ON THE COASTS OF IRELAND. 3 



effects as shown by times, and apparent age of tide as shown by titnes ; from high 

 water and from low water. 



Section IX. — Formation of the time of diurnal high water ; progress of the diurnal 

 tide-wave round the island ; comparison of its progress and range with those of the 

 semidiurnal tide. 



Section X. — Method of expressing the height of the water, throughout every indi- 

 vidual tide, by sines and cosines of arcs ; and expressions in this form for every tide 

 in the whole series of observations, except those at Courtown. 



Section XI. — Discussion of the height of mean water deduced from the analysis of 

 individual tides ; with reference to difference of station, and to variations of the phase 

 of the moon, and of the declination of the moon. 



Section XII. — Discussion of range of tide, or coefficient of first arc in the analysis 

 of individual tides ; and of semimenstrual inequality in range, apparent proportion of 

 solar and lunar effects, and age of tide as deduced from range. 



Section XIII. — Establishment of each port, as deduced from the time of maximum 

 of the first periodical term in the analysis of individual tides. 



Section XIV. — Semimenstrual inequality in time, proportion of solar and lunar 

 effects from times, and apparent age of tide as shown by times ; deduced from the 

 time of maximum of the first periodical term. 



Section XV.— ^Comparison of the results as to mean height, range, semimenstrual 

 inequality in height, age of tide obtained from height, establishment, semimenstrual 

 inequality in time, and age of tide obtained from time, deduced from high and low 

 waters only, in Sections V., VI., VII., VIII., with those deduced from the analysis of 

 individual tides in Sections XL, XII., XIIL, XIV. 



Section XVI. — Remarks on the succeeding terms of the expressions for individual 

 tides, as related to the magnitude of the tide, to the position on the sea-coast, to the 

 position on the river, &c. ; comparison with the terms given by the theory of waves ; 

 discussion of the quarto-diurnal tide. 



Section XVII. — Separate discussion of the tidal observations at Courtown. 



Section XVIII. — Examination into the question of tertio-diurnal tide. 



Section I. — Account of the Stations, Levellings, Times, and Methods of Observation. 



The following are the stations of observation : — 



1. Kilbaha. — A small bay in the Shannon, on its north side, very near to the Loop 

 Head ; latitude 62° 34', longitude 9° 52' west of Greenwich. The gauge was a gra- 

 duated post erected in the sea at a short distance from the pier; it was kept upright 

 by large stones at its base, and by guys with large stones lashed to them. 



2. Kilrush. — A small town on the north bank of the Shannon, about sixteen miles 

 above Kilbaha ; latitude 52° 38', longitude 9° 29'. The gauge was a graduated scale 

 nailed to the Revenue Pier. 



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