52 REPORTS ON THE STATE OF SCIENCE. 



first attempt it was arranged to derive the several tides in the manner 

 described by Professor Sir G. H. Darwin. Clearly, if the main tides 

 could not be recognised, it was hopeless to look for more recondite 

 effects. There is a slight want of definiteness in the edge of the photo- 

 graph ; but this defect has been to some extent removed, it is hoped, 

 by measuring both sides and using the mean. The curve was read off 

 to a tenth of a millimetre, and that unit has been used throughout. 



The results of the harmonic analysis are given in the following table. 

 About these Sir George Darwin writes as follows : ' Since the oscilla- 

 tions of the pendulum are due to the weight of sea-water, it seems best" 

 to compare them with the tidal constants, as derived from ten years of 

 observation at Hilbre Island. 1 This place being near the mouth of 

 the Dee, seems to afford a better means of comparison than does Liver- 

 pool. The constants for Liverpool, however, differ but slightly from 

 those at Hilbre Island. It is further desirable to compare the results 

 with those derived from the equilibrium theory of tides for a place 

 in lat. 53° 24', approximately that of Bidston. I gave in Table E 

 of the Eeport on Tides to the British Association for 1883 (' Scientific 

 Papers,' vol. i., p. 25) a theoretical scale of importance of the several 

 tides expressed in terms of the principal lunar semidiurnal tide M 2 as 

 unity. But this table takes no account of the latitude of the place of 

 observation, merely giving the relative importance of the several " co- 

 efficients. ' What we require is to know what would be the deflections 

 of the pendulum at Bidston if it were erected on an absolutely unyield- 

 ing soil, and were only affected by the tide-generating forces due to 

 moon and sun. The values given in that table for the semidiurnal tides 

 may be quoted directly therefrom, and give the results in terms of M 3 

 as unity. But to reduce the diurnal tides to the same measure for this 

 latitude, we must multiply the tabular values by sin 2Xsec 2 A, where A 

 is latitude. In this way we obtain a scale of relative importance for the 

 lunisolar tide-generating force at Bidston. 



Lunar semidiurnal M 2 

 Solar semidiurnal S 2 

 Lunisolar semidiurnal K 2 

 Lunisolar diurnal Kj 

 Solar diurnal P 

 Lunar diurnal 



to mm. 

 1752 

 318° 



745 



327° 



203 



327° 



3= 564 



\k = 346° 



1-88 

 346° 



1-86 



237° 



{?: 



{?= 





Since the series cf observations only extended over a fortnight, it was 

 necessary to assume that the phase of Iv 2 was the same as that of S,, 

 and the amplitude about T s T ths. Similarly the phase of P is assumed 

 to be identical with that of K x , and the amplitude one-third. Hence in 



1 See Baird and Darwin, Proc. Boy. Soc- vol. xxxix. (1885), p. 196, col. 33. 



