Haughton — On the Effects of Lunar and Solar Tides, ^r. 605 



LXXXII. — On the Effects of the Ltxae a>^d Solae, Tides rs" 

 Lengthexln-g the Dtjeatiox of the Sideeeal Day. By the Rev. 

 SAiDjEL HlnjGHTOx, M.D., Pellow of Trinity College, Dublin. 



[Eead, November 14, 1881.] 



The idea of a lengthening of the sidereal day, by means of the tidal 

 effects of the moon and sun, Tvas started by the late astronomer 

 Delaunay, as a means of explaining the difference of the coefficient 

 determining the moon's mean motion, 



10-2 w^ 



found by Halley from ancient eclipses, and confirmed by Laplace by 

 calculation; and the coefficient, found by Adams's correction of La- 

 place's calculation, 



6-11 >!-. 



Delaunay found that a lengthening of the sidereal day by one second in 

 100,000 years, would reconcile Halley's coefficient with Adams's cor- 

 rection of Laplace's coefficient; and he also made an attempt to cal- 

 culate the lengthening of the day producible by the tidal influence of 

 the moon and sun. As, however, he made his calculation on the 

 equilibrium theory of the tides, aad also assumed an inadmissible 

 range of ocean tide, it is desirable to repeat his calculations on more 

 correct data, which I have attempted to do in the following Paper.*' 



I shall consider two effects of the tidal action of the moon and 

 sun — 



1. The effect of the Residual Tidal Current, which is of the second 

 order, as compared to the second. 



2. The effect of the Distortion Couple, caused by the displacement 

 of the tid.il sphe roid by friction, and accompanied by acceleration 

 of tidal phase. 



PEOPOSITIOJf I. 



It is required to find the rate of lengthening of the sidereal day , caused 

 hy the residual current produced ly the tidal action of the moon (supposed 

 to he always in the equator) iipon the ocean, collected into an equcdorial 

 canal, of constant width and depth. 



The ocean occupies about three-fourths of the surface of the earth, 

 and is about two miles deep, on the average. If this quantity of water 



* I believe that Mr. "William Ferrel, of the U. S. A. Coast Survey, has made an 

 attempt similar to my own ; but as I have not seen it, I can only acknowledge here 

 his possible priority. 



