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*1+13, &c. is then = 2a′′ + bx.
we have 2a" + b2 = 0; and, conse
+*, &c. the value of G" in art. 9, must be equal to
&c. the value of G" in art. 11, when both se
Hence, by taking x =
and, consequently, a”” = as in art. 7.
14. From what is done in the last 5 articles, it evidently follows, that
Whence (as well as from the theorems in art. 8) may the values of a", a', a", avi, &c. be readily found, in terms of a.
multiplying by. x, and taking the correct fluents, we get H' x'a” — a′′ +
+1 x + 1 + 2s" + + + &c. s" being put for the 1.32 3.52 5.799
series + +
Now, it is obvious, that this value of н' must be equal to the value of н' in
the preceding article, when both series converge.
3x3-x-1 5.rs 3x-s 7x7-5x-5
&c. is then = x2a" - a" +
Hence, by taking a equal to x equal to 1, we find 2s" = b2 + 2 + 2s"; and,
and s" ==—, it follows, from the last article,
17. Seeing that a" is=
3.52 5.729 &c. Whence, by multiplying by, and taking the correct fluent, we get
And hence, by multiplying by xr, and taking the correct fluents, we have
64 3 9
Now, this value of н"" being equal to the value of H" in art. 15, when both
Many other instances of the use of this method might be given; but these may suffice to enable the intelligent reader to pursue the speculation farther, at his pleasure.
The above subject is much further pursued by the ingenious author, in his Mathematical Memoirs, p. 67, published 1780.
LV. Conjectures concerning the Cause, and Observations on the Phenomena of Earthquakes; particularly of that Great Earthquake of Nov. 1, 1755, which proved so fatal to the City of Lisbon, and whose Effects were felt as fa
as Africa, and more or less throughout almost all Europe. By the Rev. John Michell, M. A. P. 566.
INTRODUCTION.—It has been the general opinion of philosophers, that earthquakes owe their origin to some sudden explosion in the interior of the earth. This opinion is agreeable to the phenomena which seem to point out something of that kind. The conjectures, however, of the cause of such an explosion have not been yet sufficiently supported by facts; nor have the more particular effects which will arise from it been traced out; and the connection of them with the phenomena explained. To do this is the intent of the following pages; and the dreadful earthquake of the 1st of Nov. 1755 supplies us with more facts for this purpose than any other earthquake of which we have an
That these concussions should owe their origin to something in the air seems very ill to correspond with the phenomena. This will sufficiently appear, as those phenomena are hereafter recounted; nor does there appear to be any such certain and regular connection between earthquakes and the state of the air, when they happen, as is supposed by those who hold this opinion. It is said, for instance, that earthquakes always happen in calm still weather: but that this is not always so may be seen in an account of the earthquakes in Sicily of 1693, (Phil. Trans. N° 207,) where we are told, "the south winds have blown very much, which still have been impetuous in the most sensible earthquakes, and the like has happened at other times." Other examples to the same purpose we have in an account of the earthquakes that happened in New England in 1727 and 1728; the author of which says, that he could neither observe any connection between the weather and the earthquakes, nor any prognostic of them; for that they happened alike in all kinds of weather, at all times of the tides, and at all times of the moon. Phil. Trans. N° 409. If, however, it should still be supposed, notwithstanding these instances to the contrary, that there is some general connection between earthquakes and the weather, at the time when they happen, yet surely it is far more probable that the air should be affected by the causes of earthquakes, than that the earth should be affected in so extraordinary a manner, and to so great a depth; and that this, and all the other circumstancs attending these motions, should be owing to some cause residing in the air.
Let us then, rejecting this hypothesis, suppose that earthquakes have their origin under ground, and we need not go far in search of a cause, whose real existence in nature we have evidence of, and which is capable of producing all the appearances of these extraordinary motions. The cause I mean, says Mr. M.
* See the 10th vol. of these Abridgments.
is subterraneous fires. These fires, if a large quantity of water should be let out upon them suddenly, may produce a vapour, whose quantity and elastic force may be fully sufficient for that purpose. The principal facts, from which I would prove, that these fires are the real cause of earthquakes, are as follows. SECTION 1.-1st. The same places are subject to returns of earthquakes, not only at small intervals for some time after any considerable one has happened, but also at greater intervals of some ages.
