302 Prof. G. H. Darwin. [June 19, 



at the middle of the month, and the 12 values for the year may be 

 submitted to the ordinary processes of harmonic analysis for the evalu- 

 . ation of these two >tidas. 



We have supposed in the previous investigation that the tide 

 heights are measured from mean sea-level, and although it is not 

 necessary that this condition should be rigorously satisfied, it might 

 be well, where there is a large annual tide, to refer the heights to 

 different datum levels in the different quarters .of the year. 



13. On Gaps in the Series of Observations. 



It often happens in actual observations that a few tides are missing 

 through some accident, or are obviously vitiated by heavy weather. 

 Now the present method depends for its applicability on the evanes- 

 cence of terms in the averages. It is true that it is rigorously ap- 

 plicable even for scattered ^observations, but if applied to such a case 

 all the F, G, f, g coefficients have to be calculated, and, as every tide 

 reacts on every other, the computation would be so extensive as to 

 make the method almost impracticable. Thus, where there is a gap, 

 observations must be fabricated (of course noting that they are 

 fabrications) by some sort of interpolation, and even values which are 

 very incorrect are better than none.* If the interpolation is ex- 

 itensive, it might be well to test its correctness in a few places when the 

 reduction is done. If a whole week or fortnight be missing, and if 

 the computer cannot find a plausible method of interpolation, I can 

 only suggest a preliminary reduction from the continuous parts, and 

 the computation of a tide table for the hiatus. Each such case must 

 be treated on its merits, and it is hardly possible to formulate general 

 rules. 



APPENDIX. 



Tables and Bides of General Applicability. 



A. To find $V m . 



The following table is for finding what would be the mean moon's 

 hour-angle, if the moon had been on the meridian at the epoch. 

 This angle is denoted by |V TO or (7 a)t, and is equal to the angle 

 through which the earth has turned relatively to the mean moon (at 

 14'4920521 per mean solar hour) since epoch. 



* Fabricated times and heights would very likely be no worse than real observa- 

 tions during a few days of rough weather. A perfect tide table only claims to pre- 

 dict the tide apart from the influence of wind and atmospheric pressure ; and, 

 conversely, tidal observations must be sufficiently numerous to eliminate these influ- 

 ences by averages. 



