Some properties of squares are as fol- any number of the cubes of the natural low: 1. Of the 2. An arithmetical mean between any two squares m' and n2, exceeds their geometrical mean, by half the square of the difference of their roots. That is m+ {n2 mn + d2. 3. Of three equidistant squares in the series, the geometrical mean between the extremes is less than the middle square, by the square of their common distance in the series, or of the common difference of their roo s. =2m That is, mp n' d'; where m, n, p, are in arithmetical progres. sion, the common difference being d. 4. The difference between the two adjacent squares m2 and n2, is n m2 +1; in like manner, p2 ―n2 = 2n + 1, the difference between the next two adjacent squares n' and p'; and so on, for the next following squares. Hence the difference of these differences, or the second difference of the squares, is 2n 2m m == 2 x n - m === 2 only, because n— 1; that is, the second differences of the squares are each the same constant number 2; therefore the first differences will be found by the continual addition of the number 2; and then the squares themselves will be found by the continual addition of the first difference; and thus the whole series of squares is constructed by addition only, as here below: 2d Diff. 2 2 2 2 2 2&c. 1st Diff. 1 3 5 7 91113&c. Squares 14 916253649&c. 5. Another curious property, also noted by the same author, is, that the sum of series 1, 2, 3, 4, &c. taken from the beginning, always makes a square number, and that the series of squares, so formed, have for their roots the numbers . . . 1, 3, 6, 10, 15, 21, &c. the diffs. of which are 1, 2, 3, 4, 5, 6, &c. viz. 1 = 1', 13233', 13+23+35 13+23+33 +410; and the general 1 + 2 + 33 + n3 = (1 + 2 + 3 + n)2 = = {n.n + 1; where n is the number of the terms or cubes. Squaring the circle, is the making or finding a square whose area shall be equal to the area of a given circle. The best mathematicians have not yet been able to resolve this problem accurately, and perhaps never will. But they can easily come to any proposed degree of approximation whatever; for instance, so near as not to err so much in the area as a grain of sand would cover, in a circle whose diameter is equal to that of the orbit of Saturn. The following proportion is near enough the truth for any real use, viz. as 1 is to .88622692, so is the diameter of any circle to the side of the square of an equal area. Therefore, if the diameter of the circle be called d, and the side of the equal squares; then is s.88622692d = 32d nearly. 44 448 nearly. SQUARE root, a number considered as the root of a second power or square number; or a number, by whose multiplication into itself a square number is generated. SQUARE battle, or Battalion of Men, is one that hath an equal number of men in rank and file. SQUARE, hollow, in the military art, is a body of foot drawn up with an empty space in the middle for the colours, drums, and baggage; faced and covered by the pikes every way, to keep off horse. SQUARE, an instrument consisting of two rulers, or branches, fastened perpendicularly at one end of their extremes, so as to form a right angle; it is of great use in the description and mensuration of right angles, and laying down perpendiculars. SQUARE, in naval affairs, is a term peculiarly appropriated to the yards and their sails, either implying that they are at right angles with the mast or keel, er that they are of greater extent than demonstration their volcanic production usual. SQUIRREL. See SCIURUS. STACHYS, in botany, a genus of the Didynamia Gymnospermia class and order. Natural order of Verticillatæ, or Labiatæ. Essential character: corolla upper lip arched; lower reflexed at the sides; the middle segments larger, emarginate; stamens finally reflexed towards the sides. There are twenty-four species STÆHELINA, in botany, so named from John Henry Stahelin and his son, Swiss physicians, a genus of the Syngenesia Polygamia Equalis class and order. Natural order of Compositæ Discoideæ. Cinarocephala, Jussieu. Essential character: anthers tailed; down branched; receptacle with very short chaffs. There are ten species. STAFFA, an island situated on the coast of Scotland, three miles north-east of Iona or Columb-kill, and west of Mull, about a mile in length, and half a mile in breadth, belonging to Mr. Lauchlin Mac Quarie. This inconsiderable isle is one amongst the most wonderful productions of nature, and deserves the attention of every natural philosopher, though it is unfortunately placed in a region which prevents frequent visits, even from curious investigators. The peculiarity that renders it so interesting, arises from the basaltes composing it assuming a number of magnificent forms, equally astonishing and sublime; but as we purpose to describe them with some degree of minuteness, it will be proper to give a general sketch of the nature of the substance termed basaltes, and where it abounds, that the subject may be clearly understood. See BASALTES. According to Strabo and Agricola, the antique basaltes is found in the same pris. matical form in Egypt, which distinguishes its outline in various parts of