293] Tides: the Stability ^f the Solar System 375 



Propositions which profess to be or are commonly inter- 

 preted as being "exact" and valid throughout all future 

 time are consequently regarded with considerable distrust, 

 unless they are clearly mere abstractions. 



In the case of the particular propositions in question the 

 progress of astronomy and physics has thrown a good deal 

 of emphasis on some of the points in which the assumptions 

 required by Lagrange and Laplace are not satisfied by the 

 actual solar system. 



It was assumed for the purposes of the stability theorems 

 that the bodies of the solar system are perfectly rigid ; in 

 other words, the motions relative to one another of the parts 

 of any one body were ignored. Both the ordinary tides of 

 the ocean and the bodily tides to which modern research 

 has called attention were therefore left out of account. 

 Tidal friction, though at present very minute in amount 

 ( 287), differs essentially from the perturbations which 

 form the main subject-matter of gravitational astronomy, 

 inasmuch as its action is irreversible. The stability theorems 

 shewed in effect that the ordinary perturbations produced 

 effects which sooner or later compensated one another, so 

 that if a particular motion was accelerated at one time it 

 would be retarded at another ; but this is not the case with 

 tidal friction. Tidal action between the earth and the 

 moon, for example, gradually lengthens both the day and the 

 month, and increases the distance between the earth and 

 the moon. Solar x tidal action has a similar though smaller 

 effect on the sun and earth. The effect in each case as 

 far* as we can measure it at all seems to be minute almost 

 beyond imagination, but there is no compensating action 

 tending at any time to reverse the process. And on the 

 whole the energy of the bodies concerned is thereby lessened. 

 Again, modern theories of light and electricity require space 

 to be filled with an " ether " capable of transmitting certain 

 waves ; and although there is no direct evidence that it in 

 any way affects the motions of earth or planets, it is difficult 

 to imagine a medium so different from all known forms of 

 ordinary matter as to offer ?to resistance to a body moving 

 through it. Such resistance would have the effect of slowly 

 bringing the members of the solar system nearer to the sun, 

 and gradually diminishing their times of revolution round 



