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How surprising is it to look back, so little is useful for all sorts and degrees of men, from a way behind us, and see, that even in less the highest to the lowest. than two hundred years, all this (now so self As to the usefulness of geometry, it is as wise) part of the world did not so much as certain, that no curious art or mechanic work, know, whether there was any such place, as a can either be invented, improved, or performRussia, a China, a Guinea, a Greenland, or a ed, without its assisting principles. North Cape? That as to America, it was ne It is owing to this, that astronomers are ver supposed, there was any such place, nei- put into a way of making their observations, ther had the world, though they stood upon coming at the knowledge of the extent of the the shoulders of four thousand years' experi- heavens, the duration of time, the motions, ence, the least thought, so much as that there magnitudes, and distances of the heavenly was any land that way!
bodies, their situations, positions, risings, setAs they were ignorant of places, so of tings, aspects, and eclipses; also the measure things also; so vast are the improvements of of seasons, of years, and of ages. science, that all our knowledge of mathema It is by the assistance of this science, that tics, of nature, of the brightest part of human geographers present to our view at once, the wisdom, had their admission among us with- magnitude and form of the whole earth, the in these two last centuries.
vast extent of the seas, the divisions of emWhat was the world then, before ? And to pires, kingdoms, and provinces. what were the heads and hands of mankind It is by the help of geometry, the ingenious applied? The rich had no commerce, the poor mariner is instructed how to guide a ship no employment; war and the sword was the through the vast ocean, from one part of the great field of honour, the stage of preferment, earth to another, the nearest and safest way, and you
have scarce a man eminent in the and in the shortest time. world, for any thing before that time, but for By help of this science the architects take a furious outrageous falling upon his fellow- their just measures for the structure of buildcreatures, like Nimrod, and his successors of ings, as private houses, churches, palaces, modern memory.
ships, fortifications, &c. The world is now daily increasing in ex By its help engineers conduct all their perimental knowledge; and let no man flat- works, take the situation and plan of towns, ter the age, with pretending we have arrived forts and castles, measure their distances from to a perfection of discoveries.
one another, and carry their measure into
places that are only accessible to the eye. What's now discovered, only serves to show, That nothing's known, to what is yet to know.
From hence also is deduced that admirable art of drawing sun-dials on any plane how
soever situate, and for any part of world, to On the Usefulness of the Mathematics.- point out the exact time of the day, sun's deFrom the Pennsylvania Gazette, No. 360, clination, altitude, amplitude, azimuth, and
other astronomical matters. Oct. 30, 1735.
By geometry, the surveyor is directed how MATHEMATICS originally signifies any kind to draw a map of any country, to divide his of discipline or learning, but now it is taken lands, and to lay down and plot any piece of for that science, which teaches or contem- ground, and thereby discover the area in plates whatever is capable of being numbered acres, rods, and perches. The gauger is inor measured. That part of the mathematics structed pw to find the capacities or solid which relates to numbers only, is called contents of all kinds of vessels, in barrels, arithmetic ; and that which is concerned gallons, bushels, &c. And the measurer is about measure in general, whether length, furnished with rules for finding the areas and breadth, motion, force, &c. is called geometry. contents of superfices and solids, and casting
As to the usefulness of arithmetic, it is well up all manner of workmanship. All these known that no business, commerce, trade, or and many more useful arts, too many to be employment whatsoever, even from the mer- enumerated here, wholly depend upon the chant to the shopkeeper, &c. can be managed aforesaid sciences, viz. arithmetic and geoand carried on, without the assistance of num- metry. bers; for by these the trader computes the This science is descended from the infancy value of all sorts of goods that he dealeth in, of the world, the inventors of which were the does his business with ease and certainty, and first propagators of human kind, as Adam, informs himself how matters stand at any time Noah, Abraham, Moses, and divers others. with respect to men, money, or merchandise, There has not been any science so much to profit and loss, whether he goes forward or esteemed and honoured as this of the mathebackward, grows richer or poorer. Neither matics, nor with so much industry and vigiis this science only useful to the merchant, lance become the care of great men, and labut is reckoned the primum mobile (or first boured in by the potentates of the world, viz. mover) of all mundane affairs in general, and l emperors, kings, princes, &c.
