y=a/(c^2+x^2)
The inclination of the curve at any point is given by
dy/dx=-2*a*x/(c^2+x^2)^2,
and this is a maximum when
d^2y/dx^2 or (3*x^2-c^2)/(c^2+x^2)^3
is zero, which is satisfied when c=x*sqrt(3)
[43] _British a.s.sociation Report_, 1858, pp. 101-103.
[44] The above time would have to be increased by one second if the depth of the focus were very small, and diminished by one second if it were as great as 23 miles; the difference in either case being less than the probable error.
[45] The method employed is as follows: Let t_0 be the computed time (9h. 51m. 6s.) at the focus, _x_ seconds the error in this estimate, _t_ the reported time at a given place, _D_ its distance from the focus in miles, and _y_ the number of seconds required to travel one mile; then, a.s.suming that _y_ does not vary with the distance, we have x+Dy=t+t_0. An equation of this form is obtained from each observation, and the method of least squares is then applied to determine the most probable values of _x_ and _y_.
[46] This seems to me the more probable course. It is possible, however, that the fault-line may pa.s.s from Mount Holly Station to the east of the Woodstock epicentre as shown in Fig. 28, and then to the west of the Rantowles epicentre, the fault changing its direction of hade in the intermediate district.
CHAPTER VI.
THE RIVIERA EARTHQUAKE OF FEBRUARY 23RD, 1887.
Few earthquakes have aroused a more widespread interest than those which struck the thronged cities of the Riviera on February 23rd, 1887. The first and greatest of the shocks occurred at about 6.20 A.M., the second nine minutes later, and the third, intermediate in strength, at about 8.51 A.M.[47] All three shocks were of destructive violence, the damage wrought by them extending along the coast and for a short distance inland from Nice to beyond Savona. Most of the injury to property and nearly all the loss of life were, however, concentrated on the eastern side of the frontier; and it therefore fell to the lot of the Italian Government to provide for the scientific investigation of the earthquakes, as well as to meet the wants of those deprived of home and support. Professors Taramelli and Mercalli, who two years before had studied the earthquakes in Andalusia, were again nominated, the former to examine the geology of the central regions, and the latter to report on the seismic phenomena. Their joint memoir forms one of the most complete accounts that we possess of any earthquake, and is the chief authority for the description given in this chapter. Another valuable monograph is that prepared by Professor A. Issel, of Genoa, who received an independent appointment from the same Ministry. A third official commission was also sent to estimate the amount of damage caused by the earthquakes in the Italian towns and villages. In France, the destruction of property was much less serious, and attention was confined chiefly to the records of the shock provided by magnetographs and other instruments in distant observatories. In Switzerland, the effects remarked were merely those due to the evanescent vibrations of a remote earthquake; but many interesting records were collected by the permanent seismological commission established in that country.
DAMAGE CAUSED BY THE EARTHQUAKES.
Owing to variations in the nature, foundation, and site of buildings, there is always great diversity in the destructive effects of an earthquake. In one and the same town, most of the houses may be razed to the ground, while in their midst may be found some that are shattered but still standing, and others perhaps that are practically unharmed. The stronger after-shocks often complete the ruin of the partially damaged houses; though in such cases the real loss is as a rule comparatively small.
The close succession of the two strong after-shocks of February 23rd made it impossible as a rule to separate their effects from those due to the first shock; but it has been roughly estimated that about one-quarter of the total damage was caused by the two after-shocks together. To them also must be referred in part the comparatively small number of wounded, many persons buried beneath the ruins having no doubt perished from subsequent falls before they could be extricated.
Taking all three shocks together, the total loss to property, according to Professor Mercalli, must be valued at about 22 million francs in Italy alone. For the province of the Alpes Maritimes in France, full details are wanting, but the loss there cannot fall far short of three million francs. The total amount of damage must therefore be placed at about a million pounds. From the figures given by the official commissions, it appears that the earthquakes were most disastrous at Diano Marina and Diano Castello; while other places, such as Oneglia, Bussana, Baiardo, Pompeiana, and Vallecrosia, suffered only a little less severely. At Mentone about 155 houses, and at Nice about 61 houses, were rendered uninhabitable, and many others were badly injured.
