quainted with any ancient or foreign tongue, | sia, perfectly unknown as much as China, bethey will be masters of their own, which is of yond it, and India only by a little commerce more immediate and general use, and withal upon the coast, about Surat and Malabar; Afriwill have attained many other valuable accomplishments: the time usually spent in acquiring those languages, often without success, being here employed in laying such a foundation of knowledge and ability, as, properly improved, may qualify them to pass through and execute the several offices of civil life, with advantage and reputation to themselves and country. On Discoveries.-From the Pennsylvania THE world but a few ages since, was in a very poor condition, as to trade and navigation, nor indeed, were they much better in other matters of useful knowledge. It was a green headed time, every useful improvement was hid from them, they had neither looked into heaven, nor earth, into the sea, nor land, as has been done since. They had philosophy without experiments, mathematics without instruments, geometry without scale, astronomy without demonstration. ca had been more unknown, but by the ruin of the Carthaginians, all the western coast of it was sunk out of knowledge again, and forgotten; the northern coast of Africa, in the Mediterranean, remained known, and that was all, for the Saracens overrunning the nations which were planted there, ruined commerce, as well as religion; the Baltic Sea was not discovered, nor even the navigation of it known; for the Teutonic knights came not thither till the 13th century. America was not heard of, nor so much as a suggestion in the minds of men, that any part of the world lay that way. The coasts of Greenland, or Spitsbergen, and the whale fishing, not known; the best navigators in the world, at that time, would have fled from a whale, with much more fright and horror, than from the devil, in the most terrible shapes they had been told he appeared in. The coasts of Angola, Congo, the Gold and the Grain coasts, on the west side of Africa, from whence, since that time, such immense wealth has been drawn, not discovered, nor the least inquiry made after them. All the East India and China trade, not only undiscovered, but out of the reach of expectation! Coffee and tea, (those modern blessings of mankind) had never been heard of: all the unbounded ocean, we now call the South Sea, was hid, and unknown all the Atlantic. Ocean, beyond the mouth of the Streights, was frightful and terrible in the distant prospect, nor durst any one peep into it, otherwise than as they might creep along the coast of Africa, towards Sallee, or Santa Cruz. The North Seas was hid in a veil of impenetrable darkness; the White Sea, or Arch An They made war without powder, shot, cannon, or mortars; nay, the mob made their bonfires without squibs, or crackers. They went to sea without compass, and sailed without the needle. They viewed the stars, without telescopes, and measured latitudes without observation. Learning had no printing-press, writing no paper, and paper no ink; the lover was forced to send his mistress a deal board for a love-letter, and a billet doux might be the size of an ordinary trencher.They were clothed without manufacture, and their richest robes were the skins of the most formidable monsters; they carried on trade without books, and correspondence with-gel, was a very modern discovery; not found out posts; their merchants kept no accounts, their shop-keepers no cash-books, they had surgery without anatomy, and physicians without the materia medica, they gave emetics without ipecacuanha, drew blisters without cantharides, and cured agues without the bark. As for geographical discoveries, they had neither seen the North Cape, nor the Cape of Good Hope south. All the discovered inhabited world, which they knew and conversed with, was circumscribed within very narrow limits, viz. France, Britain, Spain, Italy, Germany, and Greece; the Lesser Asia, the west part of Persia, Arabia, the north parts of Africa, and the islands of the Mediterranean sea, and this was the whole world to them; not that even these countries were fully known neither, and several parts of them not inquired into at all. Germany was known little farther than the banks of the Elbe; Poland as little beyond the Vistula, or Hungary a little beyond the Danube; Muscovy or Rus out till sir Hugh Willoughby doubled the North Cape, and paid dear for the adventure, being frozen to death with all his crew on the coast of Lapland; while his companion's ship, with the famous Mr. Chancellor, went on to the Gulph of Russia, called the White Sea, where no Christian strangers had ever been before him. In these narrow circumstances stood the world's knowledge at the beginning of the 15th century, when men of genius began to look abroad and about them. Now, as it was wonderful to see a world so full of people, and people so capable of improving, yet so stupid, and so blind, so ignorant, and so perfectly unimproved; it was wonderful to see, with what a general alacrity they took the alarm, almost all together; preparing themselves as it were on a sudden, by a general inspiration, to spread knowledge through the earth, and to search into every thing, that it was impossible to uncover. How surprising is it to look back, so little a way behind us, and see, that even in less than two hundred years, all this (now so selfwise) part of the world did not so much as know, whether there was any such place, as a Russia, a China, a Guinea, a Greenland, or a North Cape! That as to America, it was never supposed, there was any such place, neither had the world, though they stood upon the shoulders of four thousand years' experience, the least thought, so much as that there was any