Europe. Farber, a professor of natural history at Mietau, supposes that found in the Vicentine Paduan and Veronese districts of Italy to be a crystallized lava, and asserts, that the antique basaltes is in every respect exactly similar to the compact lavas of Vesuvius and Monte Albano, which are used by statuaries to restore mutilated statues made of this material. The Egyptian basaltes contain a small proportion, in some of the varieties, of the white garnet like shorl crystallizations and lamellas common in the Italian lavas, a circumstance that seems to prove to VOL. XI. in these particular instances, though others of the oriental basaltes seem to have originated from aqueous mix tures. Dr. Von Troil, member of the Academy of Sciences at Stockholm, entertained an opinion that they were caused by the operations of fire, which he founded on that of M. Desmaret, who was the first naturalist that ventured to attribute them to that cause, in a description of some basaltes, found near St. Sandour, in Auvergne, presented by him to the attention of the French Academy of Sciences. Other naturalists, who had considered them to be a species of crystallization, ridiculed this idea as founded upon false principles, as they contended basalt pillars are discovered where it seemed highly improbable that volcanoes could ever have existed; still, however, they had the candour to enter into an examination of the assertion of M. Desmaret, the result of which was nearly a confirmation of his conjecture, that basalt pillars were produced by subterraneous fires. As a collateral support of this hypothesis, Dr. Von Troil cites the instances of Stolpenstein in Meissen, Lauban in Lusatia, of Bohemia, Leignita in Silesia, Brandau in Hessia, Sicily, Bolsenna, Montebello, and St. Forio in Italy; the district of Vicenza, Monte Rosso, in the District of Padua, Monte Diavolo in the mountains of Verona, in Lower Languedoc, in Ireland, and in the western islands of Scotland, in each of which places, he says, a doubt cannot be entertained that volcanoes have existed; besides those, he mentions St. Giovanni, Monte Castillo, Monte Nuovo, Monte Oliveta, near Cader Idris, in Wales, and almost every part of Velay and Auvergne, where the towns of Chillac and St. Fluor are situated upon basaltes. The peasantry of Iceland seem to have entertained a similar opinion of their origin to that of the lower orders of the Irish, as the former suppose them to have been piled, in the regular manner they are seen there, by giants, and thence call them Trollahland and Trollkonugardur, and the latter term their magnificent causeway, the Giant's. The pillars of the Icelandic basaltes have generally from three to seven sides; they vary in thickness from four to six feet, and some are of thirty-six, and others even forty-eight feet in length, without horizontal divisions; but such are the capricious operations of nature, that pillars are sometimes. Gg found not more than six or twelve inches long; those, however, are invariably very regular, and are made use of for doors and windows; at others they appear in the utmost confusion, broken, and overturned; in particular instances they just appear above the surface of the mountains, amongst lava and tufa, and there are places where they extend three miles together without interruption. The basalt pillars of Glockenberg in Snefialdsnas, exhibit a very different appearance from those of any other part of Iceland, as the pillars on the summit of that mountain lie horizontally, those on the sides incline, and the lowest stand erect. In some places they are found as if bent, when heated, into a semicircular form, an effect which seems to confirm the idea that violent fires have prevailed, either at their formation, or subsequently. The substance of the pillars of this island resemble those of Staffa in some parts of it, but in others they are more porous, and incline more to a grey colour. This circumstance induced the Doctor to think it would be an easy matter to trace all the gradations between the most perfect basalt pillar and the coarsest description of lava, and he even saw some at Videy, of a fine grain, extremely solid, of a blackish grey, and consisting of many joints; some porous glassy kind of stone, which he found at Laugarnas, near the sea, was so indistinctly divided, that he was undecided whether to class it with the lavas or basalt pillars; but the opinion of his friends determined him in favour of the latter. We have been the more particular in noticing the peculiarities of the basaltes of Iceland, as that island is situated in the vicinity of Staffa, to which we shall now turn our attention. The gentleman we have just mentioned was one of the first persons who had the good fortune to examine the latter with any degree of accuracy; nor indeed had the public been informed before of the distinguishing marks which render it so highly interesting, Buchanan being then the only author that had noticed this beautiful work of nature, though very slightly. Mr. Pennant, who possessed every requisite talent for informing the world, was disappointed by an adverse wind, from visiting Staffa in the year that proved