ON THE MEASUBEMENT OF THE LUNAR DISTURBANCE OF GRAVITY. Ill 



known mine wonld scarcely sensibly affect the result, because the flexure 

 of the strata at a depth so small, compared with the wave-length of 

 barometric inequalities, is scarcely different from the flexure of the 

 surface. 



The diurnal and periodic oscillations of the vertical observed by us 

 were many times as great as those which have just been computed, and 

 therefore it must not be supposed that more than a fraction, say perhaps 

 a tenth, of those oscillations was due to elastic compression of the earth. 



The Italian observers could scarcely, with their instruments, detect 

 deflections amounting to T-Joth of a second, so that the observed connec- 

 tion between barometric oscillation and seismic disturbance must be of a 

 different kind. 



It is not surprising that in a volcanic region the equalisation of pres- 

 sure, 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 conld be eliminated) with some such instrument as ours, placed 

 in a deep mine, to detect the existence 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 direction an 

 infinite incompressible elastic solid, let there be drawn a series of parallel 

 straight lines, distant I apart. Let one of these be 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 2; = to Z, let a normal 

 pressure gioh (1 — 2zjl) be applied ; and from 2 = to — Z let the sur- 

 face 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 alter- 

 nate ones are the oceans, g is gravity, lo 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 mountains and valleys 

 whose outline is given by a; = — /i (1 — 22/Z) from z = to Z, and x = 

 from z = to — Z. To utilise the analysis of the last section, it is neces- 

 sary that the mountains and valleys should present a simple-harmonic 



