In examining this diagram it must be remembered that near to an origin the difference in time between the maximum phases of an earthquake and its actual commencement may be only a few seconds, while at a great distance the records of sensitive instruments show that the same interval may be many minutes. When instruments of such sensibility are near to an origin, my own observations seem to show that they are not set into any sensible amount of motion before the ordinary seismoscopes or seismographs, and therefore for places comparatively near to the origin of a disturbance, when observations were made with the latter type of instrument, I should be inclined to think that the phases of maximum motion might be approximately coincident with the times of commencement of movement.

An inspection of the diagramı points towards the following results :

No. 1. The velocity for the first 550 km. is greater than it is to a point which is more remote.

No. 2. This is the only disturbance for which observations are made at points comparatively near to the epicentre, for which they show a very high velocity. Between stations distant 300 and 1,100 km. from the origin the velocity decreases, but beyond this limit it apparently increases.

No. 3. The chief difference between this and No. 2 is that the point of inflexion of a free curve drawn between the points of observation, instead of being at a distance of 1,100 km. from the epicentre, is at about 1,300 km. from that point.

No. 4. The velocity is apparently greater at a distance from the epicentre than near to it.

No. 5. This resembles No. 4.

If we omit the one case which shows a high velocity in the immediate neighbourhood of the origin-which, however, is in perfect accordance with results obtained with artificially produced disturbances-there remains the clearly marked observation that to Catania and Mineo the velocities are, as compared with the rate of propagation to more distant stations, relatively low. Professor A. Ricco, who discusses these observations, gives us every reason to believe that the time observations at Catania are correct, while those at Mineo may be in error, owing to the manner in which it receives the time signals from Rome, which finally reach the observatory by circolare.

Professor Ricco concludes that the low velocity between Zante and Catania may be accounted for by the fact that the motion was entirely transmitted through water, because the velocity recorded of 1,439 km. per second practically coincides with that of a sound wave in water. Professor Ricco adds that Bertelli has shown that the shocks of earthquakes felt on shipboard and the sound waves have been simultaneous. From one of Abbot's experiments, however, we have seen that a wave velocity obtained from a water path was greatly increased.

The following is Agamennone's table of velocities, which, although they represent averages, show that the lowest is the one on August 4, which had the shortest range :—

The averages of velocities to the Italian stations and the actual velocities to Mineo and Catania, which may be compared with the first determination in the preceding table, clearly show that the apparent velocity to the nearer stations was lower than it was to stations which were more distant:

Dr. A. Cancani, who has devoted much attention to the velocities with which earth disturbances are transmitted, is apparently inclined to attribute the high velocities sometimes observed near to an epicentre-which, however, is not the case with those just quoted-to the more rapid transit of a longitudinal wave. He, however, adds that at such places, and even at distant places, the normal and transversal waves may occur together, and the velocities determined on such occasions will have intermediate values. In fairly homogeneous earth it has been shown that, within 100 feet or so from the origin of an artificial disturbance, a normal movement outraces the transversal disturbance, but such a separation is not observed, nor should we expect it to be observed, at distant stations (see pages 162 and 163).

When Dr. Cancani quotes my opinions that 'velocities of 2 or 3 km. per second refer to the propagation of a motion not unlike the swell upon an ocean' as not being contrary to his ideas, it must be clearly understood that I do not refer such movements to the purely distortional elastic waves of an isotropic solid.1

Amongst other observations quoted by Dr. Cancani to show that the velocity with which earthquake waves are propagated is higher nearer to an epicentre than at a distance, I select the four following, which have reference to the Andalusian disturbance of December 25, 1894 :

Dr. Agamennone, after examining the data on which these tables are founded, shows that the conclusion to which they point disappears if the time taken at Cadiz by the stopping of two clocks was a minute too late, while the times at Greenwich and other observatories correspond to the beginning of the motion. From the calculations of Offret relating to the Ligurian earthquake of February 23, 1887, it would appear that the velocity of propagation increased as a disturbance radiated, but such anomalies may also be explained by the assumption that there were errors in the time observations near to the epicentre.

As another indication of what is apparently the reverse of the results adduced by Dr. Cancani, we may take either the earthquakes of Zante or the following Japanese earthquakes, observed in Europe by Dr. E. von Rebeur-Paschwitz :

:

The centre of the second disturbance is taken near to Kumamoto, while that of the others as being near to Tokio.

Arranging the above according to distance, we find :

6 observations for 7,910 km. give a velocity of 2.73

The numeral I. refers to the greatest increase in motion, while II. refers to the maximum itself, and it will be observed that the value for II. is always less than it is for I.

A good series, showing the widely different results which may be obtained as to the velocities with which given disturbances are propagated, may be found in the British Association Report of the Committee on Earth Tremors for 1894. The earthquakes to which these refer are those of April 20 and 24 of 1894, which originated in North-east Greece, and which were recorded by different types of instruments at 41 different stations in Europe, the length of the wave paths being from 701 to 2,455 km. The velocities obtained vary between 1.29 and 11·71 km. per second. The high velocities are those obtained from records of the com

mencement of movement by the more sensitive classes of instrument, the records from which also give the lower values, if the arrival of the disturbances is taken as being the time when they recorded maximum phases of motion.

