424 Mr. Gr. H. Darwin on Variations in the Vertical 



de cas defavorables a nos theories admises. On est done en 

 droit d'affirmer que si la mer haute attire le plus souvent le 

 pied du fil a plomb, il y a uue, et peut-etre plusieurs, autres 

 forces en jeu pour faire varier sa position." 



We must now consider the vertical displacement of the 

 land near the coast. In (21) it is shown to be 



s _e»„ 'x 2-1037, 



where « indicates the displacement corresponding to 2 = 0. 



With the assumed values, A =40, i/=3x 10 8 , Z=6'28x 10 8 , 

 I find « = 5*684 centim. Hence the amplitude of vertical 

 displacement is 11-37 centim. As long as hi remains constant 

 this vertical displacement remains the same ; hence the high 

 tides of 10 or 15 feet which are actually observed on the coasts 

 of narrow seas must probably produce vertical oscillations of 

 quite the same order as that computed. 



If the land falls, the tide of course rises higher on the coast- 

 line than it would do otherwise ; hence the apparent height of 

 tide would be h + « . But this shows there is more water 

 resting on the earth than according to the estimated value h ; 

 hence the depression of the soil is greater in the proportion 

 1 -(- ct /h to unity; this again causes more tide, which reacts and 

 causes more depression, and so on. Thus on the whole the 

 augmentation of tide due to elastic yielding is in the ratio of 



This investigation is conducted on the equilibrium theory ; 

 and it neglects the curvature of the sea-bed, assuming that 

 there is a uniform slope from mid-ocean to the sea-coast. The 

 figure shows that this is not 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 

 augmentation must correspond approximately with the ratio 



l.(l-£x*10»7) 



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*. 



* Sir William Thomson has pointed out to me, since the meeting of 

 the Association, that this augmentation will only hold true in the cases 

 of certain distributions of land. 



