These coefficients are all small, but the number of individual cases, 600 months, is so large that the probable error is greatly reduced, being only 0.027 or 0.028. Moreover, the nature of our data is such that even if there is a strong connection between solar changes and earth movements, we should not expect a large correlation coefficient.
In the first place, as already mentioned, the earthquake data are not strictly h.o.m.ogeneous. Second, an average of about two and one-half strong earthquakes per month is at best only a most imperfect indication of the actual movement of the earth"s crust. Third, the sunspots are only a partial and imperfect measure of the activity of the sun"s atmosphere. Fourth, the relation between solar activity and earthquakes is almost certainly indirect. In view of all these conditions, the regularity of Table 7 and the fact that the most important correlation coefficient rises to more than four times the probable error makes it almost certain that the solar and terrestrial phenomena are really connected.
We are now confronted by the perplexing question of how this connection can take place. Thus far only three possibilities present themselves, and each is open to objections. The chief agencies concerned in these three possibilities are heat, electricity, and atmospheric pressure.
Heat may be dismissed very briefly. We have seen that the earth"s surface becomes relatively cool when the sun is active. Theoretically even the slightest change in the temperature of the earth"s surface must influence the thermal gradient far into the interior and hence cause a change of volume which might cause movements of the crust. Practically the heat of the surface ceases to be of appreciable importance at a depth of perhaps twenty feet, and even at that depth it does not act quickly enough to cause the relatively prompt response which seems to be characteristic of earthquakes in respect to the sun.
The second possibility is based on the relationship between solar and terrestrial electricity. When the sun is active the earth"s atmospheric electrical potential is subject to slight variations. It is well known that when two opposing points of an ionized solution are oppositely charged electrically, a current pa.s.ses through the liquid and sets up electrolysis whereby there is a segregation of materials, and a consequent change in the volume of the parts near the respective electrical poles. The same process takes place, although less freely, in a hot ma.s.s such as forms the interior of the earth. The question arises whether internal electrical currents may not pa.s.s between the two oppositely charged poles of the earth, or even between the great continental ma.s.ses and the regions of heavier rock which underlie the oceans. Could this lead to electrolysis, hence to differentiation in volume, and thus to movements of the earth"s crust? Could the results vary in harmony with the sun? Bowie[127] has shown that numerous measurements of the strength and direction of the earth"s gravitative pull are explicable only on the a.s.sumption that the upheaval of a continent or a mountain range is due in part not merely to pressure, or even to flowage of the rocks beneath the crust, but also to an actual change in volume whereby the rocks beneath the continent attain relatively great volume and those under the oceans a small volume in proportion to their weight. The query arises whether this change of volume may be related to electrical currents at some depth below the earth"s surface.
The objections to this hypothesis are numerous. First, there is little evidence of electrolytic differentiation in the rocks. Second, the outer part of the earth"s crust is a very poor conductor so that it is doubtful whether even a high degree of electrification of the surface would have much effect on the interior. Third, electrolysis due to any such mild causes as we have here postulated must be an extremely slow process, too slow, presumably, to have any appreciable result within a month or two. Other objections join with these three in making it seem improbable that the sun"s electrical activity has any direct effect upon movements of the earth"s crust.
The third, or meteorological hypothesis, which makes barometric pressure the main intermediary between solar activity and earthquakes, seems at first sight almost as improbable as the thermal and electrical hypotheses. Nevertheless, it has a certain degree of observational support of a kind which is wholly lacking in the other two cases. Among the extensive writings on the periodicity of earthquakes one main fact stands out with great distinctness: earthquakes vary in number according to the season. This fact has already been shown incidentally in the table of earthquake frequency by months. If allowance is made for the fact that February is a short month, there is a regular decrease in the frequency of severe earthquakes from December and January to June. Since most of Milne"s earthquakes occurred in the northern hemisphere, this means that severe earthquakes occur in winter about 20 per cent oftener than in summer.