Mathematical demonstrations, are a logic, a mind worth cultivating, ought to apply of as much or more use, than that commonly themselves to this study.' learned at schools, serving to a just formation of the mind, enlarging its capacity, and strengthening it so, as to render the same ca- Causes of Earthquakes.-From the Pennsylpable of exact reasoning, and discerning truth
vania Gazette, No. 470, Dec. 15, 1737. from falsehood in all occurrences, even sub The late earthquake felt here, and probajects not mathematical. For which reason it bly in all the neighbouring provinces, have is said, the Egyptians, Persians, and Lacede- made many people desirous to know what monians, seldom elected any new kings, but may be the natural cause of such violent consuch as had some knowledge in the mathe- cussions ; we shall endeavour to gratify their matics, imagining those who had not, men of curiosity by giving them the various opinions imperfect judgments, and unfit to rule and of the learned on that head. govern.
Here naturalists are divided. Some ascribe Though Plato's censure, that those who did them to water, others to fire, and others to not understand the 117th proposition of the air : and all of them with some appearance of 13th book of Euclid's Elements, ought not to reason. To conceive which, it is to be ob be ranked amongst rational creatures, was un served, that the earth every where abounds in reasonable and unjust; yet to give a man the huge subterraneous caverns, veins and canals, character of universal learning, who is des particularly about the roots of mountains : titute of a competent knowlege in the mathe- that of these cavities, veins, &c. some are matics, is no less so.
full of water, whence are composed gulpbs, The usefulness of some particular parts of abysses, springs, rivulets; and others full of the mathematics in the common affairs of hu- exhalations; and that some parts of the earth man life, has rendered some knowledge of them are replete with nitre, sulphur, bitumen, vivery necessary to a great part of mankind, triol, &c. and very convenient to all the rest that are This premised, 1. The earth itself may any way conversant beyond the limits of their sometimes be the cause of its own shaking; own particular callings.
when the roots or basis of some large mass Those whom necessity has obliged to get being dissolved, or worn away by a Huid untheir bread by manual industry, where some derneath, it sinks into the same; and with its degree of art is required to go along with it, weight, occasions a tremor of the adjacent and who have had some insight into these stu- parts; produces a noise, and frequently an indies, have very often found advantages from undation of water. them sufficient to reward the pains they were 2. The subterraneous waters may occasion at in acquiring them. And whatever may earthquakes, by their overflowing, cutting out have been imputed to some other studies, new courses, &c. Add, that the water being under the notion of insignificancy and loss of heated and rarefied by the subterraneous fires, time, yet these, I believe, never caused re- may emit fumes, blasts, &c. which by their pentance in any, except it was for their re- action, either on the water or immediately on missness in the prosecution of them. the earth itself, may occasion great succus
Philosophers do generally affirm, that hu- sions. man knowledge to be most excellent, which is 3. The air may be the cause of earthconversant amongst the most excellent things. quakes: for the air being a collection of fumes What science then can there be, nore noble, and vapours raised from the earth and water; more excellent, more useful for men, more if it be pent up in too narrow viscera of the admirably high and demonstrative, than this earth, the subterraneous, or its own native of the mathematics.
heat, rarefying and expanding it, the force I shall conclude with what Plato says, lib. wherewith it endeavours to escape, may shake 7. of his Rebublic, with regard to the excel- the earth : hence there arise divers species lence and usefulness of geometry, being to of earthquakes, according to the different pothis purpose :
sition, quantity, &c. of the imprisoned aura. 66 Dear Friend-You see then that mathe Lastly, fire is a principal cause of earthmatics are necessary, because by the exact- quakes, both as it produces the aforesaid subness of the method, we get a habit of using terraneous aura or vapours; and as this aura, our minds to the best advantage: and it re- or spirit, from the different matter and commarkable, that all men being capable by na- position whereof arise sulphur, bitumen, and ture to reason and understand the sciences; other inflammable matters, takes fire, either the less acute, by studying this, though use- from some other fire it meets withal, or from less to them in every other respect, will gain its collision against hard bodies, or its interthis advantage, that their minds will be im- mixture with other fluids; by which means, proved in reasoning aright; for no study em- bursting out into a greater compass, the place ploys it more, nor makes it susceptible of at- becomes too narrow for it; so that pressing tention so much; and these who we find have against it on all sides, the adjoining parts are
shaken; till having made itself a passage, it another reason is, the paucity of pyrites in spends itself in a volcano, or burning moun- England. tain.
