104 



flow up Channel for three hours, till the particle gets to C, where for 

 an instant it has no horizontal motion backwards or forwards ; it is 

 then slack water. The particle then moves backwards towards D, 

 and its depth below the level surface, A C increases ; the tide is then 

 falling, and the tide current flowing down Channel. When the particle 

 gets to D, it is at its greatest depth, and low water occurs. The par- 

 ticle continues moving on to A ; the tide begins to rise, but the 

 current still flows down Channel for another three hours, till twelve 

 lunar hours after starting, the particle returns to A, and it is again 

 slack water. 



The positions of different particles, in their respective orbits, at 

 the same time will depend on their distances from the point where the 

 undulation commences ; thus, particles near this point will have 

 travelled further round than those which receive their motion later. 

 If, then, we draw a curve through the positions of the particles at the 

 same instant, we shall have the form of the wave at that instant. 



The interval of time by which high water at any place follows 

 the transit of the moon on* the day of full or new moons, is termed 

 the Establishment of the Port for that place. This interval is not the 

 same every day, but is subject to a semi-menstrual inequality ; it is 

 better, therefore, for scientific purposes to take not the interval on the 

 day of full or new moon, but the mean of all the intervals between 

 new and full moon ; this is termed by Whewell the Corrected Estab- 

 lishment of the Port. 



Another correction has also to be made, depending on what is 

 called the "age of the tide." The tide at London is determined by 

 the position of the sun and moon 2\ days before it occurs ; the time 

 of high water on the day of full moon takes place at two o'clock, but 

 two hours will not be the Establishment, for it must be calculated for 

 the position of the moon 2\ days before, and is thus found to be ih. 29m. 



The correct determination of the Establishment is of the greatest 

 importance both to navigation and science. By adding the corrected 

 Establishment to the time of the moon's transit, we get the time of 

 high water. This is reduced to Greenwich time, and we thus are able 

 to compare the time of high water in all parts of the world. 



If, therefore, vvc draw a curve through all places having high 

 water at the same instant, we shall have the form of the great tidal 



i 