land that way! As they were ignorant of places, so of things also; so vast are the improvements of science, that all our knowledge of mathematics, of nature, of the brightest part of human wisdom, had their admission among us within these two last centuries. What was the world then, before? And to what were the heads and hands of mankind applied? The rich had no commerce, the poor no employment; war and the sword was the great field of honour, the stage of preferment, and you have scarce a man eminent in the world, for any thing before that time, but for a furious outrageous falling upon his fellowcreatures, like Nimrod, and his successors of modern memory. The world is now daily increasing in experimental knowledge; and let no man flatter the age, with pretending we have arrived to a perfection of discoveries. What's now discovered, only serves to show, is useful for all sorts and degrees of men, from the highest to the lowest. As to the usefulness of geometry, it is as certain, that no curious art or mechanic work, can either be invented, improved, or performed, without its assisting principles. It is owing to this, that astronomers are put into a way of making their observations, coming at the knowledge of the extent of the heavens, the duration of time, the motions, magnitudes, and distances of the heavenly bodies, their situations, positions, risings, settings, aspects, and eclipses; also the measure of seasons, of years, and of ages. It is by the assistance of this science, that geographers present to our view at once, the magnitude and form of the whole earth, the vast extent of the seas, the divisions of empires, kingdoms, and provinces. It is by the help of geometry, the ingenious mariner is instructed how to guide a ship through the vast ocean, from one part of the earth to another, the nearest and safest way, and in the shortest time. By help of this science the architects take their just measures for the structure of buildings, as private houses, churches, palaces, ships, fortifications, &c. By its help engineers conduct all their works, take the situation and plan of towns, forts and castles, measure their distances from one another, and carry their measure into places that are only accessible to the eye. From hence also is deduced that admirable art of drawing sun-dials on any plane howsoever 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 Oct. 30, 1735. MATHEMATICS originally signifies any kind of discipline or learning, but now it is taken for that science, which teaches or contemplates whatever is capable of being numbered or measured. That part of the mathematics which relates to numbers only, is called arithmetic; and that which is concerned about measure in general, whether length, breadth, motion, force, &c. is called geometry. As to the usefulness of arithmetic, it is well known that no business, commerce, trade, or employment whatsoever, even from the merchant to the shopkeeper, &c. can be managed and carried on, without the assistance of numbers; for by these the trader computes the value of all sorts of goods that he dealeth in, does his business with ease and certainty, and informs himself how matters stand at any time with respect to men, money, or merchandise, to profit and loss, whether he goes forward or backward, grows richer or poorer. Neither is this science only useful to the merchant, but is reckoned the primum mobile (or first mover) of all mundane affairs in general, and other astronomical matters. By geometry, the surveyor is directed how to draw a map of any country, to divide his lands, and to lay down and plot any piece of ground, and thereby discover the area in acres, rods, and perches. The gauger is instructed how to find the capacities or solid contents of all kinds of vessels, in barrels, gallons, bushels, &c. And the measurer is furnished with rules for finding the areas and contents of superfices and solids, and casting up all manner of workmanship. All these and many more useful arts, too many to be enumerated here, wholly depend upon the aforesaid sciences, viz. arithmetic and geometry, This science is descended from the infancy of the world, the inventors of which were the first propagators of human kind, as Adam, Noah, Abraham, Moses, and divers others. There has not been any science so much esteemed and honoured as this of the mathematics, nor with so much industry and vigilance become the care of great men, and laboured in by the potentates of the world, viz. 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 capable of exact reasoning, and discerning truth from falsehood in all occurrences, even subjects not mathematical. For which reason it is said, the Egyptians, Persians, and Lacedemonians, seldom elected any new kings, but such as had some knowledge in the mathematics, imagining those who had not, men of imperfect judgments, and unfit to rule and govern. Though Plato's censure, that those who did not understand the 117th proposition of the 13th book of Euclid's Elements, ought not to be ranked amongst rational creatures, was unreasonable and unjust; yet to give a man the character of universal learning, who is destitute of a competent knowlege in the mathematics, is no less so. The usefulness of some particular parts of the mathematics in the common affairs of human life, has rendered some knowledge of them very necessary to a great part of mankind, and very convenient to all the rest that are any way conversant beyond the limits of their own particular callings. Causes of Earthquakes.