Gravitational Problem. 95 



bodies at its surface is far from providing a delicate test for 

 the existence of rapidly periodic fluctuations of gravity. The 

 simplifying assumptions which have been made above are 

 not such as to alter the essential aspect of the problem ; no 

 doubt the substitution of more correct (mean) values for the 

 elastic constants involved would lead to somewhat different 

 results, but the general character of the conclusions would 

 remain as before. 



12. The apparatus used in the Cavendish experiment, as 

 carried out, for instance, by Mr. Boys, would indicate rapid 

 fluctuations of gravity with far greater sensitiveness ; on the 

 other hand, Prof. Poynting's form of the experiment, wherein 

 a beam-balance was used, would be practically unaffected by 

 such a state of things. 



Kennington, near Oxford, 

 June 26, 1909. 



Postscript : Nov. 17, 1909. 



I have been reminded by Dr. Chree, President of the 

 Physical Society, that my simplifying assumption of an elas- 

 tically homogeneous earth must necessarily be far from the 

 truth, the pressure at the centre being something like 2800 

 tons per square inch. This I am most ready to admit ; but 

 although the assumption requires modification, we do not 

 know to what extent. Tidal phenomena afford some infor- 

 mation as to the rigidity of the earth as a whole, but it seems 

 very probable, as Dr. Chree points out, that the bulk-modulus 

 of elasticity of the more central portions is increased by the 

 pressure thereon to a far greater extent than is the rigidity- 

 modulus. This would reduce the amplitude of the actual 

 compressional waves discussed in the paper, the observable 

 effects at the earth's surface being thus correspondingly 

 increased. On the other hand, it appears that my assumed 

 values for h and //, give for Young's modulus a value consi- 

 derably higher than is sometimes assumed, and this would 

 affect the conclusions in the contrary sense. 



The problem was one which presented itself in the course of 

 some speculations regarding the mechanism of gravitation ; 

 its solution was not afterwards found to be important in that 

 connexion, but it seemed that, as a mere dynamical curiosity, 

 the matter might be worth a short note. So in the above 

 discussion the assumptions made were the simplest possible, 

 and instead of the most recent authorities being consulted for 

 geophysical data, Lord Kelvin's original rough comparison 

 between the earth and a sphere of steel was made to serve • 

 For the present it hardly seems that labour would be profitably 

 expended on a more elaborate treatment. 