more favourable to Dr. Von Troil, who would have been exactly in the same situation, in all probability, had not the tide, which flows with great strength between the western isles of Scotland, compelled the captain of the vessel employed to take him to Iceland to anchor on the night of the twelfth of August, in the sound between the Isle of Mull and Morvern on the continent, and precisely opposite to Drumnen, the seat of Mr. Maclean, by whom the Doctor and his friends were immediately invited on shore to breakfast, with the characteristic hospitality of the Highlanders. Mr. Banks, now Sir Joseph, being of the party intending to visit Iceland, eagerly accepted, with the Doctor, and others, the offer of Mr. Maclean to conduct them to Staffa, to which they were conveyed by the ship's long boat the same evening, about nine o'clock. "It was impossible," says the Doctor "for our surprise to be increased, or our curiosity to be fuller gratified than they were the next morning, when we beheld the no less than beautiful spectacle which nature presented to our view. If we even with admiration behold art, according to the rules prescribed to it, observing a certain kind of order, which not only strikes the eye, but also pleases it, what must be the effect produced upon us when we behold nature displaying, as it were, a regularity, which far surpasses every thing that art ever produced? An attentive spectator will find as much occasion for wonder and astonishment, when he observes how infinitely short human wisdom appears, when we attempt to imitate nature in this as well as any other of her grand and awful productions; and though we acknowledge nature to be the mistress of all the arts, and ascribe a greater degree of perfection to them, the nearer they approach and imitate it, yet we sometimes imagine that she might be improved, according to the rules of architecture. How magnificent are the remains which we have of the porticoes of the ancients, and with what admiration do we behold the colonnades that adorn the principal buildings of our times; and yet every one who compares them with Fingal's cave, formed by nature in the Isle of Staffa, must readily acknowledge, that this piece of nature's architecture far surpasses every thing that invention, luxury, and taste, ever produced among the Greeks." A small cave on the west side of the island affords a convenient landing place, but there are no regular basalt pillars to be met with in its immediate vicinity. On the south side of it are some narrow pillars, which are inclined, and resemble the springs of the ribs of an arch; beyond those is a small grotto, on the right hand, not composed of pillars, though they ap pear above it, disposed in the manner of the interior parts of the timbers of a ship. At a few yards distance, and opposite to the grotto, extends the peninsula of Boscha-la, consisting of regular, but smaller pillars, which are all of a conical figure. Some of these diverge as from a centre, some incline, and others, and by far the greater number, are perpendicular. The island itself, opposite to Bo-scha-la, is composed of thick columns, which extend into the sea as far as the eye is able to penetrate, but are not very high, and gradually decrease as they approach the water. Their relative connection is so admirably preserved, that a person may walk upon their ends as conveniently as if ascending or descending the steps of a staircase; these lead to Fingal's, or Finhn Mac Coul's cave or grotto, which is excavated out of that mountain from north-east to east. The cave is formed by regular pillars, extending to a great distance on each side, which support an arch composed of the obtuse points of others, placed very close together; unfortunately the floor of this wonderful place is covered by a body of clear fresh water, several feet in depth, through which may be seen an incredible number of fragments of pillars. The colour of the columns is grey, inclining to black, and the joints are distinguishable by the intervention of a yellow stalactic quarry rind, that exhales, and serves to make the separations more distinct, at the same time that it produces an agreeable effect by many different gradations of colour. A sufficient degree of light enters the cave to illuminate it to the extremity, where the ranges of pillars are perfectly discernible, and the ebbing and flowing of the tide constantly conveying and discharging air from within it, is at all times fit for respiration, and by no means noxious. This circumstance may still further originate from the passage of the water through a fissure in the rocks, rather lower than the surface, which occasions a rushing sound upon each rise of the tide, that contributes to render the effect of the whole still more singular and impressive. A boat is certainly the most convenient for visiting Fingal's cave, but it is possible to walk into it, upon the points of some of the pillars which are higher than the level of the water. The party already mentioned measured the dimensions of this beautiful grotto, and we acknowledge ourselves indebted to Dr. Von Troil for the following particulars: The length from the furthest