July 28, 1887] 



NA TURE 



299 



of the curve twice, and equate the value of the second 

 differential coefficient to zero, and deduce the correspond- 

 ing value of the abscissa x — 



.hich equation is satisfied when 



whence 



Zax"- — 2a{q^ -\-x^), 

 ^'3 



In this value of j.-, it is seen that the constant, a, has dis- 

 appeared, 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 abso- 

 lute standard of measurement of the intensity, and all 

 that we require is to find with reasonable approximation 

 the points where the intensity 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 series of observations. In the brief time at his 

 disposal he accumulated 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 engage- 

 ments 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 varia- 

 tion of intensity along several lines radiating from it. 



The suniniary 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 miles 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 having a focus of its own. 



Much of the most powerful shock centres in the 

 northernmost focus, though the other two were of suffi- 

 cient energy to have occasioned great havoc if either of 

 them had occurred alone. The southernmost was also 

 considerably more energetic than the middle one. The 

 distance between the northern and southern epicentres 

 was about twelve miles. Within this tract, except near 

 the edges of it, the motion was most conspicuously of 

 subiulton- character, ie. motion in which the vertical 

 component predominated 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 where the intensity most rapidly declines 

 may be confidently located with an error not exceeding 



10 or two miles on both sides of the epicentres. The 

 -luth Carolina Railroad crosses the tract in a straight 

 line very near the most forcible seismic vertical. The 

 first point where the intensity falls ofT with greatest 

 rapidity is near the ninth 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 probable 

 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 presump- 

 tion 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 niay be 

 anything ; and, within limits, may have its three dimen- 

 sions, length, breadth, and thickness, of any magnitude, 

 and bearing any ratios to each other. The form and 

 dimensions of it we cannot of course determine, though it 

 may be possible to obtain some notion of its most general 

 features if the data are sufficient. 



This method of computing the depth of a seismic focus 

 is here proposed for the first time. The method employed 

 by Mallet, which consists in finding the angle of emerg- 

 ence of a wave front from the earth by studying the 

 configuration of cracks in buildings is believed to be 

 valueless by nearly all seismologists. There is no definite 

 angle of emergence of the nature he contemplates dis- 

 closed at the surface. • Certainly in Charleston there was 

 nothing of the kind to be found. The method employed 

 by Seebach is sound in theory, but it requires such 

 extreme accuracy of time determinations that very small 

 errors of time give very large errors in the result. Our 

 own method consists of finding two points on opposite 

 sides of the seismic vertical, at which the changes in 

 seismic action along a given line are most strongly 

 marked. These points ought to be indicated in powerful 

 earthquakes with a fair approach to precision, and the 

 probable errors of determination should not usually 

 exceed one or two tenths of the distance between the two 

 points. The feebler the shock, however, the less is the 

 degree of precision to be expected. Whatever may be 

 the errors in the estimate of this distance, the resulting 

 error in the computed depth is smaller than the error of 

 observation in the ratio of the square root of three to two. 

 How much the estimate may be vitiated by want of 

 homogeneity in the superficial strata we have no means 

 of determining, but we do not believe that it would be so 

 affected to any great extent in such a region as South 

 Carolina. Being independent of any absolute measures 

 either of the surface intensity or of the total energy of the 

 shock, the greatest difficulty of all is at once eliminated. 

 Our opinion of this method is that it is incapable alike of 

 very great precision and of very great errors 



Probably the first thought occurring to anyone ex- 

 amining this method will be that the determination of the 

 two required points would be liable to very large errors. 

 But if he will examine the varying values of the ordinates 

 of the curve corresponding to varying values of the ab- 

 scissa;, and of the depth, we think he will be satisfied 

 that the limits within which each of the two points of in- 

 flexion must fall cannot be wide apart, and that an error 

 in the determination of the base-line greater than two- 

 tenths of its estimated length would, in such a country as 

 Carolina, be very improbable. It will appear that the 

 relations of these variables are such as to restrict the locus 

 within which the desired points are to be found to a very 

 narrow annulus around the epicentrum. We think the 

 method will greatly improve on acquaintance. 



We have endeavoured to apply our method of comput- 

 ing the depth of the focus to other earthquakes, but have 

 found difficulty in obtaining anything more than very 

 general results, such as the following : — The depth of the 



