important tides are found. These 

 are the only two tides of long period which have a practical import- 

 ance in respect to tidal prediction, but the luni-solar fortnightly 

 (MSf), the lunar fortnightly (Mf), and the lunar monthly (Mm) tides 

 have a theoretical interest. 



It will therefore be well to show how they may be found. The 

 process is short, and, although it is less accurate than the laborious 

 plan followed in the Indian reductions, it appears to give fairly good 

 results. 



For the sake of simplicity, let us consider the tide MSf. Its 

 period is about 14 days, and therefore a day does not differ very 

 largely from a twelfth part of the period. Accordingly, if about 

 two days in a fortnight are rejected by proper rales, the mean heights 

 of water on the remaining days may be taken as representatives 'of 

 twelve equidistant values of water height. 



I therefore go through the whole year and reject, according to 

 proper rules, the daily sums of the 24 hourly heights corresponding 

 to certain 69 of the days out of 369. The remaining 300 values are 

 written consecutively into a schedule of 12 columns and 25 rows, of 

 which each corresponds to a half lunation. The 12 columns are 

 summed, and the sums are harmonically analysed for the first pair of 

 harmonic components. These components have to be divided by 24 

 times 25, or by 600, because the daily mean water height is ^ h of 

 the daily sum, and there are 25 semi-lunations. 



In the same way the semi-lunar period is about 13 J days, and if 



VOL. LIT. 2 c 