In Italy, 633 persons were killed, 432 seriously wounded, and 104 slightly wounded; in France, 7 persons were killed and 30 seriously wounded, the number of persons slightly wounded being unknown. The majority of the deaths occurred in two or three places. Thus, at Diano Marina, 190 persons were killed and 102 wounded; at Baiardo, 220 were killed and 60 wounded; at Bussana, there were 53 killed and 27 wounded. The death-rates were, however, comparatively small, amounting for the above places to not more than 8-1/2, 14, and 6-1/2 per cent., respectively; figures which only slightly exceed those obtained for places in the meizoseismal area of the Andalusian earthquake.
Though the damage can hardly be regarded as excessive, it was nevertheless largely due to the peculiar architecture prevalent in the Riviera. Arches in the walls are common even in the upper storeys, and, in Oneglia and Diano Marina, if not also in other places, the floors are nearly always brick arches ab.u.t.ting against the walls and without other lateral support. Professor Mercalli believes that, in private houses, more than 90 per cent. of the dead bodies were crushed beneath these fallen arches. The height of the buildings is also great in proportion to the foundation and to the thickness of the walls; and the main walls are interrupted by numerous apertures, from the corners of which nearly all the fissures sprang. In some of the coast towns, the houses are built of rounded stones gathered from the beach, or of rubble with stones of all shapes and sizes, bound by cement of the poorest quality. Lastly, as much of the damage due to previous earthquakes had been badly repaired, it is evident that the destructiveness of the Riviera earthquakes must to a great extent be referred to preventable causes.
The occurrence of the princ.i.p.al shock shortly after six on the morning of Ash Wednesday must also have increased the death-rate; for many persons, after a night of amus.e.m.e.nt, had lain down for a short time and were sleeping heavily; while others had already risen and were collected in the churches; the circ.u.mstances in either case rendering escape more difficult.
Taking account, however, of this accidental increase in the number of victims, Professor Mercalli considers that the earthquake of 1887 was the most disastrous of all those which have visited either the Riviera or northern Italy in the last three centuries; though, during the nineteenth century, there were three Italian earthquakes of far greater destructive power, but all confined to the southern part of the peninsula--namely, the Neapolitan earthquakes of 1805 and 1857, and the Ischian earthquake of 1883.
PREPARATION FOR THE EARTHQUAKES.
It is difficult, as usual, to specify the exact moment when the first earthquake of the 1887 series took place; but it is evident that the preparation for the great shock was very brief. At Oneglia, it is alleged that faint shocks and sounds were observed many times, chiefly at night, during the month preceding February 23rd; though they were not at the time supposed to be of seismic origin. A slight shock is also reported from Diano at about midnight on February 21-22.
The first undoubted shock occurred on February 22nd, at about 8.30 P.M., or ten hours before the princ.i.p.al earthquake. Though very slight, it was felt throughout the Riviera and in part of Piedmont.
Another shock, also weak, took place at about 11 P.M.; and a third, sensible only in the eastern part of the Ligurian Apennines, on February 23rd, at about 1 A.M.; at which time the tide-gauge at Genoa recorded some abnormal oscillations. An hour later, a more important, though by no means a strong, shock occurred; this was perceptible all over the Riviera, in Piedmont, and in Corsica; in other words, it disturbed a region agreeing closely with the central area of the disastrous shock. At about 5 A.M., a fifth shock, somewhat weaker than the preceding, was felt over the same area, concurrently, or nearly so, with another abnormal oscillation of the tide-gauge at Genoa; while a sixth shock was noticed at several places a few minutes before the great shock.
During the night of February 22-23, nervous persons in many towns and villages were agitated without apparent reason. Birds and animals, more sensitive than human beings to faint tremors, were more distinctly affected, especially for some minutes before the earthquake. Horses refused food, were restless or tried to escape from their stables, dogs howled, birds flew about and uttered cries of alarm. As these symptoms were noticed at more than one hundred and thirty places within the Italian part of the central area, there can be little doubt that they were caused by microseismic movements for the most part insensible to man.
