200 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1923 



nothing in recent progress suggests any doubt that the beautiful 

 theory of Sir George Darwin is substantially correct. The main 

 features are that the moon at one time formed part of the earth, and 

 broke away. At that time the rotation period of the earth was be- 

 tween 3 and 4 hours, and the cause of the fracture was that the solar 

 tidal force synchronized with a free period of natural vibration of 

 the earth; owing to resonance the tidal deformation of the earth 

 continually increased until rupture occurred. The earth's period of 

 rotation has since lengthened to 24 hours, owing to frictional dissi- 

 pation of energy by lunar and solar tides ; and the back reaction of the 

 lunar tides on the moon has caused the moon to recede to its present 

 considerable distance. All this has well stood the test of searching criti- 

 cism, and must be considered as extremely probable. Modern research 

 has added two contributions ; it enables us to calculate the magnitude 

 of this tidal friction at the present time, and it enables us to locate 

 more exactly the region where the frictional dissipation is occurring. 



I believe it was Darwin's view that the tides most potent in wast- 

 ing energy were not water tides but tides in the solid earth; that is 

 to say, we have to do with deformations of the whole earth under 

 the tide-raising force of the moon's attraction- Undoubtedly these 

 deformations of the earth occur, but everything turns on whether 

 the process of deformation is attended with serious friction. H. 

 Jeffreys has pointed out that the phenomenon of latitude variation 

 is accompanied by similar deformations of the earth ; and in this case 

 it is clear that the friction is inconsiderable, for otherwise the devia- 

 tions of the pole from the symmetrical position would be damped 

 out almost at once. It seems, therefore, very unlikely that the solid 

 tides can have had much effect in the process of tidal evolution of 

 the earth-moon system. Ocean tides are likewise of small effect, as 

 Darwin himself had seen. The modern conclusion is a very curious 

 one ; it is in the landlocked shallow seas that nearly all the mischief 

 occurs. This was discovered by G. I. Taylor, who found that the 

 Irish Sea alone is responsible for one-fiftieth of the whole amount 

 required by observation. The remaining landlocked basins on the 

 earth are probably capable of making up the necessary total. 



The actual rate at which the earth's rotation is being slowed down 

 at the present era can probably be deduced with fair accuracy from 

 the records of ancient eclipses. The day is lengthening about one- 

 thousandth of a second per century or 1 minute in 6,000,000 years. 

 At this rate we should have to go back more than 10,000 million years 

 to the time when the day was between 3 and 4 hours and the moon was 

 born. Since the rate depends on the accidental circumstance of occur- 

 ence of shallow seas, no definite prediction can be made ; but allowing 

 for the much greater effect of the tides when the moon was nearer to 

 us, it is difficult to date the birth later than 1,000 million years ago. 



