632 



NATURE 



[October 24, 1895 



canhquakc-centre. When o, is equal to zero, v is infinitely 

 great. As a, increases, f decreases, until a, = 90'. This 

 corresponds to the ray which starts horizontally from the 

 centre, and at the point where this ray reaches the surface we 

 have V = «!. \\'hen a, becomes obtuse, the value of sin a, de- 

 creases again, and v increases, though more slowly because the 

 rays diverge more and more ; but at an infinite distance v would 

 again be infinitely great. 



The only condition by which our law is bound is that the true 

 velocity of the wave is always the same at the same depth ; but 

 the variation of velocity may follow any law. The law would 

 even remain true if the velocity were to decrease with the depth : 

 but in this case the rays would be concave downwards, and only 

 a few would reach the surface. But, as we have every reason to 

 believe that :• increases with the depth, it follows that the rays 

 must be convex downwards : and not only the ray which is hori- 

 zontal at first bends upwards, but all rays do so in time. The 

 whole disturbed area of an earthquake is thus divided into two 

 zones : an inner circle in which the apjxirent velocity ;■ decreases 

 as the distance from the epicentre increases, and an outer ling in 

 which ;• increases with the distance up to infinity. The inner 

 circle is the region of the direct rays, the outer ring that of the 

 earthquake energ)' which by refraction is brought up from below. 

 The smallest value of v, corresjwnding to the boundary between 

 the two zones, measures the velocity of projxigation at the ilejith 

 oi^he centre. 



Fiil 



l>ecomes concave downwards, and gradually becomes horizontal 

 again at infinity. If, in the lower part of the figure, we follow 

 the ray which leaves the centre horizontally until it reaches the 

 surface, a normal erected at this point passes through the 

 point of inflexion. 



It is important to study the changes in the form of the hodo- 

 graph as the depth of the centre gradually diminishes. The result 

 is that the two points of inflexion move towards the epicentre, the 

 convex portion becomes smaller, and so also does the "inner 

 zone" of the disturbed area. When the centre and epicentre 

 coincide, the convex portion of the curve and the inner zone of 

 the disturbed area disappear entirely : the hodograph consists 

 uf two symmetrical concave branches which meet at an angle at 

 the centre. This suggests to us how we should explain the 

 results of measurements of velocities in artificial earthquakes. 

 In a shock produced at the surface of the earth, the velocity 

 must increase from the centre outwards. The stronger the 

 charges of gunpowder are, the longer are the distances that can 

 be employed in the experiments, and the greater the mean values 

 of the velocity obtained. 



'* The efl'ecl of cur\ature of the earth's surface, which we have 

 so far^ncglecied, will omsist m u dimniution of the rate at 

 which the velocity increases in the outer zone. 



Tlu Earlki/iiaic Hodograph.^ — The law connecting the 

 variations in the apparent velocity at the surface is lM;.st ex- 

 plained by the upper [larts of I'igs. i and 2. .-^t the points where 

 tt,. .,,rf ,. .■ line is cut by the coseismals, normals are erected to 

 I '.f I, 2, 3, &c. , units in length, representing the 



in lime from that at the epicentre. A curve passing 

 I ilie ends of these normals represents what wc call the 

 i ■ph. The grc-ater the inclination of the curve to the 

 . the less is the apparent velocity, f, at the corre- 

 iit of the curve. Where the curve is horizontal the 

 ....... I- ■nfinitely great, where it is convex downwards the 



velocity decrease-, outwards, where it is concave the velocity 



\\v r. .I-' s. The htKlograph in I'ig. i is the hy(>crlx)la of von 



' Minnigcrode. If we use the same scale for the units 



I v<'|fK-iiy, the hy|HTl>ola is rectangular and the 



■ I I ■ u i- ihe centre. In I'ig. 2, the 



I lif ; at the epicentre it is 



M .lii'i >' N M'>>\ii»,iid.<>, gradually approaching a 



im inclination at a point of inflexion, after which it 



■ \ H.-Amillon to a ciirvc which re. 

 . nf a tnovinu ixiiril. W'c <lo not 

 \\\\\ nuinc fur uur purnov:. 



SO. 1350, VOL. 52] 



Thus, the form of the hodograph will xary much with the 

 depth of the centre, and it must also vary with the law which 

 expresses the change of velocity with the dei)lh. But, wliatever 

 be Ihe unknown law , the hodograph must alwajs be convex at 

 the epicentre, and, passing ihrough a iwint o( inflexion, after- 

 wards become slightly concave. This follows simply from Ihe 

 law of refraction without any regard to the rate at whicli llio 

 velocity increa.ses with Ihe depth. 



.\s long as we do not possess a sufliciently large numlur of 

 time-ob.scrvations for at le.ist one earthquake, it will be 

 impossible lo draw any ciinclusion concerning Ihe law of velocity 

 from the form of Ihe hodograph. i'.ven with the best observa- 

 tions, we can never, in drawing the hodograph, expect that all 

 points will fall on a regular and continuous curve. Hut what we 

 may ex|)cct is thai, with a suflicienlly large number of observa- 

 tions, the points will be distributed equally on both sides of such 

 a curve. The ho<lograph contains the observations from places 