ISOSEISMAL LINES AND DISTURBED AREA.
The only complete map of the isoseismal lines is that drawn by Professor Mercalli.[48] In this map, reproduced in Fig. 33, the continuous curves represent the princ.i.p.al isoseismal lines; the dotted curves define the disturbed areas of two of the stronger after-shocks.
The meizoseismal area, bounded by the curve marked 1 in Fig. 33, is also shown on a larger scale in Fig. 34. At the places denoted by small circles in the latter figure, the princ.i.p.al shock was "disastrous," some of the houses in each being either totally or partially ruined. At those marked by a small cross, the shock was "almost ruinous"; in other words, numerous houses were damaged, but in no case was the injury of a serious character. The meizoseismal area is thus a narrow band, skirting the Riviera coast from Mentone to Albissola, a distance of 106 miles, and extending inland for not more than from nine to twelve miles. The greatest intensity, corresponding to the ruin of many houses with considerable loss of life, was reached at only a few places between Bussano and Diano Marina, all lying within a littoral band about twenty miles in length and three to three and a half miles in width. If, however, the epicentre had lain on land, the area would have been much greater, Professor Mercalli estimates about four times greater, than its actual amount.
[Ill.u.s.tration: FIG. 33.--Isoseismal lines of the Riviera earthquake. (_Mercalli._)]
The curve marked 2 (Fig. 33) bounds the "almost ruinous" zone; its expansion towards the north and contraction towards the west, north-west, and east, being its most noteworthy features. The next zone, that of slight damage, is contained between the isoseismals 2 and 3, the latter curve probably grazing the north end of Corsica.
Beyond this lies the "strong" zone, in which the shock was generally felt without causing any damage to buildings. Its boundary (marked 4) pa.s.ses near Ma.r.s.eilles, Como, and Parma, and includes nearly the whole of Corsica; towards the north-west, in the valley of Aosta, it curves in towards the isoseismal 3.
In the outermost zone of all the shock was "slight," and towards the margin was only just perceptible. The boundary, which of course defines that of the disturbed area, reaches as far north as Basle and Dijon, to Perpignan on the west, Trento, Venice, and Pordenone on the east, and to the south as far as Tivoli (near Rome) and the northern end of Sardinia. In eastern Switzerland, it shows a marked curve inwards; possibly, as Professor Mercalli suggests, from the vibrations having to cross the northern Apennines in a direction nearly at right angles to their axis. Except for this bay, however, the curve differs little from a circle, the centre of which lies in the sea, a little to the south of Oneglia, close to the position a.s.signed by other evidence to the epicentre. The radius of this circle being about 264 miles, it follows that the disturbed area must have contained about 219,000 square miles--by no means a large amount for so strong an earthquake.
POSITION OF THE EPICENTRES.
It is evident, from the form of the meizoseismal area shown in Fig.
33, that a mere fringe of it lies upon land, and that the epicentre must be situated some distance out at sea. Other facts may be mentioned which point to the same conclusion. There were, for instance, no purely vertical movements observed, even in the districts where the damage done by the shock was greatest. Nor were any large landslips to be seen in those areas; there were no lasting changes in the underground water-system; and in general, as Professor Mercalli remarks, all the superficial distortions of the ground which are so characteristic of the epicentral area of a great earthquake were conspicuous by their absence. There is evidence, again, of some disturbance of the sea-bed in the death and flight of fishes from great depths and in the seismic sea-waves recorded by the tide-gauges at Genoa and Nice. These phenomena will be described in a later section, but reference should be made here to an interesting observation at Oneglia on the occurrence of some of the stronger after-shocks. Persons on the coast, it is said, saw the sea curling and moving, and immediately afterwards the shock was felt.
