78 Proceedings of the Royal Physical Society. 



nomenon ; and was tlius led to investigate the three following 

 physical problems : First, What is the density of the remaining 

 globe, after a shell of water of given thickness is taken away ? 

 Second, AYhat is the force of gravity at the surface of this 

 remaining sphere ? Third, What is the force tending to the 

 equator at the surfaces of each of these remaining spheres ? 

 Having obtained these results, he showed that their necessary 

 consequence was a continuous flow of the waters at the bottom 

 of the sea towards the equator, and of those at the surface to 

 the poles. 



To find the density of the remaining globe after a shell of 

 water of given thickness is taken away, he assumed the 

 following as established facts, the specific gravity of water is 

 1, and that of the whole earth including the water on its 

 surface is 5-67. Then assuming r — the mean radius of the 

 earth and x — the thickness of the shell, r and x being both 

 expressed in fathoms, or both in miles, he deduced the follow- 

 ing formula : 



Density of remainder = r^ xf ttx 5-67- {r^ — (r— a?)3}-f ttxI 



{r—xy X t TT 



The results from this formula give for x = 2000 fathoms 

 (^^ = 5-678056, for 5^ = 4000 fathoms 4= 5-686134, and for 

 X = 7000 fathoms 4 = 5-698283 ; thus showing that at 7000 

 fathoms the density has increased by a 200th part of itself. 



He next showed that if g^ represent the force of gravity at 

 X fathoms or miles below the surface, its force can be calcu- 

 lated from the formula : 



gx = \ {r-x) 4 = -000001631214 (r-x) 4 for r and x in 



fathoms. The results of this formula, for x = 2000 fathoms 

 gives g^ = 32-22723, for x = 4000 gives g^ = 32-25451, and 

 for X = 7000 fathoms gives gx — 32*29554 — which shows that 

 at the depth of 7000 fathoms the force of gravity has in- 

 creased by one 337th part of itself. 



