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



The Italian observers could scarcely with their instruments 

 detect deflections amounting to yoo" of a second; so that the 

 observed connexion between barometric oscillation and seismic 

 disturbance must be of a different kind. 



It is not surprising that in a volcanic region the equaliza- 

 tion of pressure, between imprisoned fluids and the external 

 atmosphere, should lead to earthquakes. 



If there is any place on the earth's surface free from seismic 

 forces, it might be possible (if the effect of tides as computed 

 in the following section could be eliminated) with some such 

 instrument as ours, placed in a deep mine, to detect the exist- 

 ence of barometric disturbance many hundreds of miles away. 

 It would of course for this purpose be necessary to note the 

 positions of the sun and moon at the times of observation, and 

 to allow for their attraction. 



2. On the Disturbance of the Vertical near the Coasts of 

 Continents due to the Rise and Fall of the Tide. 



Consider the following problem: — 



On an infinite horizontal plane, which bounds in one direc- 

 tion an infinite incompressible elastic solid, let there be drawn 

 a series of parallel straight lines, distance I apart. Let one of 

 these be the axis of y, let the axis of z be drawn in the plane, 

 perpendicular to the parallel lines, and let the axis of x be 

 drawn vertically downwards through the solid. 



At every point of the surface of the solid, from z=0 to I, 

 let a normal pressure gwh(l — 2z/l) be applied; and from 

 z=0 to — Z let the surface be free from forces. Let the same 

 distribution of force be repeated over all the pairs of strips 

 into which the surface is divided by the system of parallel 

 straight lines. It is required to determine the strains caused 

 by these forces. 



Taking the average over the whole surface, there is neither 

 pressure nor traction, since the total traction on the half-strips 

 subject to traction is equal to the total pressure on the half- 

 strips subject to pressure. 



The following is the analogy of this system with that which 

 we wish to discuss : the strips subject to no pressure are the 

 continents, the alternate ones are the oceans, g is gravity, 

 w the density of water, and h the height of tide above mean 

 water on the coast-line. 



We require to find the slope of the surface at every point, 

 and the vertical displacement. 



It is now necessary to bring this problem within the range 

 of the results used in the last section. In the first place, it is 

 convenient to consider the pressures and tractions as caused by 