-From the Pennsylvania Gazette, No. 470, Dec. 15, 1737. THE late earthquake felt here, and probably in all the neighbouring provinces, have made many people desirous to know what may be the natural cause of such violent concussions; we shall endeavour to gratify their curiosity by giving them the various opinions of the learned on that head. Here naturalists are divided. Some ascribe them to water, others to fire, and others to air: and all of them with some appearance of reason. To conceive which, it is to be observed, that the earth every where abounds in huge subterraneous caverns, veins and canals, particularly about the roots of mountains: that of these cavities, veins, &c. some are full of water, whence are composed gulphs, abysses, springs, rivulets; and others full of exhalations; and that some parts of the earth are replete with nitre, sulphur, bitumen, vitriol, &c. This premised, 1. The earth itself may sometimes be the cause of its own shaking; when the roots or basis of some large mass being dissolved, or worn away by a fluid underneath, it sinks into the same; and with its weight, occasions a tremor of the adjacent parts; produces a noise, and frequently an inundation of water. Those whom necessity has obliged to get their bread by manual industry, where some degree of art is required to go along with it, and who have had some insight into these studies, have very often found advantages from 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 succussions. Philosophers do generally affirm, that human knowledge to be most excellent, which is conversant amongst the most excellent things. What science then can there be, more noble, more excellent, more useful for men, more admirably high and demonstrative, than this of the mathematics. I shall conclude with what Plato says, lib. 7. of his Rebublic, with regard to the excellence and usefulness of geometry, being to this purpose: "Dear Friend-You see then that mathematics are necessary, because by the exactness of the method, we get a habit of using our minds to the best advantage: and it is remarkable, that all men being capable by nature to reason and understand the sciences; the less acute, by studying this, though useless to them in every other respect, will gain this advantage, that their minds will be improved in reasoning aright; for no study employs it more, nor makes it susceptible of attention so much; and these who we find have 3. The air may be the cause of earthquakes: for the air being a collection of fumes and vapours raised from the earth and water; if it be pent up in too narrow viscera of the earth, the subterraneous, or its own native heat, rarefying and expanding it, the force wherewith it endeavours to escape, may shake the earth: hence there arise divers species of earthquakes, according to the different position, quantity, &c. of the imprisoned aura. Lastly, fire is a principal cause of earthquakes; both as it produces the aforesaid subterraneous aura or vapours; and as this aura, or spirit, from the different matter and composition whereof arise sulphur, bitumen, and other inflammable matters, takes fire, either from some other fire it meets withal, or from its collision against hard bodies, or its intermixture with other fluids; by which means, bursting out into a greater compass, the place becomes too narrow for it; so that pressing 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. But to come nearer to the point. Dr. Lister is of opinion, that the material cause of thunder, lightning, and earthquakes, is one and the same, viz. the inflammable breath of the pyrites, which is a substantial sulphur, and takes fire of itself. The difference between these three terrible phenomena, he takes only to consist in this; that this sulphur, in the former, is fired in the air; and in the latter under ground: which is a notion that Pliny had long before him: Quidenim, says he, aliud est in terra tremor, quam in nube tonitru? This he thinks abundantly indicated by the same sulphurous smell being found in any thing burnt with lightning; and in the waters, &c. cast up in earthquakes, and even in the air before and after them. Add, that they agree in the manner of the noise; which is carried on, as in a train, fired; the one rolling and rattling through the air, takes fire as the vapours chance to drive; as the other fired under ground, in like manner, moves with a desultory noise. Thunder, which is the effect of the trembling of the air, caused by the same vapours dispersed through it, has force enough to shake our houses; and why may not there be thunder and lightning under ground, in some vast repositories there, I see no reason. Especially if we reflect, that the matter which composes the noisy vapour above us, is in much larger quantities under ground. That the earth abounds in cavities, every body allows; and that these subterraneous cavities, are, at certain times, and in certain seasons, full of inflammable vapours, the damps in mines sufficiently witness, which fired, do every thing as in an earthquake, save in a lesser degree. Add, that the pyrites alone, of all the known minerals, yields this inflammable vapour, is highly probable for that no mineral or ore, whatsoever, is sulphurous, but as it is wholly, or in part, a pyrites; and that there is but one species of brimstone, which the pyrites naturally and only yields. The sulphur vive, or natural brimstone, which is found in and about the burning mountains, is certainly the effects of sublimation; and those great quantities of it said to be found about the skirts of volcanoes, is only an argument of the long duration and vehemence of those fires; possibly, the pyrites of the volcanoes, or burning-mountains, may be more sulphurous than ours: and indeed it is plain, that some of ours in England are very lean, and hold but little sulphur; others again very much; which may be one reason why England is so little troubled with earthquakes; and Italy, and almost all round the Mediterranean sea, so very much: though Comparing our