Comparing our earthquakes, thunder and But to come nearer to the point. Dr. Lis- lightning with theirs, is observed, that ter is of opinion, that the material cause of there it lightens almost daily, especially in thunder, lightning, and earthquakes, is one summer-time, here seldom; there thunder and the same, viz. the inflammable breath of and lightning is of long duration, here it is the pyrites, which is a substantial sulphur, and soon over; there the earthquakes are frequent, takes fire of itself.
long and terrible, with many paroxysms in a The difference between these three terri- day, and that for many days; here very ble phenomena, he takes only to consist in short, a few minutes, and scarce perceptible. this; that this sulphur, in the former, is fired To this purpose the subterraneous caverns in in the air ; and in the latter under ground: England are small and few compared to the which is a notion that Pliny had long before vast vaults in those parts of the world; which him : Quidenim, says he, aliud est in terra is evident from the sudden disappearance of tremor, quam in nube tonitru?
whole mountains and islands. This he thinks abundantly indicated by the Dr. Woodward gives us another theory of same sulphurous smell being found in any earthquakes. He endeavours to show, that thing burnt with lightning; and in the wa- the subterraneous heat, or fire (which is conters, &c. cast up in earthquakes, and even in tinually elevating water out of the abyss, to the air before and after them.
furnish the earth with rain, dew, springs and Add, that they agree in the manner of the rivers) being stopped in any part of the earth, noise ; which is carried on, as in a train, fired; and so diverted from its ordinary course, by the one rolling and rattling through the air, some accidental glut or obstruction in the takes fire as the vapours chance to drive; as pores or passages, through which it used to the other fired under ground, in like manner, ascend to the surface; becomes, by such moves with a desultory noise.
means, preternaturally assembled in a greater Thunder, which is the effect of the trem quantity than usual into one place, and therebling of the air, caused by the same vapours fore causeth a great rarefaction and intumesdispersed through it, has force enough to cence of the water of the abyss; putting it shake our houses; and why may not there be into great commotions and disorders, and at thunder and lightning under ground, in some the same time making the like effort on the vast repositories there, I see no reason. Es- earth; which being expanded upon the face pecially if we reflect, that the matter which of the abyss, occasions that agitation and concomposes the noisy vapour above us, is in cussion we call an earthquake. much larger quantities under ground.
This effort in some earthquakes, he obThat the earth abounds in cavities, every serves is so vehement, that it splits and tears body allows; and that these subterraneous ca- the earth, making cracks and chasms in it vities, are, at certain times, and in certain some miles in length, which open at the inseasons, full of inflammable vapours, the stant of the shock, and close again in the indamps in mines sufficiently witness, which tervals betwixt them : nay, it is sometimes so fired, do every thing as in an earthquake, violent, that it forces the superincumbent save in a lesser degree.
strata, breaks them all throughout, and thereAdd, that the pyrites alone, of all the known by perfectly undermines, and ruins the founminerals, yields this inflammable vapour, is dation of them ; so that these failing, the highly probable : for that no mineral or ore, whole tract, as soon as the shock is over, whatsoever, is sulphurous, but as it is wholly, sinks down into the abyss, and is swallowed or in part, a pyrites; and that there is but one up by it; the water thereof immediately risspecies of brimstone, which the pyrites natu- ing up and forming a lake in the place, where rally and only yields. The sulphur vive, or the said tract before was. That this effort natural brimstone, which is found in and being made in all directions indifferently, about the burning mountains, is certainly the the fire dilating and expanding on all hands, effects of sublimation; and those great quan- and endeavouring to get room, and make its tities of it said to be found about the skirts of way through all obstacles, falls as foul on the volcanoes, is only an argument of the long du- waters of the abyss beneath, as on the earth ration and vehemence of those fires; possibly, above, forcing it forth, which way soever it the pyrites of the volcanoes, or burning-moun- can find vent or passage, as well through its tains, may be more sulphurous than ours: and ordinary exits, wells, springs, and the outlets indeed it is plain, that some of ours in England of rivers, as through the chasms then newly are very lean, and hold but little sulphur; opened; through the camini or spiracles of others again very much; which may be one Ætna, or other neighbouring volcanoes; and reason why England is so little troubled with these hiatus's at the bottom of the sea, whereearthquakes; and Italy, and almost all round by the abyss below opens into it and commuthe Mediterranean sea, so very much: though nicates with it. That as the water resident
in the abyss is, in all parts of it, stored with volcano. That therefore there are scarce a considerable quantity of heat, and more es- any countries much annoyed by earthquakes, pecially in those where those extraordinary but have one of these fiery vents; which are aggregations of this fire happen, so likewise constantly in flames when any earthquake is the water which is thus forced out of it; happens; as disgorging that fire, which whilst insomuch that when thrown forth and mixed underneath was the cause of the disaster. with the waters of wells or springs of rivers, Lastly, that were it not for these diverticula, and the sea, it renders them very sensibly hot. it would rage in the bowels of the earth much
