298 



NA TURE 



[ytdy 28, 1887 



graphic representation of the way in which the surface 

 intensity varies along a line radiating from the epi- 

 centre. 



The first noteworthy feature of this curve is the contrast 

 between the rapidity with which the intensity diminishes 

 near the epicentre and the slowness with which it dimin- 

 ishes at remote distances. Thus, at a distance from the 

 epicentre equal to the depth of the focus, the intensity 

 has fallen one-half ; at twice this distance it has fallen to 

 one-fifth ; and at three times the distance to one- tenth of 



Fig. r, 



the intensity at the epicentre. This suggests at once the 

 possibility of making an approximate estimate of the 

 depth of the focus, based upon the rate at which the 

 intensity of the shock at the surface diminishes in the 

 neighbourhood of the epicentre. If we were able to con- 

 struct upon any arbitrary scale whatever a series of 

 isoseismal curves around the central parts of the earth- 

 quake with an approach to accuracy, this depth would 

 follow at once from the relations of these isoseismals to 

 each other. In the case of a very powerful earthquake in 



0' ' $ 6 '9 



Fig. 2. — Energy constant, depth varying in ratios i, 2, 3, and 4. 



a region which is so flat and uniform in its features as the 

 vicinity of Charleston, this can be done with a rough 

 approach to accuracy. 



To appreciate more fully the validity of this mode of 

 reasoning, let us take a series of these intensity curves 

 and vary the values of the constants. And first let us 

 suppose the total energy of the shock measured by the 

 constant, a, remains the same, while the depth of the 

 focus varies. The first series of curves (Fig. 2) will enable 

 us to make a comparison of the effect of two or more 



shocks of the same total energy but originating at dif- 

 ferent depths. The intensity at the epicentre being in- 

 versely proportional to the square of the depth, the 

 shallower shock would be much more energetic than the 

 deeper one ; while at a great distance from the epicentre 

 the two would be approximately equal in their effects. 

 The rate of diminution of intensity would be correspond- 

 ingly varied, and we might commit large errors in esti- 

 mating these ratios on the ground, while the error of the 

 depth deduced for the focus would be less than our errors 

 of estimate. In short, the method is not sensitive to small 

 or moderate errors of observation. 



The second series of curves (Fig. 3) is conditioned upon 

 the assumption that the depth remains constant while the 



Fig. 3. — Depth constant, energy varying from i to 6. 



energy of the shock varies. In these curves, the ordin- 

 ates corresponding to any abscissa are proportional to 

 each other in a simple ratio. In the first series they are 

 proportional to each other in a duplicate ratio. 



The third series (Fig. 4) represents the effect of varying 

 both the energy and the depth in such a way that the 

 intensity at the epicentre is constant. 



It will appear, therefore, that every shock must have 

 some characteristic intensity curve, depending upon the 

 total energy and the depth below the surface. The in- 

 tensity at any point along the surface will therefore depend 

 upon these two quantities : energy and depth. It still 

 remains to find some means of discriminating whetheV 

 the intensity at any point is due to a more energetic 



Fig. 4 — Depth and energy both varying, but with constant intensity at the 

 epicentrum. 



shock deeply seated, or to a less energetic one nearer the 

 surface. The criterion is soon given. 



It is obvious that in any shock there is some point at 

 some particular distance from the epicentre at which the 

 rate of diminution of surface intensity has a maximum 

 value. As we leave the epicentre and proceed outwards 

 in any direction, the intensity diminishes at first more 

 and more rapidly, but further 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 represented at the point of in- 

 flexion 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- 



M\ 



