October 24, 1895] 



NATURE 



631 



period of growth the apex of this] organ became more or less 

 spherical, and finally withered away. 



Similar results had been obtained with the haustoria (modi- 

 fied roots) of Cuscuta, in a former research of George Peirce's. 



Another interesting achievement of the .*;ame worker was to 

 grow specimens of Pisum as parasites uix>n other plants, from 

 the seedling stage until flowering. The host which gave the 

 most favourable results appears to have been Inipatiens sullani. 



The young Pisum grown under these unwonted conditions 

 produced an almost normal root .system, with numerous side 

 branches ; but the stem was stunted in its growth, although it Ijore 

 leaves and a few flowers. The roots, it may be mentioned, were 

 here also devoid of hairs. This experiment is extremely interest- 

 ing in a great man)' ways. It shows, in the first place, how fine 

 is the line of demarcation between an ordinar)' earth-grown 

 ])lant, such as Pisum, and a phanerogamous parasite, especially a 

 partial parasite like mistletoe. 



Again, it has a physiological interest : it is suggestive of a new 

 path of research. -V strict and careful comparison of the details 

 of outwar<l form and internal anatomy in a normally grown 

 Pisum, or other plant, with those found in one which is, so to 

 speak, an inducetl jiarasite, must, Ixiyond all doubt, shed much 

 light upon the relationship between the shape and structure of 

 an organism and its surroundings. 



We know but too little of this branch of biology at pre.sent. 



Why an organ should be shaped this way in o'le individual 

 and that way in another, may indeed be jxirtially answered in 

 some cases ; but these instances are few, and the answers are in- 

 complete, to say the least nf them. Ri'doi.f Hi;i;r. 



DR. A. SCHMIDTS THEORY OF EARTH- 

 (-J QUAKE-MOTIOA. 



[NoTK. — The following pages contain a summary of an in- 

 teresting but little known jKiper by Dr. August Schmidt, of Stutt- 

 gart. .An English translation was prepared by the late Dr. E. von 

 Rebeur-Paschwit/ for the Seisiiwlogical Journal of /apan, but 

 arrived too late for publication in the concluding volume of the 

 series. The original being too long for insertion in N'.vruKE, I 

 have condensed it at the translator's rec|uest, at the same time 

 adhering as closely as possible to the author's words. The title 

 of the paper is " Wellenbewegung und Erdbeben ein Beitrag 

 zur D\Tiamik der Erdbeben " (/a/irishe/tc ila Vcrcius fiirvatiii. 

 Natiirkintdi in Wiirttcmhirg, iSSS, pp. 24S-270). In a later 

 [japer (same journal, 1S90, pp. 200-232), Dr. Schmidt applies 

 his Iheor)' to the Swiss earthquake of January 7, 1889, and the 

 Charleston earthquake of August 31, 1SS6. — C. Daviso.s.] 



CEISMOLOGISTS assume the proiagalion of earthquake- 

 "-^ waves to take place uniformly in all directions ; they regard 

 the coseismal or wave-surfaces as concentric spheres, the rays as 

 straight lines normal to the spheres. This, however, is an 

 entirely unjustified assun^ption, which certainly facilitates the 

 calculations, but leads to verj' doubtful results in determinations 

 of the velocity of propagation and of the depth of the earthquake- 

 centre. It is impo.ssible that seismic rays should be straight 

 lines, because the conditions on which the velocity dejwnds 

 undergo change with increasing depth below the surface. 

 Though experimental determinations of the velocity do not agree 

 with the theoretical \alue iji:ld, yet it is clear that the velocity 

 must depend on the density and cl.asticity of the rocks through 

 which the wave is proijagated. Now, the modulus of elasticity, 

 owing to increased pressure, must increase w ith the depth Ijelow 

 the surface ; and therefore the velocity of the earthquake-wave 

 mu.st also increase with the depth. 



As the velocity of proi)agation increases, the energy of a 

 vibrating particle diminishes : and thus, as is well known to be 

 the case, earthquakes should be less noticeable in mines than on 

 the surface of the earth. 



Amt>idiii<:»t of Hopkhii Law. — Let us imagine a wave em- 

 anating from a deep centre and propagated in all directions. 