Both these facts sufficiently appear from the accounts we have of earthquakes. The tremblings and shocks of the earth at Jamaica in 1692, at Sicily in 1693, and at Lisbon in 1755, were repeated sometimes at larger and sometimes at smaller intervals, for several months. The same thing has been observed in all other very violent earthquakes. At Lima, from the 28th of October 1746, to Feb. 24, 1747, there had been numbered no less than 451 shocks, many of them little inferior to the first great one which destroyed that city.
The returns of earthquakes also, in the same places, at larger distances of time, are confirmed by all history. Constantinople, and many parts of Asia Minor, have suffered by them, in many different ages: Sicily has been subjected to them, as far back as the remains even of fabulous history can inform us of: Lisbon did not feel the effects of them for the first time in 1755: Jamaica has frequently been troubled with them, since the English first settled there; and the Spaniards, who were there before, used to build their houses of wood, and only one story high, for fear of them: Lima, Callao, and the parts adjacent, were almost totally destroyed by them twice, within the compass of about 60 years; nor were these the only instances of the like kind which happened there; for, from the year 1582 to 1746, they have had no less than 16 very violent earthquakes, besides an infinity of less considerable ones; and the Spaniards, at their first settling there, were told by the old inhabitants, when they saw them building high houses, that they were building their own sepulchres.
2dly, Those places that are in the neighbourhood of burning mountains are always subject to frequent earthquakes; and the eruptions of those mountains, when violent, are generally attended with them.
Asia Minor and Constantinople may be considered as in the neighbourhood of Santerini. The countries also about Etna, Vesuvius, mount Hæcla, &c. afford us sufficient proofs to the same purpose. But of all the places in the known world, probably no countries are so subject to earthquakes as Peru, Chili, and all the western parts of South America; nor is there any country in the known world so full of volcanos: for, throughout all that long range of mountains, known by the name of the Andes, from 45 degrees south latitude to several degrees north of the line, as also throughout all Mexico, being about 5000 miles in extent, there is a continued chain of them.
3dly, The motion of the earth in earthquakes is partly tremulous, and partly propagated by waves, which succeed one another sometimes at larger and sometimes at smaller distances; and this latter motion is generally propagated much farther than the former.
The former part of this proposition wants no confirmation: for the proof of the latter, viz. the wave-like motion of the earth, we may appeal to many accounts of earthquakes: it was very remarkable in the two which happened at Jamaica in 1687-8 and 1692. In an account of the former, it is said that a gentleman there saw the ground rise like the sea in a wave, as the earthquake passed along, and that he could distinguish the effects of it to some miles distance, by the motion of the tops of the trees on the hills. Again, in an account of the latter, it is said "the ground heaved and swelled like a rolling swelling sea," insomuch that people could hardly stand on their legs by reason of it. The same has been observed in the earthquakes of New England, where it has been very remarkable. A gentleman giving an account of one that happened there Nov. 18, 1755, says, the earth rose in a wave, which made the tops of the trees vibrate 10 feet, and that he was forced to support himself, to avoid falling, while it was passing. The same also was observed at Lisbon, in the earthquake of the 1st Nov. 1755, as may be plainly collected from many of the accounts that have been published concerning it, some of which affirm it expressly and this wave-like motion was propagated to far greater distances than the other tremulous one, being perceived by the motion of waters, and the hanging branches in churches, through all Germany, among the Alps, in Denmark, Sweden, Norway, and all over the British isles.
4thly, It is observed in places which are subject to frequent earthquakes, that they generally come to one and the same place from the same point of the compass. It may be added also, that the velocity with which they proceed, (as far as one can collect it from the accounts of them) is the same; but the velocity of the earthquakes of different countries is very different.
Thus all the shocks that succeeded the first great one at Lisbon in 1755, as well as the first itself, came from the north-west. This is asserted by the person who says he was about writing a history of the earthquakes there: all the other accounts also confirm the same thing; for what some say, that they came from the north, and others, that they came from the west, cannot be considered as any reasonable objection to this, but rather the contrary. The velocity also with which they were all propagated was the same, being at least equal to that of sound; for they all followed immediately after the noise that preceded them, or rather the noise and the earthquake came together: and this velocity agrees well with the intervals between the time when the first shock was felt at Lisbon, and the time when it was felt at other distant places, from the comparison of