The most thorough investigation of this subject seems to have been that of Davisson.[128] His results have been worked over and amplified by Knott,[129] who has tested them by Schuster"s exact mathematical methods. His results are given in Table 8.[130] Here the northern hemisphere is placed first; then come the East Indies and the Malay Archipelago lying close to the equator; and finally the southern hemisphere. In the northern hemisphere practically all the maxima come in the winter, for the month of December appears in fifteen cases out of the twenty-five in column D, while January, February, or November appears in six others. It is also noticeable that in sixteen cases out of twenty-five the ratio of the actual to the expected amplitude in column G is four or more, so that a real relationship is indicated, while the ratio falls below three only in j.a.pan and Zante. The equatorial data, unlike those of the northern hemisphere, are indefinite, for in the East Indies no month shows a marked maximum and the expected amplitude exceeds the actual amplitude. Even in the Malay Archipelago, which shows a maximum in May, the ratio of actual to expected amplitude is only 2.6. Turning to the southern hemisphere, the winter months of that hemisphere are as strongly marked by a maximum as are the winter months of the northern hemisphere. July or August appears in five out of six cases. Here the ratio between the actual and expected amplitudes is not so great as in the northern hemisphere. Nevertheless, it is practically four in Chile, and exceeds five in Peru and Bolivia, and in the data for the entire southern hemisphere.
TABLE 8
SEASONAL MARCH OF EARTHQUAKES
AFTER DAVISSON AND KNOTT
A: _Region_ B: _Limiting Dates_ C: _Number of Shocks_ D: _Maximum Month_ E: _Amplitude_ F: _Expected Amplitude_ G: _Ratio of Actual to Expected Amplitude_
A B C D E F G
Northern Hemisphere 223-1850 5879 Dec. 0.110 0.023 4.8 Northern Hemisphere 1865-1884 8133 Dec. 0.290 0.020 14.5 Europe 1865-1884 5499 Dec. 0.350 0.024 14.6 Europe 306-1843 1961 Dec. 0.220 0.040 5.5 Southeast Europe 1859-1887 3470 Dec. 0.210 0.030 7.0 Vesuvius District 1865-1883 513 Dec. 0.250 0.078 3.2 Italy: Old Tromometre 1872-1887 61732 Dec. 0.490 0.007 70.0 Old Tromometre 1876-1887 38546 Dec. 0.460 0.009 49.5 Normal Tromometre 1876-1887 38546 Dec. 0.490 0.009 52.8 Balkan, etc. 1865-1884 624 Dec. 0.270 0.071 3.8 Hungary, etc. 1865-1884 384 Dec. 0.310 0.090 3.4 Italy 1865-1883 2350 Dec.(Sept.)0.140 0.037 3.8 Grecian Archip. 1859-1881 3578 Dec.-Jan. 0.164 0.030 5.5 Austria 1865-1884 461 Jan. 0.370 0.083 4.4 Switzerland, etc. 1865-1883 524 Jan. 0.560 0.077 7.3 Asia 1865-1884 458 Feb. 0.330 0.083 4.0 North America 1865-1884 552 Nov. 0.350 0.075 4.7 California 1850-1886 949 Oct. 0.300 0.058 5.2 j.a.pan 1878-1881 246 Dec. 0.460 0.113 4.1 j.a.pan 1872-1880 367 Dec.-Jan. 0.256 0.093 2.8 j.a.pan 1876-1891 1104 Feb. 0.190 0.053 3.6 j.a.pan 1885-1889 2997 Oct. 0.080 0.032 2.5 Zante 1825-1863 1326 Aug. 0.100 0.049 2.0 Italy, North 1865-1883 1513 Sept.(Nov.) 0.210 0.046 4.6 of Naples East Indies 1873-1881 515 Aug., Oct., 0.071? 0.078 0.9 or Dec.?