 A vertical plane through the centre cuts all the successive 

 coseismal surfaces, as well as the earth's surface. Let us suppose 

 the section of the latter to be a horizontal straight line. The 

 lower ))arts of Figs, i and 2 show the successive positions of the 

 coseismal surfaces from minute to minute. Fig. I, with its equi- 

 distant concentric coseismals and its straight rays, corresponds 

 to the ordinarj' earthquake theory. Kig. 2, with its excenlric 

 coseismals approaching each other 4is they rise and with its curved 



NO. 1356, VOL. 52] 



rays convex downwards, represents our new theory. The 

 horizontal straight line, dividing the upper part of the figures 

 from the lower, represents the surface of the earth. In both 

 figures, the rays at first apjjear equally distributed in all directions 

 from the centre ; in Eig. i they remain so, but in Fig. 2, in 

 order to continue :iormal to the wave-surfaces, they must diverge 

 at a much more rapid rate below than above, thus becoming 

 convex downwards. Of course. Fig. 2 only repre.sents a special 

 law of increase of velocity with the depth — the velocity is sup- 

 ])osed to var)' as the depth — but the general character of the 

 figure with its rays convex below remains the same if the law 

 is a different one. 



-K comparison of the figures shows that in Fig. 2 there is a 

 greater condensation of the seismic rays, and therefore a greater 

 intensity of the shock, in the neighbourhood of the epicentre, 

 and this corres|X)nds better with the effects observed within the 

 area of greatest disturbance. 



But more important for our purpose are the sections of the 

 earth's surface contained between two successive coseismals. 

 Each of these sections is a measure of the distance through which 

 the wave appears to progress firom minute to minute at the sur- 

 face. In reality it progre.s.ses obliquely from below in the 

 direction of the rays, and the real distance through which it 

 moves is smaller than the apparent one. We can only observe 

 the apparent velocity at the surface. If we have at our disposal 

 a sufficient number of good time-observations, we can draw the 

 horizontal coseismal lines on a map and determine the apparent 

 velocity from their relative distances. In both figures, the 

 apparent velocity has its greatest value at the epicentre and 

 decreases outwards. In Fig. i, it gradually approaches asympto- 

 tically the true value in the direction of the rays. This is the 

 law which Hopkins propounded in 1S47. In Fig. 2, the ap- 

 [Kireni velocity at first diminishes rather ra|)idly, until it 

 reaches the value of the true velocity at the depth of the centre, 

 but afterwards it again increases gradually with the distance. 

 We thus arrive at the following amendment of Hopkins' law, 

 which will be expanded afterwards : the apparent velocity at the 

 surface is never less than the true velocity at the centre, and 

 varies with it. 



Differences in Eartluitiake Velocilies. — According to the old 

 iheorj', ever)' substance ought to possess its own velocity, de- 

 pendent on its internal structure. The limit, which is defined 

 by Hopkins' law as the lowest po.ssible value of the apparent 

 velocity, ought always to be the same in any given region. Ex- 

 periments Ijy Pfaff, Mallet, and .Vbbot lead to different values 

 for different substances, as was to be expected. But they also 

 show- considerable variations in the .same material, the velocity 

 increasing w ith the strength of the initial impulse. Real earth- 

 qua'Kes show even larger differences in velocity than artificial 

 ones, and often earthquakes of less intensity are iiro|iagated with 

 a greater velocity in the same region than very strong ones. 



■These diflerences are inconsistent with Hopkins' law. To be 

 explained by the old theory, they require for the centres of 

 earthquakes with great velocities an enormous depth below the 

 surface, a near approach to the centre of the earth, for an earth- 

 quake emanating from the centre itself would arrive simul- 

 taneously at all points of the surface. With our new hypothesis, 

 such differences are necessary, and even with the largest 

 velocities the earthquake-centre may be at a considerable distance 

 from the centre of the earth. 



Proof of the Law. — The law that the velocity at the surface is 

 never less than that at the earthquake-centre includes Hopkins' 

 law. This indicates th&t the law is a general one. Its mathe- 

 matical demonstration is contained in the law of retraction. We 

 may distinguish the following three velocities: (I) the velocity 

 at the centre, //, : (2) the tnie velocity at the surface, i.e. that 

 part of an earthquake-ray through which the wave progresses in 

 one minute, « ; (3) the apparent velixrity at the surface, i.e. the 

 horizontal distance between two successive co.scismals corre- 

 sponding to an interval of one minute, z\ -Vs an example, let us 

 lake in Fig. 2 the horizontal distance between the fourth and 

 fifth coseismals from the epicentre .as a representative of v, and 

 let the section of the ray between the .same coseismals near the 

 surface represent 11, and the di'^tance between the centre and the 

 first coseismal «,. Then, if a be the .angle between the ray and 

 the vertical at the point where it meets the surface, we have 

 !• = «/sin a ; and, if a, be the angle which the same ray makes 

 with the vertical through the earthi|uake-centre, we have by the 

 law of refraction v = «/sin a = «,/sin o,. 



Now, let us consider the different rays emanating from the 



