May 20 1887. J 



SCIENCE. 



495 



epicentre and proceed outwards in any direction, 

 the intensity diminishes, at first more and more 

 rapidly, but farther on diminishes less and less 

 rapidly. We wish to find the point at which the 

 rate of decline changes from an increasing to a 

 decreasing rate. In the curve, this point is repre- 

 sented at the point of inflexion, where the curve 

 ceases to be concave towards the earth, and begins 

 to be convex towards it. To find the co-ordinates 

 of this point, we differentiate the equation of the 

 curve twice, and equate the value of the second 

 differential coefficient to zero, and deduce the 

 corresponding value of the abscissa x. 



dx^~ {q'' + xy 



which equation is satisfied when 



:0, 



whence 



±a7= 





In this value of x it is seen that the constant a 

 has disappeared ; and the abscissa of the point of 

 inflexion is therefore independent of the energy of 

 the shock, and dependent upon the depth alone. 

 The meaning of this is, that the distance from the 

 epicentre to the point where the rate of decline of 

 the intensity is greatest is simply proportional to 

 the depth of the focus, and is the same whether 

 the energy be greater or less. This property of 

 the intensity curves makes us independent of any 

 absolute standard of measurement for the in- 

 tensity, and all that we require is to find with 

 reasonable approximation the points where the in- 

 tensity falls off most rapidly. The depth of the 

 focus follows at once. 



The determination of the epicentral tract is 

 chiefly the work of Mr. Earle Sloan of Charleston, 

 a young civil engineer, who, immediately after 

 the disaster, made an extensive sei'ies of observa- 

 tions. In the brief time at his disposal he ac- 

 cumulated a surprisingly large amount of detailed 

 information, and in searching for it exercised a 

 discrimination and sagacity which would have 

 been highly creditable to the most experienced 

 and learned observer. It is to be regretted that 

 his business engagements prevented him from 

 continuing the work. As it is, he has located 

 with considerable precision the epicentral tract, 

 and has furnished data which show well the vari- 

 ation of intensity along several lines radiating 

 from it. 



The summary obtained from the examination 

 of Mr. Sloan's data is as follows : the tract which 

 includes the most forcible action of the earthquake 

 is an elliptical area about twenty-six miles in 



length, and with a maximum width of about 

 eighteen miles. The major axis of this area is 

 not a straight line, but a curve, which is concave 

 towards Charleston, and is situated from fourteen 

 to sixteen iniles west and north-west of that city. 

 Along this line there are three points, each of 

 which has all the characters of an epicentrum, 

 determined by as many distinct shocks, each hav- 

 ing a focus of its own. Much the most powerful 

 shock centres in the northernmost focus, though 

 the other two were of sufficient energy to have 

 occasioned great havoc if either of them had oc- 

 curred alone. The southernmost was also con- 

 siderably more energetic than the middle one. 

 The distance between the northern and southern 

 epicentrum was about twelve miles. Within this 

 tract, except near the edges of it, the motion was 

 most conspicuously of subsultory character ; i.e., 

 motion in which the vertical component predomi- 

 nated over the horizontal. The marginal portions 

 of this area, where the character of the movement 

 changes, and where the intensity falls off most 

 rapidly, seem to be very well indicated. The 

 positions vvhere the intensity most rapidly declines 

 may be located vpith an error not exceeding one 

 or two miles on both sides of the epicentres. The 

 South Carolina railroad crosses the tract in a 

 straight line very near the most forcible seismic 

 vertical. The first point where the intensity falls 

 off with greatest rapidity is near the nine-mile 

 post, measuring from the railway depot in 

 Charleston ; and so well marked upon the ground 

 are the indications of this change, that it seems 

 very improbable that this point is more than a 

 mile distant either way from the precise point we 

 seek to locate. Passing north-westward through 

 Summerville to the opposite side of the tract, we 

 find the corresponding point of most rapid decline 

 in the vicinity of the twenty-third-mile post. 

 This gives us a base-line with which to measure 

 the depth of the focus of the principal shock. 

 The computed depth is twelve miles, with a prob- 

 able error of one or two miles. The computed 

 depths of the other foci are about the same, but 

 the probable errors are somewhat larger. 



In speaking of a focal point of a shock, it must 

 be understood as referring to the centre of all the 

 forces, considered with reference both to amount 

 and direction, which constitute a great seismic 

 impulse. The presumption is, that this impulse 

 originates in a large subterranean tract of which 

 this ideal focus is merely the central point, or 

 nearly so. The form of the subterranean tract 

 may be any thing, and, within limits, may have 

 its three dimensions (length, breadth, and thick- 

 ness) of any magnitude, and bearing any ratios to 

 each other. The form and dimensions of it, we 



