n8 A TEXTBOOK OF OCEANOGRAPHY 



periods, arising from the different relative positions and 

 varying distances from the earth of the disturbing bodies, the 

 sun and moon, and of the variation of certain elements of their 

 orbits. Of these waves, each of which has a typical analytical 

 expression, the twenty-three following are the most important : 



Two : The lunar monthly and solar annual 

 (elliptic). 



Two : The lunar fortnightly and solar semi-annual 

 (declinational). 



Four : The lunar and solar diurnal (declinational). 



Two : The lunar and solar semi-diurnal. 



Seven : The lunar and solar elliptic diurnal. 



Four : The lunar and solar elliptic semi-diurnal. 



Two : The lunar and solar declinational semi- 

 diurnal. 



The numerous calculations necessary in the harmonic 

 analysis can be performed by a machine the tidal predictor 

 invented by Lord Kelvin. This machine mechanically deline- 

 ates the tidal curves from day to day, and, indeed, from instant 

 to instant. There are four of these instruments in existence, 

 belonging to the Governments of Great Britain, France, India, 

 and the United States. 



According to Airy, the equilibrium theory of tides of 

 Newton is one of the most contemptible theories that was ever 

 applied to explain a collection of important physical facts. It 

 is entirely false in its principles, and entirely inapplicable in 

 its results. It has, however, been of historical utility, since it 

 has served to show that there are forces in Nature following 

 laws which bear a not very distant relation to some of the most 

 conspicuous phenomena of the tides. It has given an algebraic 

 form to its results which coincides with those of more accurate 

 theories. The greatest mathematicians and the most laborious 

 observers have agreed equally in rejecting the foundation of 

 this theory and comparing all their observations with its 

 results. 



The theory of Laplace assumes the earth to be covered with 