of The depth of the water at `entrance Of the inside end Ft. In. 371 6 53 7 20 0 117 6 70 0 39 6 54 0 18 0 9 0 36 8 S2 6 31 4 34 4 From the water to the foot of the pillars Height of the pillars Height of the arch, or vault, above the top of the pillars The stratum above The stratum beneath the pillars was considered by the party to be no other than tufa, which being heated at the period when this phenomenon was produced, received into its depths fragments of basalt; that above them tinged with red, appears to be lava, containing other fragments scattered in various unequal directions; although it is evident the most violent heat must have acted upon it, yet there are not the least traces in its exterior, the pillars having been removed by it, for the whole enormous mass rests upon them. On the north side of the island is ano ther cave, called Corvoranti, where the stratum is raised, and the pillars consequently appear shortened; those are tolerably distinct, and continue so till the intervention of a bay, that extends some distance inland, and there the pillars are discontinued. The mountains in this neighbourhood are composed of dark brown stone, which may or may not be lava: but there is no sort of regularity observable in its texture. On passing further, and on the south-east side of the Island, the basalt columnar appearance commences, though almost imperceptibly; hence they gradually assume their characteristic form, till at last the spectator finds himself on the spot where they are in full perfection. The shape of the columns vary from three to seven sides, though the majority have five and six; the former are so numerous, that a heptagonal pillar is surrounded with seven others, which join closely to its seven sides. In some instances inconsiderable fissures may be perceived, but those are generally filled with quartz, and in one particular place that had penetrated through several pillars, without interrupting the regularity of their arrangement; one of the greatest wonders attending this operation of nature, is, the separation of each pillar into pieces, which are so closely jointed, that it is almost impossible to introduce a knife between the interstices. Upon an attentive examination of many of those pieces, it was found that the uppermost was generally concave, in some cases flat, but very rarely convex. When the upper surface was flat, the lowest joint was the same; but when it was excavated, the lower one was rounded and reversed. The sides of the pillars are of unequal dimensions, to prove which, we shall give the measurement of two, extracted from the Letters on Iceland, containing Dr. Von Troil's communication on this subject. One with four sides. The angles are as sharp and well de. fined as those of the pillars of the Giant's Causeway in Ireland, and their colour is generally black, the inclination to yellow being confined to the external sides, which are exposed to, and in some degree bleached by, the action of the sun, rain, and wind. The texture of their substance much resembles, and is proba bly the same as the Icelandic agate. Professor Bergman was divided in opinion, whether these pillars were produced by first acting upon particular substances, or whether subterraneous fires, sending forth vapour, may have softened the superincumbent earth, which becoming soft, and yielding to the force below, ascended in this peculiar form, and became gradually petrified. This latter supposition met the ideas of Von Troil, who illustrates it by saying, he has observed the distinct and regular appearance alluded to in dried clay, snd even starch, when dried in a basin. "For," adds the latter, "it may be demonstated, that they are not crystals formed by nature, by their not being produced, as all other crystals are, by external apposition (per appositionem,) nor in any other matrix, as is common among crystals." He further observes, "The following may, however, serve as a proof that I did not, without due foundation, believe them to be a kind of lava, which burst in growing cold and hard. First, you find both in the Island of Staffa, and many other places, that the pillars stand on lava or tufa, and are surrounded by this matter. Secondly, at Staffa there was a large stratum above the pillars, in which there were many pieces of those pillars irregularly thrown one among another, which leaves us to conjecture that they must have been more in number, and higher, after an old eruption of fire; but that a subsequent eruption had overthrown them, and mixed them with the whole mass. STAIRCASE, in architecture, an ascent inclosed between walls, or a balustrade, consisting of stairs, or steps, with landing-places and rails, serving to make a communication between the several stories of a house. The construction of a complete staircase is one of the most curious works in architecture. STAKE, the name of a small anvil, used by smiths; sometimes it stands on a broad iron foot on the work-bench, to be moved up and down occasionally; and sometimes it hath a strong iron spike at the bottom, by which it is fixed to some place on the work-bench. Its use is to sit small and cold work straight, by hammer |