ORIGIN OF THE SOLAR SYSTEM 59 



The physical basis of the theory is very simple. The 

 attractive force due to the moon is always greatest on the side 

 of the earth nearest to it, and least on that farthest away, 

 while its value at the centre of the earth is intermediate. The 

 centre of the earth being regarded as fixed, then, the moon 

 tends to cause the parts of the earth nearest to and farthest 

 from it to protrude, thus forming a bodily tide. If the earth 

 were perfectly elastic, the high tide would always occur with 

 the moon in the zenith or nadir ; no energy would be dissipated, 

 and there would be no secular effect. If, however, it is viscous 

 the tides would lag somewhat, and their attractions on the moon 

 would, in general, produce a calculable secular effect on the 

 moon's motion and the rotation of the earth. The only case 

 where viscosity would produce no secular effect is when the 

 deformed body rotates in the same time as the deforming one 

 revolves. The tide then does not move round relatively to the 

 body, but becomes a constant fixed deformation, directly under 

 the deforming body, and ceases to produce a secular effect. 

 In the ultimate steady state of a viscous system, then, the 

 viscous body will always keep the same face turned towards 

 the perturbing one. In the solar system there are certainly 

 two examples of this condition, and no other explanation of 

 it has been advanced. Mercury always keeps the same 

 face towards the sun, and the moon towards the earth ; with 

 less certainty it is believed that the same is true of Venus 

 and the satellites of Jupiter. 



Now if the viscosity of a substance be zero, that substance is 

 a perfect fluid, and there can be no dissipation of energy inside it. 

 If, on the other hand, it be infinite, then we have the case of 

 perfect elasticity, and again there can be no dissipation. If the 

 viscosity steadily increase from o to infinity, then the rate of 

 dissipation of energy when the same periodic stress is applied 

 increases to a maximum and then diminishes again to zero. 

 The balance of probability seems to imply that the earth was 

 formerly fluid, and, if this can be granted, the fact that most of 

 it is now almost perfectly elastic at once indicates that dissipa- 

 tion of energy by tidal friction must have been important in 

 the past. On this hypothesis Sir G. H. Darwin traced the 

 system of the earth and moon back to a state where the moon 

 was close to the earth, the two always keeping the same face 

 towards each other, and revolving in some time between three 



