Great Neapolitan Earthquake of 1857/Part II. Ch. XIV

by Robert Mallet

CHAPTER XIV.

DIFFERENCE IN AZIMUTHS OF PRIMARY AND OF SECONDARY SHOCKS AT CERTOSA—ANGLE OF INTERSECTION.

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I now proceed to consider the angle of intersection in an horizontal plane, made by these two shocks at the Certosa. Referring again to the two great stone balls (one along with its base) projected from the top of the Campanile upon the roofs of the front square, (Fig. 1 Diagram No. 238 and Diagram No. 240, and Photog. No. 227 (Coll. Roy. Soc.) in which the ball B is seen lying, where it fell), we are enabled from these to infer the wave-path of the first shock with some certainty.

Both balls were projected from the Campanile in a direction 64° W. of north, and precisely alike.

The first shock, arriving from somewhere between north and east, caused the Campanile to oscillate from west to east and east to west; i. e. in the line of its narrowest dimension of base.

The balls were thrown off in the second semiphase of the wave; therefore, and as the time of oscillation of the tower (from its altitude) was large, and greater than that of the whole phase of the wave they were projected with a velocity less than that due to the shock; the top of the tower moving, by its elasticity and inertia, towards the east, at the same time that the forward movement of the whole mass towards the west, by the wave of shock, projected the balls with a velocity equal the difference.

We shall take the velocity from the ball B, which fell unencumbered by its base, and whose mark where the sphere struck and fractured the tiling of the roof, at B, (Fig. 1, Diagram No. 238, and Fig. 2, Diagram No. 240,) left no doubt as to its precise range.

This ball was projected a horizontal range of 12 feet, along the plane of projection, and descended vertically 42 feet from the summit of the Campanile to the roof tiling.

We may assume the angle of emergence for this shock $e=20^{\circ }$, the same as that of the primary shock (15° W. of north to south) here; because although coming from the limestone in which (at Padula) we found the emergence greater = 25° 30′, yet we are here some hundreds of feet lower, and the shock, in passing from the limestone into the clays and gravel, intervening before reaching the Certosa, must have suffered some refraction into a rarer medium, both tending to reduce the value of $e$.

Both these balls were attached to their pedestals or bases by a small wrought-iron dowal inserted into both, sufficient in strength to communicate its velocity from the base to the ball, but permitting easy separation of the two (i. e. ball and base) when not rusted into the sockets. It was so rusted, in the ball A which fell with its base, but in B, the dowal, which was about half an inch diameter, was found broken off, either previous to, or during the fall of the ball.

It must be borne in mind, in considering what follows, that these balls, and more particularly that B, were projected by the transverse shock, the impressed movement being therefore in the same direction as that of the wave, but had their plane of projection altered by the immediately following main shock, which, acting on them by inertia, impressed a movement in the contrary direction to that of the wave. Unless this were understood the path obtained by the following method would appear erroneous.

We obtain the velocity of projection from the equation

$\mathrm {V} ^{2}={\frac {a^{2}g}{2\cos ^{2}e\left(b+a\tan e\right)}}$,

in which

$e=20^{\circ },~b=42{\mbox{ feet}},~a=12{\mbox{ feet}},$

and

$\mathrm {V} =11.54{\mbox{ feet per second.}}$

This was the velocity in the plane of projection 64° W. of north, but this direction was not that of either shock but a resultant of both, the ball having necessarily received a certain amount of impulse from the first shock, and before it had completely parted hold from its support, been exposed to the impulse of the second. Now the direction of the second (i. e. the main) shock was 15° W. of north to south, and we have already ascertained at several points that its velocity was 12.97 feet per second. We have, therefore, two velocities, and the direction of the resultant, and of one component given, to find the direction of the other component.

Resolving, we find that the transverse shock made an angle with the primary or main one of 56° 40′, and that the wave-path or direction of the former was 41° 30′ E. of north to south, which is precisely the direction of a line drawn from the extremity of the mountain range northward and eastward of Padula and to the Certosa, as may be seen by examining Zannoni's great map (Sheet 19). The range, after running nearly north and south, terminates at Padula, after having made an abrupt bend to the westward in the above azimuth (by compass) from the Certosa. Hence it is to be inferred that the transverse shock (the first in point of time) was delivered from the free extremity of the range of limestone mountain, along the axis of which it had followed, while the great primary or direct shock (the second in point of time) came normally through the clays, gravels, and other formations, beneath and in, the Vallone di Diano, both intersecting at the Certosa.