due to Elasticity of the Earth's Surface. 421 



as representing the tides over large areas ; iv, the density of 

 the water, is of course unity. 



If we suppose it is the Atlantic Ocean and the shores 

 of Europe with Africa, and of North and South America, 

 which are under consideration, it is not unreasonable to take 

 I as 3900 miles, or 6'28 x 10 8 centim. Then 2irz/l=z x 10~ 8 . 



Taking vjg as 3 x 10 8 (that is to say, assuming a rigidity 

 greater than that of glass), w r e have for the slope in seconds of 

 arc, at a distance z from the sea-shore, 



40 



C0SeC X " X 2ttx3x10 8 X l0ge 10 x ( 8 ~ lo gio z ) 

 = 0"-01008(8-log 10 *). . . 



(22) 



From this the following table may be computed by simpk 

 multiplication : — 



Distance from 

 mean water-mark. 



1 centim. 



10 „ 



io 2 „ 



io 3 „ 



io 4 „ 



io 5 „ 



IO 6 „ 



= 1 centim 



= 10 „ 

 = 1 metre 



= 10 metres 

 = 100 „ 

 = 1 kilom. 



= 10 „ 



2 xlO 6 centim. = 20 



5 x IO 6 

 10 7 centim. 



= 50 

 = 100 



Slope. 

 0"-0806 

 •0706 

 •0605 

 •0504 

 •0403 

 •0302 

 •0202 

 •0170 

 •0131 

 •0101 



On considering the formula (22), it appears that z must be 

 a very small fraction of a millimetre before the slope becomes 

 even as great as V . This proves that the rounded nick in the 

 surface, which arises from the discontinuity of pressure at our 

 ideal mean water-mark, is excessively small ; and the vertical 

 displacement of the surface is sensibly the same, when mea- 

 sured in centimetres, on each side of the nick, in accordance 

 with the first of (21). 



The result (5) of section 1 shows that, with rigidity 3 x IO 8 , 

 the true deflection of plumb-line due to attraction of the 

 water is a quarter of the slope. Hence an observer in a gra- 

 vitational observatory at distance z from mean water-mark, 

 would note deflections from the mean position of the vertical 

 \\ times as great as those computed above ; and as high 

 water changes to low, there would be oscillations of the ver- 

 tical %\ times as great. We thus get the practical results in 

 the following table: — 