He adds, that though the abyss be liable to more furiously, and make greater havoc than those commotions in all parts ; yet the effects it doth. are no where very remarkable except in those We have seen what fire and water may countries which are mountainous, and conse- do, and that either of them are sufficient for quently stony or cavernous underneath; and all the phenomena of earthquakes; if they especially where the disposition of the strata should both fail, we have a third agent, scarce is such, that those caverns open into the inferior to either of them: the reader must abyss, and so freely admit and entertain the not be surprised when we tell him it is air. fire; which assembling therein is the cause Mons. Amontons, in the Memoires de of the shock: it naturally steering its course l’Acad. des Sciences, An. 1703, has an express that way where it finds the readiest recep- discourse to prove, that on the foot of the new tion, which is towards those caverns. Besides, experiments of the weight and spring of the that those parts of the earth which abound air, a moderate degree of heat may bring the with strata of stone or marble, making the air into a condition capable of causing earth, strongest opposition to this effort, are the quakes. It is shown, that at the depth of most furiously shattered ; and suffer much 43,528 fathoms below the surface of the earthmore by it, than those which consist of gravel air is only one fourth less heavy than mercury. sand, and the like laxer matter, which more Now, this depth of 43,528 fathoms is only a easily give way, and make not so great re- 74th part of the semi-diameter of the earth. sistance; but, above all, those countries which And the vast sphere beyond this depth, in diyield great store of sulphur and nitre, are, by ameter 6,451,538 fathoms, may probably be far, the most injured by earthquakes; those only filled with air; which will be here greatly minerals constituting in the earth a kind of condensed, and much heavier than the heavinatural gunpowder, which taking fire upon est bodies we know in nature. But it is found this assemblage, and approach of it, occasions by experiment, that the more air is compressed that murmurring noise, that subterraneous the more does the same degree of heat inthunder, which is heard rumbling in the bow- crease its spring, and the more capable does els of the earth during earthquakes, and by it render it of a violent effect: and that, for the assistance of its explosive power, renders instance, the degree of heat of boiling water the shock much greater, so as sometimes to increases the spring of the air above what it make miserable havoc and destruction. has in its natural state, in our climate, by a
And it is for this reason, that Italy, Sicily, quantity equal to a third of the weight whereAnatolia, and some parts of Greece, have with it is pressed. Whence we may conbeen so long, and often alarmed and harassed clude, that a degree of heat, which on the bý earthquakes ; these countries being all surface of the earth, will only have a mode. mountainous and cavernous, abounding with rate effect, may be capable of a very violent stone and marble, and affording sulphur and one below. And as we are assured, that nitre in great plenty.
there are in nature degrees of heat, much Further, that Ætna, Vesuvius, Hæcla, and more considerable than that of boiling water: the other volcanoes, are only so many spira- it is very possible there may be some, whose cles, serving for the discharge of this subter- violence, further assisted by the exceeding raneous fire, when it is thus preternaturally weight of the air, may be more than sufficient assembled. That where there happens to be to break and overturn this solid orb of 43,528 such a structure and conformation of the in- fathoms; whose weight, compared to that of terior parts of the earth; as that the fire may the included air, would be but a trifle. pass freely, and without impediment, from the Chemistry furnishes us a method of makcaverns wherein it assembles unto those spi- ing artificial earthquakes, which shall have racles: it then readily and easily gets out all the great effects of natural ones : which, from time to time, without shaking or dis- as it may illustrate the process of nature in turbing the earth: but where such commu- the production of these terrible phenomena nication is wanting, or passage not sufficient- under ground, we shall here add. ly large and open, so that it cannot come at To twenty pounds of iron filings, add as the spiracles, it heaves up and shocks the many of sulphur: mix, work, and temper the earth with greater or lesser impetuosity, ac- whole together with a little water, so as to cording to the quantity of fire thus assembled, form a mass, half moist and half dry. This betill it has made its way to the mouth of the ling buried three or four feet under ground, in
six or seven hours time, will have a prodigious | Fa. Anthon. Serovita, being on his way thither, effect : the earth will begin to tremble, crack and at the distance of a few miles, observed å and smoke, and fire and flame burst through. black cloud, like night, hovering over the city;
Such is the effect even of the two cold bo- and there arose from the mouth of Mongibeldies, in cold ground : there only wants a suf- lo, great spires of fame, which spread all ficient quantity of this mixture to produce a around. The sea all of a sudden began to roar, true Ætna. If it were supposed to burst out and rise in billows; and there was a blow, as under the sea, it would produce a spont. And if all the artillery in the world had been at if it were in the clouds, the effect would be once discharged. The birds flew about astothunder and lightning.