In determining the position of the epicentre, Professor Mercalli had recourse as usual to observations on the direction of the shock, especially those derived from the oscillation of lamps or other suspended objects, the projection or fall of bodies free to move, fractures, etc., in damaged houses, and the stopping of pendulum clocks. Such observations were made at 120 places--72 in the western Riviera and the Alpes Maritimes, and 48 at Piedmont, Lombardy, and Tuscany.
At many of these places the movement was extremely complicated. In nearly all parts of the area most strongly shaken, for instance, the direction of the shock changed more than once; and it was therefore necessary to select whenever possible the princ.i.p.al direction of the shock at each place. In some towns, such as Oneglia, Mentone, Antibes, Cuneo, etc., the shock had two dominant directions, and these appeared to be sensibly at right angles to one another; an inclination which, as Professor Mercalli suggests, may be due in part to the approximation of the real directions to those of the princ.i.p.al walls of the houses in which the observations were made.
Most of the lines of direction, when plotted on the map, converge towards an area lying between the meridians of Oneglia and San Remo, and between nine and fifteen miles from the coast. For places near the epicentre, the most trustworthy, in Mercalli"s opinion, are those made at Oneglia, Mentone, Taggia, Bordighera, Castel Vittorio, Nice, and Genoa; and the points in which these lines Intersect one another are Indicated by small crosses on the map of the meizoseismal area (Fig.
34). All of them lie at sea at distances between six and fifteen miles to the south of Oneglia. The most probable position of the princ.i.p.al epicentre is that marked by the small circle A, which is situated about fifteen miles south of Oneglia.
[Ill.u.s.tration: FIG. 34.--Meizoseismal area of the Riviera earthquake. (_Taramelli and Mercalli._)]
There are, however, several lines of direction which can have no connection with this epicentre. Besides the east and west lines at Nice, Mentone, and Antibes, there are others at the same places which run north and south or nearly so. Professor Mercalli believes that they were due to vibrations coming from a second focus lying to the south of Nice, and there are also several lines of direction at more distant places which converge towards the neighbourhood of the corresponding epicentre.
This conclusion receives unexpected support from some of the best time-records. At the railway-stations of Loano and Pietra Ligure, the times of occurrence were given as 6h. 20m. 5s. and 6h. 20m.
respectively--estimates which are probably accurate to within a few seconds; for, at the moment of the shock, the officer who brought the exact time along the railway-line from Genoa was at Loana, and had just pa.s.sed through Pietra Ligure. On the other hand, the estimates for Mentone and Nice--namely, 6h. 18m. 35s. and 6h. 19m. 43s., if not equally exact, cannot err by many seconds, certainly not by so much as one minute. Since the distances of Loana and Pietra Ligure from the princ.i.p.al epicentre are 31 and 32 miles, and those of Mentone and Nice 28 and 37 miles, it is therefore clear that the vibrations which arrived first at Nice and Mentone must have come from a local focus, where the impulse preceded that at the princ.i.p.al focus by several seconds.
DEPTH OF THE PRINc.i.p.aL FOCUS.
Inaccurate as are all the methods of determining the depth of focus, it seems probable, as Professor Issel argues, that the princ.i.p.al Riviera focus was situated at a considerable distance from the surface. In no part of the meizoseismal area was the shock a really violent one; yet its intensity must have faded very slowly outwards, for it was strong enough to stop clocks at places in Switzerland and elsewhere not less than 250 miles from the origin.
Professor Mercalli regards Mallet"s method with greater favour than most seismologists. He points to the gradual increase in the angle of emergence from the outer zones disturbed by the Riviera earthquake towards the meizoseismal area, where several good observations were made from fissures in walls parallel to the dominant direction of the shock. The angles of emergence which he considers as most trustworthy are those of 35 at Taggia, 40 at Oneglia, and about 30 at Bordighera. The corresponding depths for the focus are 10.4, 10.4, and 11.6 miles, giving an average of about 10-3/4 miles.
There are no similar observations forthcoming for the depth of the secondary focus near Nice and Mentone; but Professor Mercalli observes that it must have been shallower than the other, for the vertical component of the vibrations from this focus was much less sensible than that of the motion coming from the princ.i.p.al focus.