166 PROCEEDINGS OF THE [July, 1887. 



the farther we proceed from the focus, and therefore from this cause, each of 

 the above effects, vertical and horizontal, supposed already calculated, must be 

 diminished in a ratio also easily calculable. As the intensity in the upward di- 

 rection is diminished by each of these causes, it will continually diminish as we 

 go outward, until it becomes imperceptible. But the intensity in the horizon- 

 tal direction is Httle or nothing at the surface- cenfrre, and continually increases 

 from one cause, the obhquity, as we proceed outwards from that centre, while 

 it diminisJies from the other cause, namely the decrease of the intensity of the 

 original disturbance, as it proceeds to greater distances from the focus. But it 

 may be shown that the increase and the diminution follow different laws, and 

 the horizontal disturbance will, at a certain distance from the surface-centre, 

 attain its greatest intensity and afterwards diminish continuaUj". These points 

 of maximum horizontal disturbance, will He approximately in a circle around 

 the surface-centre and the radius of this circle can be calculated when there is 

 given, the rate of diminution of the intensity of the disturbance along the lines 

 radiating from the focus. 



In the first of the two cases mentioned above, the intensity of disturbance 

 along the radiating lines, is supposed to vary inversely as the distance from 

 the focus. In this case it can be shown that the radius of the circle of great- 

 est horizontal disturbance is equal to the depth of the focus below the surface- 

 centre ; so that if one of these quantities can be found, the other -^dll become 

 known. Supposing Charleston and Summerville to be at the two extremities 

 of a diameter of that circle, then the surface-centre would be midway, say at 

 about 11 mUes from each ; and the focus woiild be about 11 miles below that 

 centre. 



In the second case, the intensity is supposed to vary inversely as the square 

 of the distance from the focus, when it can be shown that the radius of circle of 

 greatest horizontal disturbance is to the depth of focus as the side of a square is 

 to its diagonal. This would put the depth of the focus at about 15 miles. 



These two methods of investigating the position of the focus, were used, and 

 their demonstrations, by means of the adcidus, given by Mr. Eobert Mallet 

 nearly 30 years ago. He apphed them, if I mistake not, to the discussion of the 

 depth of the focus observed in the earthquake which so severely injured the 

 City of Naples, on 17th Dec, 1857, two days before the shock felt in this City 

 the same year, as already mentioned. In the appendix to the present paper, I 

 have given a geornetrical explication of the first method, which will be easily 

 apprehended by those who understand the geometrical properties of the circle. 

 The second method is one degree more complex, and the explanation is there- 

 fore less simple. 



I have shown in my preceding paper that the average direction of the most 

 powerful shocks in om- earthquake, was towards a point about north, and this 

 direction we now see, is towards the focus of disturbance and not froni it. It 

 would seem then that this disturbance is not of the nature of an explosion or 

 release of an outward stress, in which the wave is one of compression, proceed- 

 ing from the focus outwards, the motion of each successive particle being also 

 in the same direction, outwards ; but rather of a release of an inward stress, 



