("Report of British Association, 1847"), it will be seen that the solutions of the problems which he there gives for finding the depth of focus of shock are founded upon the velocity of propagation of the wave in the interior of the mass, the apparent horizontal velocity and the horizontal direction of propagation at any proposed point being known (p. 82).

By this it appears plainly that at that time Mr. Hopkins supposed that it was the velocity of translation of the wave of shock that did the mischief, and not the velocity of the wave particle, or wave itself. And, further, that the former might be obtained by reference simply to the modulus of elasticity of the rock of any given formation, as, indeed, was my own earliest view when I produced my "Dynamics of Earthquake" in 1846. From the remarks already made as to the vast difference between the actual transit velocity in more or less discontinuous rocks—such as they occur in Nature—it will be equally obvious that Mr. Hopkins's methods, as above mentioned, are impracticable, even were there no confusion between the velocity of translation of the wave and that of the wave particle or wave itself.

This applies also to the demonstration and diagram (taken from Hopkins) given by Professor Phillips ("Vesuvius," pp. 258-259).

In December, 1857, occurred the great Neapolitan Earthquake, which desolated a large portion of that kingdom; and an opportunity then arose for practically applying to the problems of finding the directions of earthquake shock at a given point through which it has passed, and ultimately the position and depth of focus, other methods, which I had seen, from soon after the date of publication of my original Paper (1846), were easily practicable, and the details of which I had gradually matured.

Bearing in mind that, in the case of the normal vibration in any elastic solid of indefinite dimensions, the direction of motion in space of the wave particle coincides in the first semiphase of the wave, and at the instant of its maximum velocity with the right line joining the particle and the focus or centre of disturbance, it follows that, in the case of earthquakes, the normal vibration of the wave of shock is always in a vertical plane passing through the focus and any point on the earth's surface through which the shock passes (assuming for the present no disturbing causes after the impulse has been given), and that at such a point the movement of the wave particle in the first semiphase of the wave is in the same direction or sense as that of translation; and at the moment of maximum velocity the direction in space of the motion of the wave particle is that of the right line joining the point through which the wave has passed with the focus or centre of impulse.

If, therefore, we can determine the direction of motion of the wave particle in the first semiphase, and its maximum velocity, we can obtain, from any selected point, a line (that of emergence of the shock) somewhere in which, if prolonged beneath the earth, the focus must have been; and if we can obtain like results for two or more selected points, we decide the position and the depth of the focus, which must be in the intersection of the several lines of direction of the wave particle motion at each point, when prolonged downwards.

Now, as I have said, it is the vibration of the wave itself, i.e., the motion of the wave particle that does the mischief—not the transit of the wave from place to place on the surface; just as in the analogous (but not similar) case of a tidal wave of translation running up an estuary and passing a ship anchored there, it is not the transit up the channel, but the wave form itself—i.e., the motion of the wave particles—that lifts the ship, sends her a little way higher up channel, drops her to her former level, and sends her down channel again to the spot she lay in just before the arrival of the wave.

Everything, therefore, that has been permanently disturbed by an earthquake shock has been thus moved in the direction and with the maximum velocity impressed upon it by the wave particle in the first semiphase of the wave; and thus almost everything that has been so disturbed may, by the application of established dynamical principles, be made to give us more or less information as to the velocity of the wave particle (or as we, for shortness, say, the velocity of shock), the direction of its normal vibration, and the position and depth beneath the earth's surface, from which came the generating impulse. We thus arrive at these as simply and as surely as we can infer from the position taken by a billiard ball, on which certain forces are known to have acted, the forces themselves and their direction; or, from a broken beam, the pressure or the blow which fractured it.

It is obvious, then, that nearly every object disturbed, dislocated, fractured or overthrown by an earthquake shock is a sort of natural seismometer, and the best and surest of all seismometers, if we only make a judicious choice of the objects which being found after such a shock, we shall employ for our purpose. This was the principle which I proposed to the Royal Society at once to apply to the effects of the then quite recent great Neapolitan Earthquake of 1857, and which, through the liberality and aid of that body, I was enabled to employ with the result I had pretty confidently anticipated, namely, the ascertainment of the approximate depth of the focus.

Every shock-disturbed object in an earthquake-shaken country is capable of giving some information as to the shock that acted upon it; but it needs a careful choice, and some mechanical νους, to select proper and the best objects, so as to avoid the needless perplexity of disturbing forces not proper to the shock, or other complications.

When properly chosen, these natural seismometers, or evidences fitted for observation after the shock, are of two great classes, by which the conditions of the earthquake motion are discoverable:

• 1. Fractures or dislocations (chiefly in the masonry of buildings), which afford two principal sources and sorts of information, namely:
  
  • a. From the observed directions of fractures or fissures, by which the wave path, and frequently the angle of emergence, may be immediately inferred.
  • b. Information from the preceding, united with known conditions as to the strength of materials to resist fracture, by which the velocity of the fracturing impulse may be calculated.
• 2. The overthrow or the projection, or both, of bodies large or small, simple or complex. From these we are enabled to infer:
  
  • c. By direct observation, the direction in azimuth of the wave path.
  • d. By measurements of the horizontal and vertical distances of overthrow or of projection, to infer either the velocity of projection, or angle of emergence.

Fractures by shock present their planes always nearly in directions transverse to the wave path. Projections or overthrow take place (unless secondarily disturbed) in the line of the wave path, or in the vertical plane passing through it: but the direction of fall or overthrow may be either in the same direction as the wave transit (i.e., as the motion of the wave particle in the first semiphase), or contrary to it.

It is thus obvious that the principal phenomena presented by the effects of