nished, the cattle in the fields ran crying, &c. An earthquake is defined to be a vehement His and his companion's horse stopped short, shake, or agitation of some considerable place, trembling; so that they were forced to alight. or part of the earth; from natural causes ; at- They were no sooner off, but they were lifted tended with a huge noise like thunder, and from the ground above two palms; when frequently with an eruption of water, or fire, casting his eyes towards Catanea, he with or smoke, or winds, &c.
amazement saw nothing but a thick cloud of They are the greatest and most formidable dust in the air. This was the scene of their phenomena of nature. Aristotle and Pliny calamity: for of the magnificent Catanea, distinguish two kinds, with respect to the there is not the least footstep to be seen. S. manner of the shake, viz. a tremor and a Bonajutus assures us, that of 18,914 inhabipulsation; the first being horizontal, in alter- tants, 18,000 perished therein. The same aunate vibrations, compared to the shaking of a thor, from a computation of the inhabitants, person in ague. The second perpendicular, before and after the earthquake, in the several up and down, their motion resembling that of cities and towns, finds that near 60,000 peboiling
rished out of 254,900. Agricola increases the number, and makes Jamaica is remarkable for earthquakes. four kinds, which Alb. Magnus again reduces The inhabitants, Dr. Sloan informs us, expect to three, viz. inclination, when the earth li- one every year. That author gives us the brates alternately from right to left; by which history of one in 1687: another horrible one mountains have been sometimes brought to in 1692, is described by several anonymous meet, and clash against each other: pulsation, authors. In two minutes time it shook down when it beats up and down like an artery: and and drowned nine tenths of the town of Port trembling, when it shakes and totters every Royal. The houses sunk outright, thirty or way, like a flame.
forty fathoms deep. The earth opening, swalThe Philosophical Transactions furnish us lowed up people; and they rose in other with abundance of histories of earthquakes ; streets; some in the middle of the harbour, particularly one at Oxford, in 1665, by Dr. and yet were saved; though there were 2000 Wallis and Mr. Boyle. Another at the same people lost, and 1000 acres of land sunk. All place in 1683, by Mr. Pigot. Another in Si- the houses were thrown down throughout the cily, in 1692-3 by Mr. Hartop, Fa. Allessan- island. One Hopkins had his plantation redro Burgos, and Vin. Bonajutus, which last is moved half a mile from its place. Of all wells, one of the most terrible ones in all history. from one fathom to six or seven, the water
It shook the whole island; and not only flew out at the top with a vehement motion. that, but Naples and Malta shared in the shock. While the houses, on the one side of the It was of the second kind mentioned by Aris- street were swallowed up, on the other they totle and Pliny, viz. a perpendicular pulsation, were thrown on heaps; and the sand in the or succession. It was impossible, says the street rose like waves in the sea, lifting up noble Bonajutus, for any body, in this country, every body that stood on it, and immediately to keep on their legs, on the dancing earth; dropping down into pits; and at the same inaay, those that lay on the ground, were toss- stant, a flood of waters breaking in, roller d from side to side, as on a rolling billow: them over and over; some catching hold of ligh walls leaped from their foundations seve- beams and rafters, &c. Ships and sloops in
the harbour were overset and lost; the Swarı The mischief it did is amazing : almost all frigate particularly, by the motion of the sea, he buildings in the countries were thrown and sinking of the wharf, was driven over lown. Fifty-four cities and towns, besides an the tops of many houses. It was attende! ncredible number of villages, were either de- with a hollow rumbling noise like that of troyed or greatly damaged. We shall only thunder. In less than a minute three quar. nstance the fate of Catanea, one of the most ters of the houses, and the ground they stoo i amous, ancient, and flourishing cities in the on with the inhabitants, were all sunk quit: cingdom; the residence of several monarchs, under water; and the little part, left behin is nd an university. This once famous, now was no better than a heap of rubbish. The nhappy Catanea, to use the words of Fa. shake was so violent, that it threw peop?": Burgos, had the greatest share in the tragedy. I down on their knees, or their faces, as they OL II. ...3 M