THE TIDES 523 



theory of a westerly motion of the waters thus had its origin in the 

 assumed motion of the primum mobile. The flood tide was associated 

 with this westward motion by Scaliger and Bacon. Kepler also as- 

 serts that the flood has a westerly direction, although, as already stated, 

 he attributes the tides to the attraction of the moon. 



Descartes's vortex theory also gave a westward progression to the 

 tidal wave because he assumed that low water would always occur when 

 the moon crossed the local meridian. 



Newton, Bernoulli and Laplace evidently contemplated tide waves 

 progressing westward around the earth, completing the circuit in 24 

 lunar hours, or 24 hours and 50 minutes solar time, although they were 

 aware that the land masses must produce many irregularities in this 

 hypothetical motion. 



In order to see how any tide wave progresses, it is necessary to re- 

 duce to a common time. This is generally taken as Greenwich lunar 

 time. Consequently, if tides in a given locality are found to follow the 

 meridian passage of the moon by a certain interval (expressed in lunar 

 hours), this interval must be increased by the longitude, expressed in 

 hours, if the place be in west longitude and decreased if in east longi- 

 tude. Places having high water at the same tidal hour are said to lie 

 upon the same cotidal line. 



The first extensive charts of cotidal lines were constructed by Whe- 

 well about 75 years ago ; and these charts, or these charts slightly modi- 

 fied, have been in common use in atlases and astronomies ever since. 



The Impoetance of Stationary Waves suggested 



The analogy between the tides and the oscillatory motion of water 

 in a vase, or other vessel, had been noted by many even before the 

 moon's attraction had been universally recognized as the principal and 

 primary cause of the phenomenon. But in order that the water should 

 oscillate, it must first be disturbed from its position of equilibrium. 

 Galileo imagined that he had found this necessary disturbance in the 

 non-uniform motion of different parts of the earth as it rotates upon 

 its axis and revolves about the sun. 



Cesar d'Arcons (1667) supposes the solid earth to move a short 

 distance back and forth along its axis, thus causing the flood in the 

 northern hemisphere to appear to move from south to north and the 

 ebb in the reverse direction. According to his views the entire Atlantic 

 Ocean is a huge vessel of water, the surface rising and falling consider- 

 ably at the two ends (i. e., in high latitudes), but having little vertical 

 motion near the middle {i. e., in equatorial regions), where he logically 

 infers the horizontal motion to be great. 



John Bryanston (1683) supposes the moon to produce in the earth 

 a small east-and-west libration, not detected by astronomers, and this 