Malay Archip. 1865-1884 598 May 0.190 0.072 2.6 New Zealand 1869-1879 585 Aug.-Sept. 0.203 0.073 2.8 Chile 1873-1881 212 July 0.480 0.122 3.9 Southern Hemisphere 1865-1884 751 July 0.370 0.065 5.7 New Zealand 1868-1890 641 March, May 0.050 0.070 0.7 Chile 1865-1883? 316 July, Dec. 0.270 0.100 2.7 Peru, Bolivia 1865-1884 350 July 0.480 0.095 5.1
The whole relationship between earthquakes and the seasons in the northern and southern hemispheres is summed up in Fig. 12 taken from Knott. The northern hemisphere shows a regular diminution in earthquake frequency from December until June, and an increase the rest of the year. In the southern hemisphere the course of events is the same so far as summer and winter are concerned, for August with its maximum comes in winter, while February with its minimum comes in summer. In the southern hemisphere the winter month of greatest seismic activity has over 100 per cent more earthquakes than the summer month of least activity. In the northern hemisphere this difference is about 80 per cent, but this smaller figure occurs partly because the northern data include certain interesting and significant regions like j.a.pan and China where the usual conditions are reversed.[131] If equatorial regions were included in Fig. 12, they would give an almost straight line.
The connection between earthquakes and the seasons is so strong that almost no students of seismology question it, although they do not agree as to its cause. A meteorological hypothesis seems to be the only logical explanation.[132] Wherever sufficient data are available, earthquakes appear to be most numerous when climatic conditions cause the earth"s surface to be most heavily loaded or to change its load most rapidly. The main factor in the loading is apparently atmospheric pressure. This acts in two ways. First, when the continents become cold in winter the pressure increases. On an average the air at sea level presses upon the earth"s surface at the rate of 14.7 pounds per square inch, or over a ton per square foot, and only a little short of thirty million tons per square mile. An average difference of one inch between the atmospheric pressure of summer and winter over ten million square miles of the continent of Asia, for example, means that the continent"s load in winter is about ten million million tons heavier than in summer.
Second, the changes in atmospheric pressure due to the pa.s.sage of storms are relatively sharp and sudden. Hence they are probably more effective than the variations in the load from season to season. This is suggested by the rapidity with which the terrestrial response seems to follow the supposed solar cause of earthquakes. It is also suggested by the fact that violent storms are frequently followed by violent earthquakes.
"Earthquake weather," as Dr. Schlesinger suggests, is a common phrase in the typhoon region of j.a.pan, China, and the East Indies. During tropical hurricanes a change of pressure amounting to half an inch in two hours is common. On September 22, 1885, at False Point Lighthouse on the Bay of Bengal, the barometer fell about an inch in six hours, then nearly an inch and a half in not much over two hours, and finally rose fully two inches inside of two hours. A drop of two inches in barometric pressure means that a load of about two million tons is removed from each square mile of land; the corresponding rise of pressure means the addition of a similar load. Such a storm, and to a less degree every other storm, strikes a blow upon the earth"s surface, first by removing millions of tons of pressure and then by putting them on again.[133] Such storms, as we have seen, are much more frequent and severe when sunspots are numerous than at other times. Moreover, as Veeder[134] long ago showed, one of the most noteworthy evidences of a connection between sunspots and the weather is a sudden increase of pressure in certain widely separated high pressure areas. In most parts of the world winter is not only the season of highest pressure and of most frequent changes of Veeder"s type, but also of severest storms. Hence a meteorological hypothesis would lead to the expectation that earthquakes would occur more frequently in winter than in summer. On the Chinese coast, however, and also on the oceanic side of j.a.pan, as well as in some more tropical regions, the chief storms come in summer in the form of typhoons. These are the places where earthquakes also are most abundant in summer. Thus, wherever we turn, storms and the related barometric changes seem to be most frequent and severe at the very times when earthquakes are also most frequent.
[Ill.u.s.tration: _Fig. 12. Seasonal distribution of earthquakes. (After Davisson and Knott.)_
solid line ---- Northern Hemisphere.
dashed line .... Southern Hemisphere.]
