338 ON THE MOVEMENTS OF THE EARTH's CRUST. 



"Here therefore the eccentricity acts in the opposite direction, namely, 

 so that the force diminishes as the eccentricity increases; but as tlie 

 factor (J-, by which 3/2 e'' is multiplied, is only about 3/400, while the 



magnitude outside the brackets - ,0=5 /3. — (the lunar tides being in 



(X (Is 



proportion to the solar tides most nearly as 5 : 2), its action upon the 

 whole tidal wave is jilo . ^ = 5-3 of the former." 



Tlius we see that the tidal force rises and sinks with the eccentricity 

 of the earth's orbit. It varies by about -^5-, of its value from the highest 

 to the lowest eccentricity. This force is the most important force for the 

 alteration of the day, and it makes it longer. The most important force 

 for shortening the day, according to Thomson, will be the refrigeration 

 of the earth, but he has calculated its value at only ^ f,\,-o of the tidal force 

 and (he has only taken into account the marine tidal wave). If, therefore, 

 the tidal force diminishes and increases by -ig- of its value, this period- 

 ical variation can not compete with forces which act in the opposite 

 direction ; and we may therefore conclude that the sidereal day is con- 

 stantly becoming longer, but that its increase is periodically stronger 

 and weaker. It increases in length more and more rapidly so long as 

 the eccentricity of the earth's orbit increases, more and more slowly so 

 long as the ecccentricity diminishes. In other words, the centrifugal 

 force diminishes and the equatorial regions increase in weight more and 

 more rapidly under an increasing, and more and more slowly under a 

 diminishing, eccentricity. 



As has been stated, there prevails, even among physicists, a disa- 

 greement as to how far the earth will change its form in case the cen- 

 trifugal force varies. Thomson is most inclined to believe that it will 

 not; Darwin is of opinion that it will. And among other physicists 

 whom I have consulted a similar divergence prevails upon this point- 

 One thinks that a lengthening of the day even by several hours will be 

 incapable of altering the form of the solid earth ; another believes that 

 the solid earth will probably change its form just as easily as the sea. 

 And with regard to the rapidity with which the sidereal day lengthens, 

 opinions are just as much divided. Darwin regards as possible, varia- 

 tions much greater than those which agree with the action of the tidal 

 waves calculated by Tliomson for recent times. It is therefore clear 

 that this problem can hardly yet be finally solved, and that different 

 hypotheses will be for the present admissible. We will therefore select 

 that which is best fitted to explain the facts, assuming that the varia- 

 tion of the tidal wave with the eccentricity of the orbit may possibly 

 be the cause of the periodical displacement of coast-lines. But we i)ut 

 forth this hypothesis with all possible reserve. Divergencies of opin- 

 ion between the most esteemed physicists upon this matter, and the 

 neat manner in which the hypothesis is supported by many facts, alone 

 give ns the courage to put forward conjectures which many will proba- 

 bly regard as not only bold, but even improbable. 



