ON THE METHOD OF DEDUCING NDMERICAL VALUES OF TIDES. 325 



Therefore supposing the phases in those years to have been snch as 

 to make the result a maximum, the following would have been the erroi's 

 in the height of mean water : — 



From tide M 

 From tide N 

 From tide O 



Table III. 



1857-8 

 Feet 

 . 0-00379 

 . 0-00035 

 . 0-00037 



Total 



000451 



1869-70 



Feet 

 000398 

 000036 

 0-00027 



0-00461 



We thus see that the effect of working with unpurified diurnal means 

 would be small, although sensible. 



I next go on to compute the value of the coefficient 



1 S 3 » 4 S 



sin 12 n r sin 182^ (r + \) 

 tan i 71 I 



sin ^ (r + \)" 



sin 182^ (r - X) 



sin ^ (f — X) 



r-X)/ 



for the combinations of the M, N, tides with the five long tides. In 

 computing the factor arising from the influence of the M tide on the lunar 

 synodic fortnightly, we must remember that sin 182^ (»' + X) / sin ^ (v + A), 

 which becomes %, is equal to 365. 



Table IV. 



At the intersection of any column and row is found the factor corre- 

 sponding to the maximum undue influence of the short tide on the long. 

 For example, the efiect of the M tide (2-y — 2<t) on the synodic fort- 

 nightly tide (2(t — 2r]) may be as great as '034175 of the semi-range E of 

 the M tide. 



Applying these factors to the cases of Liverpool, as quoted above, in 

 1857-8 and 1869-70 ; that is to say, multiplying the M row by 9-6745 and 

 10-1443, the N row by 1-86U8 and 1-8917, and the O row by -4410 and 

 •3314, we get the following superior limits, expressed in feet, to the undue 

 influence on the semi-range Jv of the several long-period tides : — 



Table V. 



Having regard to the values of the long tides, as given in the results 

 of the harmonic analysis of the tides in the Reports and the Indian Tide 



