due to Elasticity of the Earth's Surface. 425 



"With the previous numerical values we have ot /h (which is 

 independent of A) equal to "1421, and 1— ctjh — -8579 = f- very 

 nearly . 



Thus the long-period tides may probably undergo an aug- 

 mentation at the coasts of the Atlantic in some such ratio as 

 6 to 7. 



The influence of this kind of elastic yielding is antagonistic 

 to that reduction of apparent tide which must result from an 

 elastic yielding of the earth's mass as a whole. 



The reader will probably find it difficult to estimate what 

 degree of probability of correctness there is in the conjectural 

 value of the rigidity, which has been used in making the 

 numerical calculations in this paper. The rigidity has not 

 been experimentally determined for many substances; but a 

 great number of experiments have been made to find Young's 

 modulus. Now, in the stretching of a bar or wire the com- 

 pressibility plays a much less important part than the rigidity; 

 and the formula for Young's modulus shows that for an in- 

 compressible elastic solid the modulus is equal to three times 

 the rigidity*. Hence a third of Young's modulus will form a 

 good standard of comparison with the assumed rigidity, namely 

 3 x 10 8 grammes weight per square centimetre. The follow- 

 ing are a few values of a third of Young's modulus and of 

 rigidity, taken from the tables in Sir William Thomson's 

 article on Elasticity t in the Encyclopedia Britannica: — 



A third of Young's modulus and 

 Material. rigidity in terms of 10 s grammes 



weight per square centimetre. 

 Stone .... About 1*2 



Slate 

 Glass 

 Ice . 

 Copper 

 Steel 



About 3 to 4. 



Eigidity 1-5 to 2*4. 



4-7. 



4, and rigidity 4*6 to 5*4. 



7 to 10, and rigidity 8*4. 



It will be observed that the assumed rigidity 3 is probably 

 a pretty high estimate in comparison with that of the mate- 

 rials of which we know the superficial strata to be formed. 



It is shown, in another paper read before the Association at 

 this meeting, that the rigidity of the earth as a whole is pro- 

 bably as great as that of steel. That result is not at all incon- 

 sistent with the probability of the assumption that the upper 

 strata have only a rigidity a little greater than that of glass. 



* Thomson aud Tait's ' Natural Philosophy,' § 683. 



t Also published separately by Black (Edinburgh). 



Phil. Mag. S. 5. Vol. 14. No, 90. Bee. 1882. 2F 