Other meteorological factors, such as rain, snow, winds, and currents, probably have some effect on earthquakes through their ability to load the earth"s crust. The coming of vegetation may also help. These agencies, however, appear to be of small importance compared with the storms. In high lat.i.tudes and in regions of abundant storminess most of these factors generally combine with barometric pressure to produce frequent changes in the load of the earth"s crust, especially in winter.
In low lat.i.tudes, on the other hand, there are few severe storms, and relatively little contrast in pressure and vegetation from season to season; there is no snow; and the amount of ground water changes little.
With this goes the twofold fact that there is no marked seasonal distribution of earthquakes, and that except in certain local volcanic areas, earthquakes appear to be rare. In proportion to the areas concerned, for example, there is little evidence of earthquakes in equatorial Africa and South America.
The question of the reality of the connection between meteorological conditions and crustal movements is so important that every possible test should be applied. At the suggestion of Professor Schlesinger we have looked up a very ingenious line of inquiry. During the last decades of the nineteenth century, a long series of extremely accurate observations of lat.i.tude disclosed a fact which had previously been suspected but not demonstrated, namely, that the earth wabbles a little about its axis. The axis itself always points in the same direction, and since the earth slides irregularly around it the lat.i.tude of all parts of the earth keeps changing. Chandler has shown that the wabbling thus induced consists of two parts. The first is a movement in a circle with a radius of about fifteen feet which is described in approximately 430 days. This so-called Eulerian movement is a normal gyroscopic motion like the slow gyration of a spinning top. This depends on purely astronomical causes, and no terrestrial cause can stop it or eliminate it. The period appears to be constant, but there are certain puzzling irregularities. The usual amplitude of this movement, as Schlesinger[135] puts it, "is about 0".27, but twice in recent years it has jumped to 0".40. Such a change could be accounted for by supposing that the earth had received a severe blow or a series of milder blows tending in the same direction." These blows, which were originally suggested by Helmert are most interesting in view of our suggestion as to the blows struck by storms.
The second movement of the pole has a period of a year, and is roughly an ellipse whose longest radius is fourteen feet and the shortest, four feet; or, to put it technically, there is an annual term with a maximum amplitude of about 0".20. This, however, varies irregularly. The result is that the pole seems to wander over the earth"s surface in the spiral fashion ill.u.s.trated in Fig. 13. It was early suggested that this peculiar wandering of the pole in an annual period must be due to meteorological causes. Jeffreys[136] has investigated the matter exhaustively. He a.s.sumes certain reasonable values for the weight of air added or subtracted from different parts of the earth"s surface according to the seasons. He also considers the effect of precipitation, vegetation, and polar ice, and of variations of temperature and atmospheric pressure in their relation to movements of the ocean. Then he proceeds to compare all these with the actual wandering of the pole from 1907 to 1913. While it is as yet too early to say that any special movement of the pole was due to the specific meteorological conditions of any particular year, Jeffreys" work makes it clear that meteorological causes, especially atmospheric pressure, are sufficient to cause the observed irregular wanderings. Slight wanderings may arise from various other sources such as movements of the rocks when geological faults occur or the rush of a great wave due to a submarine earthquake. So far as known, however, all these other agencies cause insignificant displacements compared with those arising from movements of the air. This fact coupled with the mathematical certainty that meteorological phenomena must produce some wandering of the pole, has caused most astronomers to accept Jeffreys" conclusion. If we follow their example we are led to conclude that changes in atmospheric pressure and in the other meteorological conditions strike blows which sometimes shift the earth several feet from its normal position in respect to the axis.
