200 



ANNUAL REPORT SMITHSONIAN INSTITUTION, 1921. 



estimate of the age of the earth agrees well. We have, in fact, the 

 following comparison : 



Area compressed (km. 2 ) 



Greatest depth of considerable cooling (km.) 

 Depth of compressive movements (km.) 



Calculated. 



Assumed age of 

 earth. 



1.6X10? 

 years. 



49 XW 



300 



70 



1.6X10' 

 years. 



5X10 3 

 30 



1 



Actual. 



> 19X105 



100-400 



>10 



I do not agree with Lord Rayleigh's suggestion that the earth must 

 be becoming hotter. That hypothesis is not acceptable on cosmo- 

 gonical grounds, and Doctor Holmes has shown that it is impossible 

 to reconcile it with the existence of volcanic temperatures, and that 

 there must be a concentration of radio-active matter in the upper 

 layers of the crust. Doctor Holmes has told me privately that there 

 is reason to believe that in a fluid magma the radio-active materials 

 will be concentrated in the upper layers on account of the volatility 

 of their compounds, but I do not know whether this argument has 

 been published. The numerical estimates here given rest on the sup- 

 position of such a concentration. 



An alternative estimate of the age may be made from the tidal 

 theory of the origin of the solar system, the only theory which is 

 not unsatisfactory on dynamical grounds. The planets must, on this 

 theory, have moved originally in highly eccentric orbits, and have 

 had their eccentricities gradually reduced by the action of a gaseous 

 resisting medium. If the density of the medium near Mercury was 

 />, the time needed to reduce the eccentricity to its present value would 

 be of the order of 4000//?, C. G. S. units being used. On the other 

 hand, the time it would take the medium to be dispersed by viscosity 

 and diffusion would be of the order of 16 X 10 29 />. These must be 

 equal ; for if the former was the greater the medium would have dis- 

 persed before doing the work, and if the latter was the greater the 

 medium would still be a conspicuous object. This shows that the 

 time needed was of the order of 8 X 10 18 sec. or 2.5 X 10 9 years, agree- 

 ing with the estimate given by the uranium-lead ratios. 