As a last example of the different results which may be obtained from the same record, I take that observed at Rocca di Papa on March 23, 1894. The shock originated beneath the ocean about 70 miles S.E. of Nemuro, on the north-east coast of Yezo (Lat. 42° N., Long. 146° E.). It was observed at Nemuro in Greenwich mean time at 10.20.45 A.M. The times at Rocca di Papa and the resulting velocities were as follows:

In Tokio it was observed at 10.27.40 G.M.T., after which four aftershocks were noted. The average time difference between the observations at Tokio and Nemuro was 6 min. 43 sec., and the difference in their distances from the origin is about 600 miles, from which an average velocity of about 2-3 km. per second is calculated. If it is assumed that the first tremors reached Rocca di Papa by direct radiation along a chord or through the earth, then their velocity may be reduced to 8 or 10 km. per second (see example on p. 149).

3. Conclusions.

Very many records might be added to those which have been given, but it does not seem likely that, until we are in possession of a series of records taken at long distances apart on the surface of our globe by means of instruments which are similar, which have sufficient sensibility to record preliminary tremors, and which record upon surfaces moving sufficiently quickly to allow of accurate time determinations, that our present knowledge will be greatly increased. Because the waves of a disturbance change in period as they travel, while one wave breaks up to form two or more waves, and this even in ground which is apparently homogeneous, a given earthquake may show as many velocities as there are waves between which we choose to make measurements. What we know from experiments, and what we should expect from à priori reasoning, is that the rate at which a disturbance is propagated varies with the nature of the medium through which it is transmitted. Experiments have shown that the vibrations following an artificial disturbance, where the initial impulse has been strong, travel more quickly than those where the originating cause has been feeble; also that there is apparently a higher velocity very near to an origin than at a distance. The latter phenomenon seems to find confirmation in the records of certain earthquakes. Although it may be difficult to interpret the meaning of these latter observations, when we endeavour to find an explanation for the existence of the long series of preliminary tremors. which are recorded at places nearly a quarter of the earth's circumference from an origin, and which have apparently reached these places by travelling at rates of 9 to 12 km. per second, the difficulties which confront us are still greater. The next section is an attempt to explain these phenomena.

(e) On the Probable Nature and Velocity of Propagation of the

Movements resulting from an Earthquake Disturbance.

If it is assumed that the crust of the earth has the character of an isotropic elastic solid, then from an earthquake centrum two types of waves may emanate. In one of these the direction of vibration of a particle is parallel to the direction of propagation of the wave or normal to its front, as in a sound wave, whilst in the other it is transverse to such a direction, or, so far as this character is concerned, it is like the movements in a ray of light.

These two types of movements, which are respectively known as condensational and distortional waves, are propagated with different velocities, which depend upon certain clastic moduli and the density of the

material.

These velocities may be respectively expressed by the quantities m/p and no, where p is the density of the material, n the modulus of rigidity or resistance to distortion, and m a modulus depending upon the modulus of rigidity and the bulk modulus or resistance to compression k, which is equal to k+n.

From

The first conclusion to which the theory leads is that the condensational wave has a higher velocity than the distortional wave, and therefore the first ought to outrace the latter. With artificially produced disturbances at points near to origins in fairly homogeneous earth, a phenomenon similar to this has been observed, but whether the preliminary tremors preceding more decided movements observed at great distances represent condensational waves propagated from an origin is yet uncertain. experiments made in conjunction with Professor T. Gray to determine the elastic moduli of granite, marble, tuff, clay rock, and slate, and the velocities with which normal and transverse movements have been propagated in alluvium, Dr. C. G. Knott drew up the following table as representing average constants involved when determining the velocities with which disturbances may be propagated through fairly solid rocks :

Density
Rigidity

Ratio of the wave moduli

p=3

n = 1.5 x 10" C.G.S. units m/n=3

With the above numbers the velocity of a distortional wave would be 2-235 km. per second, while the condensational wave would have a value about double this quantity. Should we accept the records made of decided movements which had their origin in Japan, but which have been recorded in Europe as representing distortional waves, then our expectations based upon theory closely accord with what has been observed.

On the other hand, because it has been shown that small vibrations have been noted which have travelled at rates of from 9 to 12 km. per second, the fact must not be overlooked that we are not yet in possession of sufficient constants to apply the theory to all the cases which have been observed. Even if we had the constants referring to the elasticity and density of material in the interior of our earth, when we consider the heterogeneity of the materials through which a disturbance probably passes, as Dr. C. G. Knott and other writers point out, there are serious objections to the assumption that waves with a high velocity are due to the transmission of normal motions, while those with a lower velocity represent the less rapid transversal vibrations. At every boundary