ON THE COASTS OF IRELAND. |(^ 



= linear velocity of a point at the equator produced by the earth's rotation, supposing 

 the moon fixed, we easily find =13 miles nearly ; and thus our observations give 



Depth of the sea =^=22 miles. 



If the channel were supposed to be a small circle of the earth instead of a large 

 one, the resulting depth of the sea would be diminished in the proportion of the 

 square of its diameter. 



Whatever may be supposed of the error of this result, or the inapplicability of the 

 theory by which it is obtained to the circumstances of the seas, I may remark that it 

 agrees generally with a result deduced from Mr. Whewells discussions of the obser- 

 vations at Bristol with reference to the moon's declinations*. 



Assuming however that we have correctly determined — v—V ^® "^^y proceed to 

 remark that-j- the moon's hydrodynamical effect is represented by her statical effect 

 multiplied by ,_^,2^2 and by constants ; and that the sun's hydrodynamical effect 

 is represented by his statical effect multiplied by 7._^2^2 and by the same constants. 



w^ 15 



If we consider "72=14' then the hydrodynamical effect of the moon contains the 

 multiplier 



i. JL_- J_ ^ . J_ ^ 

 gk _^~gk2 ^^' gk lo' 



5 



while that for the sun contains the multiplier 



J_ 1 _ 1 .14 . J_ 28 

 gk \^^~gk 5 ^^ gk 10 

 14*5 



And therefore the proportion of the moon's statical effect to the sun's is greater than 

 the proportion of her dynamical effect to the sun's in the ratio of 28 to 25. And as 

 the moon's hydrodynamical effect, deduced from the values of M and s above (93-4 



and 16*37), by the considerations in page 34, is nearly =i^;^x sun's hydrodynamical 



effect, it follows that the moon's statical effect =^7^5 X sun's statical effect =4X sun's 



statical effect. This conclusion differs widely from Laplace's ; yet it is formed, as I 

 believe^ on grounds as good as Laplace's. 



For particular results applying to each individual station, regarding the semi- 

 menstrual inequality in range and the apparent proportion of the solar and lunar 

 hydrodynamical effects ; the mean value of C\ for large tides is found by taking the 

 mean of the three values in the three periods of the last Table, and the mean value 

 for small tides by taking the mean of the four values in the four periods of the last 



* Tides and Waves, Art. 553. t Ibid. Art. 448. 



MDCCCXLV. P 



