20 THE TIDAL PROBLEM. 



history, his mathematics ceased to tell what lay beyond. At the same time, 

 the hypothesis is hospitable to any smaller numerical values for the fric- 

 tional effect of the tides which revised data may be found to imply. 



We are now prepared to inquire with equanimity what is the degree 

 of trustworthiness of the astronomic data relative to the recent time- 

 relations of the earth and moon. 



THE EVIDENCES OF A PRESENT CHANGE OF ROTATION. 



Near the middle of the last century Adams, from a study of certain 

 data relative to the secular acceleration of the moon's mean motion, reached 

 the conclusion that the earth was then losing time at the rate of 22 seconds 

 per century. It is proper to add, however, that Adams laid but little stress 

 on the actual numerical values which he used in computation, and that he 

 was of the opinion that the amount of tidal retardation of the earth's 

 rotation is quite uncertain.^ At a later date, Newcomb made a computa- 

 tion based on the data then available, with the result that the rate was 

 reduced to 8 seconds per century.^ Darwin verified the computative part 

 of Adams' results and added a neglected factor for the obliquity of the 

 ecliptic and the diurnal tide which raised the estimate to 23.4 seconds per 

 century. Newcomb's estimate similarly revised is 8.3 seconds.^ 



A reliable answer to the question whether the earth's rate of rotation 

 is or is not now departing from constancy, and at what rate, depends not 

 only upon extremely refined astronomical observations, but upon the 

 interpretation of these observations by means of a perfect theory of the 

 lunar motions. This latter has not yet been attained. In a case where the 

 suspected variation from constancy is so slight, and where the logical 

 structure to be built upon it in tracing it back through tens of millions of 

 years involves so great a multiplication of any error it may contain, it is 

 obvious that extreme accuracy and complete soundness are necessary to 

 trustworthy results. In the judgment of cautious astronomers, these 

 prerequisites are not yet attainable. It is not, therefore, too much to say 

 that the deductions thus far made have not a sufficiently secure obser- 

 vational basis to give them authoritative value. This is not to say, by any 

 means, that these results, based on the best data heretofore available, 

 do not fully justify the elaborate mathematical investigations based upon 

 them, for these have proved extremely illuminating and stimulative, 

 and were almost necessary ^s precursors to the more critical work on both 

 observational and theoretical lines which is necessary to give the firm 

 foundation so eminently to be desired. 



1 Thomson and Tail's Natural Philosophy, II, p. 419; also pp. 415-520 and 503-505, 

 edition of 1890, and the papers of Darwin previously referred to. 



* Researches on the motion of the Moon, Washington, 1873. See also Thomson and 

 Tait's Natural Philosophy, II, p. 418. 



^ Thomson and Tait's Natural Philosophy, II, p. 505. 