[Ill.u.s.tration: _Fig. 13. Wandering of the pole from 1890 to 1898._ (_After Moulton._)]
If the foregoing reasoning is correct, the great and especially the sudden departures from the smooth gyroscopic circle described by the pole in the Eulerian motion would be expected to occur at about the same time as unusual earthquake activity. This brings us to an interesting inquiry carried out by Milne[137] and amplified by Knott.[138] Taking Albrecht"s representation of the irregular spiral-like motion of the pole, as given in Fig. 13, they show that there is a preponderance of severe earthquakes at times when the direction of motion of the earth in reference to its axis departs from the smooth Eulerian curve. A summary of their results is given in Table 9. The table indicates that during the period from 1892 to 1905 there were nine different times when the curve of Fig. 13 changed its direction or was deflected by less than 10 during a tenth of a year. In other words, during those periods it did not curve as much as it ought according to the Eulerian movement. At such times there were 179 world-shaking earthquakes, or an average of about 19.9 per tenth of a year. According to the other lines of Table 9, in thirty-two cases the deflection during a tenth of a year was between 10 and 25, while in fifty-six cases it was from 25 to 40. During these periods the curve remained close to the Eulerian path and the world-shaking earthquakes averaged only 8.2 and 12.9. Then, when the deflection was high, that is, when meteorological conditions threw the earth far out of its Eulerian course, the earthquakes were again numerous, the number rising to 23.4 when the deflection amounted to more than 55.
TABLE 9
DEFLECTION OF PATH OF POLE COMPARED WITH EARTHQUAKES
_No. of _No. of _Average No.
_Deflection_ Deflections_ Earthquakes_ of Earthquakes_ 0-10 9 179 19.9 10-25 32 263 8.2 25-40 56 722 12.9 40-55 19 366 19.3 over 55 7 164 23.4
In order to test this conclusion in another way we have followed a suggestion of Professor Schlesinger. Under his advice the Eulerian motion has been eliminated and a new series of earthquake records has been compared with the remaining motions of the poles which presumably arise largely from meteorological causes. For this purpose use has been made of the very full records of earthquakes published under the auspices of the International Seismological Commission for the years 1903 to 1908, the only years for which they are available. These include every known shock of every description which was either recorded by seismographs or by direct observation in any part of the world. Each shock is given the same weight, no matter what its violence or how closely it follows another. The angle of deflection has been measured as Milne measured it, but since the Eulerian motion is eliminated, our zero is approximately the normal condition which would prevail if there were no meteorological complications. Dividing the deflections into six equal groups according to the size of the angle, we get the result shown in Table 10.
TABLE 10
EARTHQUAKES IN 1903-1908 COMPARED WITH DEPARTURES OF THE PROJECTED CURVE OF THE EARTH"S AXIS FROM THE EULERIAN POSITION
_Average angle of deflection_ _Average daily number (_10 periods of 1/10 year each_) of earthquakes_ -10.5 8.31 11.5 8.35 25.8 8.23 40.2 8.14 54.7 8.86 90.3 11.81
Here where some twenty thousand earthquakes are employed the result agrees closely with that of Milne for a different series of years and for a much smaller number of earthquakes. So long as the path of the pole departs less than about 45 from the smooth gyroscopic Eulerian path, the number of earthquakes is almost constant, about eight and a quarter per day. When the angle becomes large, however, the number increases by nearly 50 per cent. Thus the work of Milne, Knott, and Jeffreys is confirmed by a new investigation. Apparently earthquakes and crustal movements are somehow related to sudden changes in the load imposed on the earth"s crust by meteorological conditions.
This conclusion is quite as surprising to the authors as to the reader--perhaps more so. At the beginning of this investigation we had no faith whatever in any important relation between climate and earthquakes. At its end we are inclined to believe that the relation is close and important.
It must not be supposed, however, that meteorological conditions are the _cause_ of earthquakes and of movements of the earth"s crust. Even though the load that the climatic agencies can impose upon the earth"s crust runs into millions of tons per square mile, it is a trifle compared with what the crust is able to support. There is, however, a great difference between the cause and the occasion of a phenomenon.
Suppose that a thick sheet of gla.s.s is placed under an increasing strain. If the strain is applied slowly enough, even so rigid a material as gla.s.s will ultimately bend rather than break. But suppose that while the tension is high the gla.s.s is tapped. A gentle tap may be followed by a tiny crack. A series of little taps may be the signal for small cracks to spread in every direction. A few slightly harder taps may cause the whole sheet to break suddenly into many pieces. Yet even the hardest tap may be the merest trifle compared with the strong force which is keeping the gla.s.s in a state of strain and which would ultimately bend it if given time.
