116 THE EVOLUTION OF SATELLITES. , 



circular orbit so as nearly to touch its surface and continuously to face 

 the same side of the planet. If now, for some cause, the satellite's 

 month comes to differ very slightly from the planet's day, the satellite 

 will no longer continuously face the same side of the planet, but will 

 pass over every part of the planet's equator in turn. This is the con- 

 dition necessary for the generation of tidal oscillations in the planet, 

 and as the molten lava, of which we suppose the planet to be formed, 

 is a sticky or viscous fluid, the tides must be subject to friction. Tidal 

 friction will then begin to do its work, but the result will be very dif- 

 erent according as the satellite revolves a little faster or a little slower 

 than the planet. If it revolves a little faster, so that the month is 

 shorter than the day, we have a condition not contemplated in the 

 figure above. It is easy to see, however, that as the satellite is always 

 leaving the planet behind it, the apex of the tidal protuberance must 

 be directed to a point behind the satellite in its orbit. In this case the 

 rotation of the planet must be accelerated by the tidal friction, and the 

 satellite must be drawn inward toward the planet, into which it must 

 ultimately fall. In the application of this theory to the earth and the 

 moon, it is obvious that the very existence of the moon negatives the 

 hypothesis that the initial month was even intinitesimally shorter than 

 the day. We must then suppose that the moon revolved a little more 

 slowly than the earth rotated. In this case the tidal friction would 

 retard the earth's rotation, and force the moon to recede from the earth, 

 and so perform her orbit more slowly. Accordingly, the primitive day 

 and the primitive month lengthen, but the month increases much more 

 rapidly than the day, so that the number of days in the month becomes 

 greater. This proceeds until that number reaches a maximum, which 

 in the case of our planet is about twenty-nine. 



After the epoch of maximum number of days in the month, the rate 

 of change in the length of the day becomes less rapid than that in the 

 length of the month 5 and although both periods increase, the number 

 of days in the month begins to diminish. The series of changes then 

 proceeds until the two periods come again to an identity, when we have 

 the earth and the moon, as they were at the beginning, revolving in the 

 same period, with the moon always facing the same side of the i)lanet. 

 But in her final condition the moon will be a long way off from the 

 earth, instead of being quite close to it. 



Although the initial and final states resemble each other, yet they 

 differ in one respect, which is of much importance; for in the initial 

 condition the motion is unstable, while finally it is stable. The mean- 

 ing of this is that if the moon were even infiuitesimally disturbed from 

 the initial mode of motion, she would necessarily either fall into the 

 planet or recede therefrom, and it would be impossible for her to con- 

 tinue to move in that neighborhood. She is unstable in the same sense 

 in which an egg balanced on its point is unstable, the smallest mote of 

 dust will upset it, and practically it can not stay in that position. But 



