612 



Proceedings of the Royal Irish Academy. 



From this we calculate the friction corresponding to any value 

 of X : — 



Acceleration 

 of phase 



X. 



2.x. 



I 



7 



Number of years 



required to lengthen the 



day by one second. 



n. 



5° 



10° 



38,993 



148,800 



10 



20 



18,890 



75,548 



15 



30 



11,190 



51,668 



20 



40 



8,194 



40,291 



25 



50 



6,769 



33,731 



30 



60 



3,970 



29,836 



35 



70 



2,502 



27,497 



40 



80 



1,212 



26,238 



441 



89 



120 



25,843 



45 



90 







25,839 



Corollary (1). — If we take account of the sun, as well as of the 

 moon, the number of years in the last column should be reduced by one- 



thii'd ; so that a friction whose coefi&cient is , corresponding to a 



38,993 



tidal acceleration of phase of 5° (or 20"), would increase the length of 

 the day by one second in 100,000 years. This is the amount of retar- 

 dation necessary to reconcile Halley's coefficient of the moon's secular 

 increase of mean motion, derived from ancient eclipses, with the cor- 

 rection in Laplace's coefficient made by Professor Adams. 



Corollary (2). — With an amount of fiiction corresponding to an 

 acceleration of phase of 5° (or 20"), the water at the equator should 

 rise 812 feet above the level before a surface current could flow 

 towards the poles. 



