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XLVII. On the Influence of the Tidal Wave on the Motion of the 

 Moon. By James CroliA 



IN a paper " On the Influence of the Tidal Wave on the Mo- 

 tion of the Moon/' which appeared in the Philosophical 

 Magazine for August last, I inadvertently represented Professor 

 William Thomson as having come to the conclusion that the earthy 

 regarded as a time-keeper, is actually losing about four seconds 

 in a year. This, however, is incorrect. In Professor Thomson's 

 paper on the subject a certain state of circumstances as to the 

 tides is specified, not as a probable hypothesis, but as one on 

 which a superior limit of the amount of tidal influence on the 

 earth's rotation may be estimated. On that hypothesis the 

 earth would, one hundred years hence, be rotating so much slower 

 than at present as to be then losing four seconds a year on a 

 perfectly accurate chronometer regulated according to the earth's 

 present rate. 



In my two former papers on the influence of the tides, I en- 

 deavoured to show that the solar wave must exercise a retarding 

 effect on the earth's motion round the common centre of gravity 

 of the earth and moon, similar to what the lunar wave exercises 

 upon the earth's rotation or motion round its own centre of gra- 

 vity f. This, as was pointed out, follows as a direct consequence 

 from the fact that, supposing the earth to have no rotation, still 

 the waters of the ocean would have to rise and fall in order to 

 maintain the solar wave, which in this case would move round 

 the earth, not once in twenty-four hours as at present, but once 

 in a month. And as this motion of the waters, slow as it no 

 doubt would be, could not take place without heat being gene- 

 rated by friction and dissipated into space, the vis viva thus lost 

 must be at the expense of the earth's motion round the common 

 centre of gravity of the earth and moon ; for, by supposition, 

 there is no other motion from which it could be derived. It can 

 be easily proved that this would tend to bring the earth nearer 

 to the moon, and thus increase the moon's angular motion. 



It has been shown by Professor William Thomson, and also 

 by the Astronomer Royal, that, owing to the position of the 

 tidal wave, the moon is drawn not exactly in the direction of the 

 earth's centre of gravity, but a little to the east of that centre, 

 and that in consequence of this, she is made to recede from the 

 earth. Her orbit is enlarged, and her angular motion dimi- 

 nished. 



It would therefore seem that the tides produce two distinct 

 classes of effects, the one to a certain extent neutralizing the 



* Communicated by the Author. 



t Phil. Mag. for April 1864 and August 1866. 



