July 8, 1887.] 



SCIENCE. 



23 



The destruction about the epicentnjm of an earthquake depends 

 mamly, perhaps, upon the amount of motion, but partly also upon 

 the direction of motion ; horizontal motion being far more destruc- 

 tive than vertical. Now, the whole amount of motion is assumed 

 to decrease as the square of the radius of the agitated sphere in- 

 creases {i<x^) ; but the horizontal element of the motion 

 increases as the cosine of the angle of emergence. Under these 

 two conditions, there will be a certain distance all about the epi- 

 centrum, bearing a fixed relation to the depth of the focus, where 

 the horizontal element will be a maximum. This is at dd' (Fig. 3), 

 where the angle of emergence is 54° 44'. In other words, the 

 ■ circle of principal disturbance ' is the base of a cone whose apex 

 is at the focus, and whose apical angle is 70" 32'. The distance 

 ad of this circle from the epicentrum is to the depth of focus ax as 

 I toyz 



Now, it is e\'ident that in violent earthquakes the destruction over 

 the whole area of this circle might be nearly the same ; for in the 

 central parts the whole motion would be greater, and on the mar- 

 gins the sideways motion would be greater. But beyond this 

 circle the destructiveness would very rapidly decrease, because the 

 whole motion and the sideways element are both decreasing : in 

 other words, if we used the graphic method, the curve of de- 

 structiveness would be like the curve of intensity (Fig. i), except 



pose the spherical wave were cut off, not on one side only, but on 

 both sides; in other words, suppose a shock generating normal 

 circular elastic waves of compression to occur in the centre of a 

 thin plate : is it not evident that the intensity of these would vary 

 simply inversely as the radius (//a-)? Or, if the plane be re- 

 duced to a bar, such waves would be substantially constant in 

 intensity. 



But we are not left to general reasonings on the subject. If the 

 intensity or wave-height follow the law of inverse squares, it is im- 

 possible to understand how the waves should carry so far as we 

 actually find. In the Charleston earthquake the motion at the 

 distance of six hundred miles was still sufficient to create alarm 

 and to produce seasickness. Now, the amount of motion at the 

 epicentrum was not more than ten or twelve inches. Let us take 

 twelve inches as the greatest motion, and the epicentrum as ten 

 miles from the focus. At the distance of six hundred miles, ac- 

 cording to the usually assumed law of decrease, the amount of 

 motion or wave-height would be only a three-hundredth of an 

 inch ; but if the spherical wave is reflected back from the surface, 

 and combines with the advancing wave, it is probable that its de- 

 crease is only as the increase of the radius. In that case, at six 

 hundred miles the motion would still be a fifth of an inch, which is 

 a very sensible motion. 



that it would be flatter on the top, and the descent more abrupt at 

 a certain distance from the epicentrum. The decrease of destruc- 

 tiveness is more rapid at a certain point than is the decrease of 

 intensity. 



Now, since the intensity is estimated largely, if not wholly, by 

 destructiveness, and since destructiveness depends largely upon the 

 sideways motion, is it not possible, is it not even probable, that the 

 supposed place of maximum decrease of intensity is really the place 

 of maximum decrease of destructiveness ; i.e., the circle of princi- 

 pal disturbance ? If so, then the depth of the focus would be about 

 ten miles instead of twelve miles. 



We have assumed all along that the intensity or excursion of the 

 earth-particle, or the height or amplitude of the wave, varies in- 

 versely as the square of the radius of the agitated sphere (/ix-^). 

 The authors as well as all other writers assume this law. But is 

 there not good reason to doubt its accuracy .' The law is probably 

 true so long as the wave is spherical ; i.e., until it emerges on the 

 surface. But when it emerges, what becomes of the energy which 

 would have continued the wave if it had not been cut off by 

 emergence ? Some of it is doubtless consumed in more violent 

 motion, and perhaps rupture, at the surface ; but is not much of it 

 reflected back into the earth to combine with the advancing waves ? 

 All other elastic waves, whether light-waves or sound-waves, com- 

 ing out of a denser medium into a rarer (or vice versa), are largely 

 reflected from the surface : why not earthquake-waves also ? Sup- 



It is very important that investigations should be undertaken to 

 determine the law of decrease of wave-motion of earthquakes. This, 

 however, cannot be done without seismographs. 



While on this subject, it may be well to say something about 

 Seebach's method of determining the depth of the focus. The 

 method by the circle of principal disturbance, and that by maximum 

 decrease of intensity, are based on the law of inverse squares, and 



Fig. 



therefore fail if this law be untrue. Seebach's method, on the con- 

 trary, is based on the law of decrease of velocity of the surface 

 wave ; supposing, of course, a constant velocity of the spherical 

 wave. I have been in the habit of representing Seebach's method 

 as follows : on the co-ordinate axes A, B, C, D (cd being the 

 earth surface), of the earth, let equal times be taken on AB, and 

 spaces passed over in equal times on CD. The one represents the 