The earth as a whole appears to stand between steel and gla.s.s in rigidity. It is a matter of common observation that rocks stand high in this respect and in the consequent difficulty with which they can be bent without breaking. Because of the earth"s contraction the crust endures a constant strain, which must gradually become enormous. This strain is increased by the fact that sediment is transferred from the lands to the borders of the sea and there forms areas of thick acc.u.mulation. From this has arisen the doctrine of isostasy, or of the equalization of crustal pressure. An important ill.u.s.tration of this is the oceanward and equatorial creep which has been described in Chapter XI. There we saw that when the lands have once been raised to high levels or when a shortening of the earth"s axis by contraction has increased the oceanic bulge at the equator, or when the reverse has happened because of tidal r.e.t.a.r.dation, the outer part of the earth appears to creep slowly back toward a position of perfect isostatic adjustment. If the sun had no influence upon the earth, either direct or indirect, isostasy and other terrestrial processes might flex the earth"s crust so gradually that changes in the form and height of the lands would always take place slowly, even from the geological point of view. Thus erosion would usually be able to remove the rocks as rapidly as they were domed above the general level. If this happened, mountains would be rare or unknown, and hence climatic contrasts would be far less marked than is actually the case on our earth where crustal movements have repeatedly been rapid enough to produce mountains.
Nature"s methods rarely allow so gradual an adjustment to the forces of isostasy. While the crust is under a strain, not only because of contraction, but because of changes in its load through the transference of sediments and the slow increase or decrease in the bulge at the equator, the atmosphere more or less persistently carries on the tapping process. The violence of that process varies greatly, and the variations depend largely on the severity of the climatic contrasts. If the main outlines of the cyclonic hypothesis are reliable, one of the first effects of a disturbance of the sun"s atmosphere is increased storminess upon the earth. This is accompanied by increased intensity in almost every meteorological process. The most important effect, however, so far as the earth"s crust is concerned would apparently be the rapid and intense changes of atmospheric pressure which would arise from the swift pa.s.sage of one severe storm after another. Each storm would be a little tap on the tensely strained crust. Any single tap might be of little consequence, even though it involved a change of a billion tons in the pressure on an area no larger than the state of Rhode Island. Yet a rapid and irregular succession of such taps might possibly cause the crust to crack, and finally to collapse in response to stresses arising from the shrinkage of the earth.
Another and perhaps more important effect of variations in storminess and especially in the location of the stormy areas would be an acceleration of erosion in some places and a r.e.t.a.r.dation elsewhere. A great increase in rainfall may almost denude the slopes of soil, while a diminution to the point where much of the vegetation dies off has a similar effect. If such changes should take place rapidly, great thicknesses of sediment might be concentrated in certain areas in a short time, thus disturbing the isostatic adjustment of the earth"s crust. This might set up a state of strain which would ultimately have to be relieved, thus perhaps initiating profound crustal movements.
Changes in the load of the earth"s crust due to erosion and the deposition of sediment, no matter how rapid they may be from the geological standpoint, are slow compared with those due to changes in barometric pressure. A drop of an inch in barometric pressure is equivalent to the removal of about five inches of solid rock. Even under the most favorable circ.u.mstances, the removal of an average depth of five inches of rock or its equivalent in soil over millions of square miles would probably take several hundred years, while the removal of a similar load of air might occur in half a day or even a few hours. Thus the erosion and deposition due to climatic variations presumably play their part in crustal deformation chiefly by producing crustal stresses, while the storms, as it were, strike sharp, sudden blows.