earthquakes, thunder and lightning with theirs, it is observed, that there it lightens almost daily, especially in summer-time, here seldom; there thunder and lightning is of long duration, here it is soon over; there the earthquakes are frequent, long and terrible, with many paroxysms in a day, and that for many days; here very short, a few minutes, and scarce perceptible. To this purpose the subterraneous caverns in England are small and few compared to the vast vaults in those parts of the world; which is evident from the sudden disappearance of whole mountains and islands. Dr. Woodward gives us another theory of earthquakes. He endeavours to show, that the subterraneous heat, or fire (which is continually elevating water out of the abyss, to furnish the earth with rain, dew, springs and rivers) being stopped in any part of the earth, and so diverted from its ordinary course, by some accidental glut or obstruction in the pores or passages, through which it used to ascend to the surface; becomes, by such means, preternaturally assembled in a greater quantity than usual into one place, and therefore causeth a great rarefaction and intumescence of the water of the abyss; putting it into great commotions and disorders, and at the same time making the like effort on the earth; which being expanded upon the face of the abyss, occasions that agitation and concussion we call an earthquake. This effort in some earthquakes, he ob serves is so vehement, that it splits and tears the earth, making cracks and chasms in it some miles in length, which open at the instant of the shock, and close again in the intervals betwixt them: nay, it is sometimes so violent, that it forces the superincumbent strata, breaks them all throughout, and thereby perfectly undermines, and ruins the foundation of them; so that these failing, the whole tract, as soon as the shock is over, sinks down into the abyss, and is swallowed up by it; the water thereof immediately rising up and forming a lake in the place, where the said tract before was. That this effort being made in all directions indifferently, the fire dilating and expanding on all hands, and endeavouring to get room, and make its way through all obstacles, falls as foul on the waters of the abyss beneath, as on the earth above, forcing it forth, which way soever it can find vent or passage, as well through its ordinary exits, wells, springs, and the outlets of rivers, as through the chasms then newly opened; through the camini or spiracles of Etna, or other neighbouring volcanoes; and these hiatus's at the bottom of the sea, whereby the abyss below opens into it and communicates with it. That as the water resident We have seen what fire and water may do, and that either of them are sufficient for all the phenomena of earthquakes; if they should both fail, we have a third agent, scarce inferior to either of them: the reader must not be surprised when we tell him it is air. 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 countries which are mountainous, and consequently stony or cavernous underneath; and especially where the disposition of the strata is such, that those caverns open into the abyss, and so freely admit and entertain the 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 heavi natural 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 the assistance of its explosive power, renders the shock much greater, so as sometimes to make miserable havoc and destruction. And it is for this reason, that Italy, Sicily, Anatolia, and some parts of Greece, have been so long, and often alarmed and harassed by earthquakes; these countries being all mountainous and cavernous, abounding with stone and marble, and affording sulphur and nitre in great plenty. Further, that Etna, Vesuvius, Hæcla, and the other volcanoes, are only so many spiracles, serving for the discharge of this subter raneous fire, when it is thus preternaturally assembled. That where there happens to be such a structure and conformation of the interior parts of the earth; as that the fire may pass freely, and without impediment, from the caverns wherein it assembles unto those spiracles: it then readily and easily gets out from time to time, without shaking or disturbing the earth: but where such communication is wanting, or passage not sufficiently large and open, so that it cannot come at the spiracles, it heaves up and shocks the earth with greater or lesser impetuosity, according to the quantity of fire thus assembled, till it has made its way to the mouth of the it render it of a violent effect: and that, for instance, the degree of heat of boiling water increases the spring of the air above what it has in its natural state, in our climate, by a quantity equal to a third of the weight wherewith it is pressed. Whence we may conclude, that a degree of heat, which on the surface of the earth, will only have a moderate effect, may be capable of a very violent one below. And as we are assured, that there are in nature degrees of heat, much more considerable than that of boiling water: it is very possible there may be some, whose violence, further assisted by the exceeding weight of the air, may be more than sufficient to break and overturn this solid orb of 43,528 fathoms; whose weight, compared to that of the included air, would be but a trifle. Chemistry furnishes us a method of making artificial earthquakes, which shall have all the great effects of natural ones: which, as it may illustrate the process of nature in the production of these terrible phenomena under ground, we shall here add. To twenty pounds of iron filings, add as many of sulphur: mix, work, and temper the whole together with a little water, so as to form a mass, half moist and half dry. This be ing buried three or four feet under ground, in |