138 The Rev. Samuel Haughton on the Solar and Lunar 



In this Table, the second column contains the 7nean Age of the Tide ; the 

 third column the Acceleration of the Tide, both expressed in hours ; the fourth 

 column contains the ratio of the Age to the Acceleration ; and the last column 

 exhibits the mean depth of the sea, deduced in a manner which will be ex- 

 plained. 



The mean sea depths of the preceding Table are deduced, as follows, from 

 Mr. Airy's Theory of Tide Waves with Friction. It is proved ("Tides and 

 Waves," p. 333), that 



Age of Lunidiurnal Tide _ ^' + ^^'wi^ / 1 a-^ 



Acceleration of Lunidiurnal Tide ~ r — gkm^' 



which becomes, introducing the values already given, and expressing k in miles, 



Age of Lunidiurnal Tide _ 12-938 + k ,, ,. 



Acceleration of Lunidiurnal Tide ~ 12'938 — k' 



The sea depths are calculated from the preceding equation, and their mean 

 value 11-32 miles, is a striking confirmation of the mean depth derived from 

 the comparison of the Limitidal and Solitidal Intervals ; and at the same time 

 a confirmation of Mr. Airy's Theory of Tide Waves with Friction. In fact, 

 the existence of a Tidal Age or Acceleration is altogether due to friction, and, 

 therefore, the similarity of the two independent results must be regarded as 

 proving that the values of the Lunitidal Age, and Solitidal and Lunitidal Inter- 

 vals deduced from observation, agree with each other in the manner indicated 

 by Theory. 



It may be as'ked, how are we to reconcile this value of the mean sea depth 

 with that deduced from Diurnal Heights, and from Laplace's results of the 

 Semidiurnal Tides at Brest. Although this question is difficult to answer fully, 

 yet it should be observed that the results deduced from Intervals and Ages 

 are more consistent with each other than those deduced from Heights, and also 

 that they are confirmed by the sea depth deducible from Mr. Airy's Irish 

 Observations. And it may be also suggested, that probably the depth inferred 

 from Age and Acceleration is the depth of the sea at a greater distance from 

 the coast, while the depth deduced from Heights is the depth of the sea after 

 it has began to shoal, the tide being composed partly of a derivative and partly 

 of the original Atlantic Tide. 