Suppose now that a prolonged period of world-wide mild climate, such as is described in Chapter X, should permit an enormous acc.u.mulation of stresses due to contraction and tidal r.e.t.a.r.dation. Suppose that then a sudden change of climate should produce a rapid shifting of the deep soil that had acc.u.mulated on the lands, with a corresponding localization and increase in strains. Suppose also that frequent and severe storms play their part, whether great or small, by producing an intensive tapping of the crust. In such a case the ultimate collapse would be correspondingly great, as would be evident in the succeeding geological epoch. The sea floor might sink lower, the continents might be elevated, and mountain ranges might be shoved up along lines of special weakness. This is the story of the geological period as known to historical geology. The force that causes such movements would be the pull of gravity upon the crust surrounding the earth"s shrinking interior. Nevertheless climatic changes might occasionally set the date when the gravitative pull would finally overcome inertia, and thus usher in the crustal movements that close old geologic periods and inaugurate new ones. This, however, could occur only if the crust were under sufficient strain. As Lawson[139] says in his discussion of the "elastic rebound theory," the sudden shifts of the crust which seem to be the underlying cause of earthquakes "can occur only after the acc.u.mulation of strain to a limit and ... this acc.u.mulation involves a slow creep of the region affected. In the long periods between great earthquakes the energy necessary for such shocks is being stored up in the rocks as elastic compression."
If a period of intense storminess should occur when the earth as a whole was in such a state of strain, the sudden release of the strains might lead to terrestrial changes which would alter the climate still further, making it more extreme, and perhaps permitting the storminess due to the solar disturbances to bring about glaciation. At the same time if volcanic activity should increase it would add its quota to the tendency toward glaciation. Nevertheless, it might easily happen that a very considerable amount of crustal movement would take place without causing a continental ice sheet or even a marked alpine ice sheet. Or again, if the strains in the earth"s crust had already been largely released through other agencies before the stormy period began, the climate might become severe enough to cause glaciation in high lat.i.tudes without leading to any very marked movements of the earth"s crust, as apparently happened in the Mid-Silurian period.
FOOTNOTES:
[Footnote 125: E. Kirk: Paleozoic Glaciation in Alaska; Am. Jour. Sci., 1918, p. 511.]
[Footnote 126: J. Milne: Catalogue of Destructive Earthquakes; Rep.
Brit. a.s.so. Adv. Sci., 1911.]
[Footnote 127: Wm. Bowie: Lecture before the Geological Club of Yale University. See Am. Jour. Sci., 1921.]
[Footnote 128: Chas. Davisson: On the Annual and Semi-annual Seismic Periods; Roy. Soc. of London, Philosophical Transactions, Vol. 184, 1893, 1107 _ff._]
[Footnote 129: C. G. Knott: The Physics of Earthquake Phenomena, Oxford, 1908.]
[Footnote 130: In Table 8 the first column indicates the region; the second, the dates; and the third, the number of shocks. The fourth column gives the month in which the annual maximum occurs when the crude figures are smoothed by the use of overlapping six-monthly means. In other words, the average for each successive six months has been placed in the middle of the period. Thus the average of January to June, inclusive, is placed between March and April, that for February to July between April and May, and so on. This method eliminates the minor fluctuations and also all periodicities having a duration of less than a year. If there were no annual periodicity the smoothing would result in practically the same figure for each month. The column marked "Amplitude" gives the range from the highest month to the lowest divided by the number of earthquakes and then corrected according to Schuster"s method which is well known to mathematicians, but which is so confusing to the layman that it will not be described. Next, in the column marked "Expected Amplitude," we have the amplitude that would be expected if a series of numbers corresponding to the earthquake numbers and having a similar range were arranged in accidental order throughout the year.
This also is calculated by Schuster"s method in which the expected amplitude is equal to the square root of "pi" divided by the number of shocks. When the actual amplitude is four or more times the expected amplitude, the probability that there is a real periodicity in the observed phenomena becomes so great that we may regard it as practically certain. If there is no periodicity the two are equal. The last column gives the number of times by which the actual exceeds the expected amplitude, and thus is a measure of the probability that earthquakes vary systematically in a period of a year.]
[Footnote 131: N. F. Drake: Destructive Earthquakes in China; Bull.