118 REPOET — 1882. 



slope from mid-ocean to the sea-coasfc. The figure shows that this is uot 

 rigorously the case, but it is quite near enough for a rough approximation. 

 The phenomena of the short period tides are so essentially kinetic that 

 the value of this augmentation must remain quite uncertain, but for 

 the long-period tides (the fortnightly and monthly elliptic) the augmen- 

 tation must correspond approximately with the ratio 



1 : fl-^J^ X 2-1037. ^ 



The augmentation in narrow seas will be small, but in the Atlantic Ocean 

 the augmenting factor must agree pretty well with that which I now 

 compute.' 



With the previous numerical values we have og/Zi (which is inde- 

 pendent of h) equal to '1421, and 1 — uqIJi = '8579 = i very nearly. 



Thus the long-period tides may px'obalDly undergo an augmentation at 

 the coasts of the Atlantic in some such ratio as 6 to 7. 



The influence of this kind of elastic yieldiilg 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 difEculfc to estimate what degree of 

 jn'obability 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 comj^ressibility 

 plays a much less important part than the rigidity, and the formula for 

 Young's modulus shows that for an incompressible 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** grammes weight per square centimeter. The 

 following 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'' in 

 the ' Encyclopa3dia Britannica.' 



Materiil ■^ third of Young's mod. and rigidity in 



terms of lO^ grammes weight per sq. cm. 



Stone About 1-2 



Slate About 3 to 4 



Glass Kigidity 1-5 to 24 



Ice 4-7 



Copper 4 and rigidity 4-0 to .5-4 



Steel 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 materials 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 probably as great as 

 that of steel. That result is not at all inconsistent with the probability 

 of the assumption that the upper strata have only a rigidity a little greater 

 than that of glass. 



_ ' It has been pointed out to me since this meeting, by Sir William Thomson, that 

 this kind of augmentation of apparent tide vfill only hold true with certain distribu- 

 tions of land. 



2 Thomson and Tait's Met. Phil. § 683. 



» Also published separately by Black, Edinburgh. 



