326 



BEroRT — 1882. 



Tables, we see tliat in the case of the synodic fortnightly the results 

 of undue influence are very serious, and improper purification of daily 

 means will have rendered the results utterly worthless. The value of 

 the monthly elliptic tide may be very perceptibly affected by the M, IS", O 

 tides, but the values of the fortnightly, semiannual, and annual tides will 

 not have been very considerably altered. M, N, O are, however, only 

 three of the tides exercising influence, and it will be shown below that 

 the monthly elliptic tide may be further affected. 



The other tides, whose effects it is well to consider, are those in which 

 aC'' =b ^) is a multiple of 180", for, as shown above, in these cases the 

 method of procedure by diurnal means leads to a cumulative influence. 



Referring back to Table I. we see that the following are the cases 

 of this peculiar influence : (1) the semidiurnal X tide on the elliptic 

 monthly ; (2) the semidiurnal M tide on the synodic fortnightly (already 

 considered) ; (3) the semidiurnal K tide on the semiannual ; (4) the 

 diurnal K and P tides, and the semidiurnal R and T tides on the annual 

 tide. 



A rough approximation will suffice in these cases, and this may be 

 made by only paying attention to that one of the two terms representing 

 undue influence, in which there occurs the indeterminate expression %. 

 It has already been shown that % is here equal to 365. Then remember- 

 ing that the 183 in the denominator of the expression for undue influence 

 is itself approximate, and may be treated as a half of 365, we see that 

 the required expression is simply 



^^ R sin 12n cot ^n. 



The numerical values of n, the speed in degrees per m.s. hour, for the 

 X, K, K, R, T tides will be found in the Report for 1876. 



From these we may compute J^^ sin 12n cot ^i. Then, as a numerical 

 example we may take tlie corresponding- semi-ranges B for the X, K, K, R, T 

 tides for Liverpool in the years 1857-8 and 1860-70, and assuming that 

 the phases in those years were such as to make the influence a maxi- 

 mum, we may compute the maximum influence. The results of these 

 calculations are embodied in the following Table VI. 



Table VI. 



