Chase.J 4:Ub [Oct. c, 



Photodynumic Notes, VI. By Pliny Earle Chase, LL.D. 



{Rettd before tJie American Philosophical Society, October 6, 1SS^\) 



242. Stability of Harmonies. 



In Note 220, I presented several reasons for believing that the mean 

 l)eriods of planetary rotation are stable. They are all dependent upon 

 more general principles which regulate the haiTQony of persistent oscilla- 

 tions in elastic media, and consequently furnish strong a ^rion presump- 

 tions against all hypotheses which seem, in any way, to conflict with har- 

 monic tendencies. The certainty (Note 213), which Proctor admits, 

 of Earth's having a pulsation period, with which its rotation must once 

 have begun to approach to synchronism, springs from a like source with 

 tiie harmonic tendencies in Jupiter's satellite system, and Laplace's 

 reasoning is equally applicable to both cases. The "pulsation period" 

 which is due to luminous vibration is constant, and if it should ever be 

 suddenly or greatly disturbed, rotation would immediately begin again to 

 approach to its normal synchronism. After the synchronism is once 

 reached, all the influences from which it originated continue to contribute 

 towards its perpetual maintenance. 



343. Improbahility of Belaunay's Hypothesis. 



Newcomb and Holden {Astronomy, p. 148) close their note on the secu- 

 lar acceleration of the Moon, as follows : — "The present theory of accelera- 

 tion is, therefore, that the Moon is really accelerated about six seconds 

 in a century, and that the motion of the Earth on its axis is gradually 

 diminishing at such a rate as to produce an apparent additional accelera- 

 tion which may range from two to six seconds." The former portion is 

 known to be cyclical, to be followed, after a long interval, by a corre- 

 sponding retardation ; there is not a particle of evidence to discredit the 

 probability that the latter portion is also cyclical. Neither is there a parti- 

 cle of evidence that there is any tidal friction except at the shores of the 

 ocean, where any accelerating tendencies at one period are counterbal- 

 anced by retarding tendencies at another. The frictional hypothesis was a 

 gratuitous assumption, to explain a, doubtful phenomenon, and although 

 the explanation would be satisfactory if the frictional retardation could be 

 proven, the assumption violates the ordinary rules of framing scientific 

 hypotheses so completely, that its chief claim for consideration rests upon 

 the reputation of its originator. On the other hand, the harmonic 

 liypothesis makes no assumption ; starting from acknowledged facts and 

 principles, it asks wliat results may be reasonably anticipated, and there 

 are few, if any, modern researclies, in wliich the anticipations have been 

 so abundantly verified. Even if we grant frictional retardation, there is 

 " no way of determining the amount of this retardation unless we assume 



