110 Influence of the Tidal Wave on the Motion of the Moon. 



water ascends and descends must tend to diminish the vis viva 

 of rotation. 



That the solar wave must diminish the earth's motion round 

 the common centre of gravity of the earth and moon appears 

 evident from the following considerations. 



Suppose the diurnal rotation of the earth to be stopped, or, 

 rather we should say, reduced to the same as that of the moon, 

 viz. to one revolution in a month. In this case the earth would 

 always present the same side to the moon. The lunar wave 

 would of course exist the same as at present, only it would remain 

 stationary on the earth's surface, seeing that the earth would 

 always present the same side to the moon. As the water would be 

 motionless, of course there could be no friction; no heat generated, 

 and consequently no loss of rotation. But let us look at the in- 

 fluence of the solar wave. The solar wave would also, of course, 

 exist the same as it does now, but it would move round the earth 

 not once in twenty-four hours, as at present, but, only once in a 

 month. But however slow the water would rise and fall, a con- 

 siderable amount of heat would be generated by friction. The 

 question now arises, from what source would this energy lost in 

 the form of heat be derived ? The source would evidently be 

 the rotation of the earth round the common centre of gravity ; 

 for it is to this source that the motion of the water is due. Sup- 

 pose now the diurnal rotation of the earth to commence; new 

 effects would certainly result, but these would not prevent the 

 occurrence of those we are now considering. In other words, 

 the effects which, we have seen, would take place under the 

 above conditions, do actually at present take place. The two sets 

 of effects do not interfere with each other. Consequently the 

 solar wave must be slowly consuming the vis viva of the earth's 

 rotation round the common centre of gravity. But it is the vis 

 viva of rotation that keeps the two orbs separate from each other. 

 Hence as this vis viva is being consumed, the two must be ap- 

 proaching nearer to each other. And this must accelerate the 

 angular motion of the moon. 



The solar wave does not consume the vis viva of the moon's 

 motion around the common centre. It only consumes the 

 earth's motion around that centre. The motion of the earth is 

 retarded, but not the motion of the moon. Now, since the earth 

 is gradually approaching nearer and nearer to the moon in con- 

 sequence of the consumption of the centrifugal force keeping it 

 separate from that orb, the moon must therefore be moving with 

 all its original stock of vis viva in an orbit which is gradually 

 becoming less and less. Consequently the period of its revolu- 

 tion must be diminishing in length. 



There is still another effect which results from this condition 



