THE TIDES. (APP. B) 203 



proportionate contributions of the three causes to 

 the whole effect. 



7. According to Fourier's elementary principles 

 of harmonic analysis all deviations from regular 

 simple harmonic rise and fall of the tide within 

 twelve hours are to be represented by the super- 

 position of simple harmonic oscillations in six- 

 hours period, and four-hours period, and three-hours 

 period, and so on like the " overtones " which give 

 the peculiar characters to different musical sounds 

 of the same pitch. The six-hourly oscillation 

 which gives the double low-water at Portland and 

 the protracted duration of the high-water at Havre * 

 is probably in part due to the complex-harmonic 

 character of the current through the Straits of 

 Dover ; that is to say, definitely, to a six-hourly 

 periodic term in the Fourier-series representing the 

 quantity of water passing through the Straits 

 per unit of time, at any instant of the twelve 

 hours. 



8. The double high-water experienced at South- 

 ampton, and in the Solent, and at Christchurch 

 and Poole, and still further west, generally attributed 

 to the doubleness of the influence experienced 

 from the tidal streams on the two sides of the Isle 



1 At Havre, on the French coast, the high- water remains station- 

 ary for one hour, with a rise and fall of three or four inches for 

 another hour, and only rises and falls thirteen inches for the space of 

 three hours ; this long period of nearly slack water is very valuable to 

 the traffic of the port, and allows from fifteen to sixteen vessels to 

 enter or leave the docks on the same tide. 



