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Some properties of squares are as fol. any number of the cubes of the natural low : 1. Of the
series 1, 2, 3, 4, &c. taken from the be
ginning, always makes a square number, Natural series of squares 1., 2., 3., 4., &c. and that the series of squares, so formed, which are equal to 1,4,9, 16, &c. have for their roots the numbers ... 1,
3, 6, 10, 15, 21, &c. the diff's, of which The mean proportional m n between are 1, 2, 3, 4, 5, 6, &c. viz. any two of these squares mé and n’, is 1j = 1, equal to the less square plus, its root 13 + 23 = 3, multiplied by the difference of the roots; 13 + 23 + 33 = 6, or also equal to the greater square mi- 13 + 2 + 33 +4=102; and the ge. nus, its root multiplied by the said dif- neral 1? 2 + 33 + 1) = (1 + 2 + 3 ference of the roots. That is
+ n): = $n.n + 1; where n is the mn1 = m + dm = n - dn; number of the terms or cubes. where d = n − m is the difference of Squaring the circle, is the making or their roots,
finding a square whose area shall be 2. An arithmetical mean between any equal to the area of a given circle. two squares m and n', exceeds their geo. The best mathematicians have not yet metrical mean, by half the square of the been able to resolve this problem accu. difference of their roots.
rately, and perhaps never will. But That is met n = m n + 1d. they can easily come to any proposed 9. Of three equidistant squares in the degree of approximation whatever; for series, the geometrical mean between the instance, so near as not to ert so much extremes is less than the middle square, in the area as a grain of sand would by the square of their common distance cover, in a circle whose diameter is in the series, or of the common differ- equal to that of the orbit of Saturn. ence of their roois,
The following proportion is near enough That is, m p = n - ds;
the truth for any real use, viz. as 1 is where m, n, p, are in arithmetical progres. to .88622692, so is the diameter of any sion, the common difference being d. circle to the side of the square of an
4. The difference between the two ad. equal area. Therefore, if the diameter jacent squares m’ and n', is n -- m =2m
of the circle be called d, and the side of +1; in like manner, p: -na 2n + 1,
the equal square s; the difference between the next two ad.
then is 8 = .886226920 = 39d nearly. jacent squares ni and p?; and so on, for the next following squares. Hence the
and d = 88622697 = *** nearly. difference of these differences, or the se. cond difference of the squares, is 21
SQUARE root, a number considered as
the root of a second power or square 2m = 2 x n - m=2 only, because n - number; or a number, by whose multim = 1; that is, the second differences of plication into itself a square number is the squares are each the same constant generated. number 2 ; therefore the first differences SQUARE battle, or Battalion of Men, is will be found by the continual addition of one that hath an equal number of men in the number 2; and then the squares rank and file. themselves will be found by the con SQUARE, hollow, in the military art, is tinual addition of the first difference; a body of foot drawn up with an empty and thus the whole series of squares is space in the middle for the colours, constructed by addition only, as here drums, and baggage; faced and coverbelow :
ed by the pikes every way, to keep off horse.
Squane, an instrument consisting of 2d Diff.
two rulers, or branches, fastened per.
pendicularly at one end of their ex1st Diff. 1 3 5 7 9 11 13&c.
tremes, so as to form a right angle; it
is of great use in the description and Squares il 4 9 16 25/36/49&c.
mensuration of right angles, and laying down perpendiculars.
SQUARE, in naval affairs, is a term pe.
culiarly appropriated to the yards and 5. Another curious property, also not their sails, either implying that they are ed by the same author, is, that the sum of at right angles with the mast or keel;
er that they are of greater extent than demonstration their volcanic production usu.l.
in these particular instances, though SQUIRREL. See Sciurus.
others of the oriental basaltes seem STACHYS, in botany, a genus of the to have originated from aqueous mixDidynamia Gymnospermia class and or- tures. der. Natural order of Verticillatæ, or Dr. Von Troil, member of the AcadeLabiatæ · Essential character: corolla my of Sciences at Stockholm, entertained upper lip arched; lower reflexed at the an opinion that they were caused by the sides ; the middle segments larger, operations of fire, which he founded on emarginate ; stamens finally reflexed to that of M. Desmaret, who was the first wards the sides. There are twenty-four naturalist that ventured to attribute them species.
to that cause, in a description of some STÆHELINA, in botany, so named basaltes, found near St. Sandour, in Aufrom John Henry Stæhelin and his son, vergne, presented by him to the attenSwiss physicians, a genus of the Synge. tion of the French Academy of Sciences. nesia Polygamia Æqualis class and order, Other naturalists, who had considered Natural order of Compositæ Discoideæ. them to be a species of crystallization, Cinarocephalæ, Jussieu. Essential cha ridiculed this idea as founded upon false racter: anthers tailed ; down branched; principles, as they contended basalt pilreceptacle with very short chaffs. There lars are discovered where it seemed are ten species.
highly improbable that volcanoes could STAFFA, an island situated on the ever have existed; still, however, they coast of Scotland, three miles north-east had the candour to enter into an exof lona or Columb-kill, and west of amination of the assertion of M. Des. Mull, about a mile in length, and half maret, the result of which was nearly a mile in breadth, belonging to Mr. a confirmation of his conjecture, that Lauchlin Mac Quarie. This inconsider basalt pillars were produced by subterable isle is one amongst the most won- raneous fires. As a collateral support derful productions of nature, and de- of this hypothesis, Dr. Von Troil cites serves the attention of every natural the instances of Stolpenstein in Meissen, philosopher, though it is unfortunately Lauban in Lusatia, of Bohemia, Leignitz placed in a region which prevents fre. in Silesia, Brandau in Hessia, Sicily, quent visits, even from curious investi. Bolsenna, Montebello, and St. Forio in gators. The peculiarity that renders it Italy; the district of Vicenza, Monte so interesting, arises from the basaltes Rosso, in the District of Padua, Monte composing it assuming a number of mag- Diavolo in the mountains of Verona, in nificent forms, equally astonishing and Lower Languedoc, in Ireland, and in the sublime ; but as we purpose to describe western islands of Scotland, in each of them with some degree of minuteness, it which places, he says, a doubt cannot be will be proper to give a general sketch entertained that volcanoes have existed ; of the nature of the substance termed besides those, he mentions St. Giovanni, basaltes, and where it abounds, that the Monte Castillo, Monte Nuovo, Monte subject may be clearly understood. See Oliveta, near Cader Idris, in Wales, and BASALTES.
almost every part of Velay and Auvergne, According to Strabo and Agricola, the where the towns of Chillac and St. Fluor antique basaltes is found in the same pris- are situated upon basaltes. matical form in Egypt, which distinguish. The peasantry of Iceland seem to have es its outline in various parts of Europe. entertained a similar opinion of their ori. Farber, a professor of natural history at gin to that of the lower orders of the Irish, Mietau, supposes that found in the Vi. as the former suppose them to have been centine Paduan and Veronese districts of piled, in the regular manner they are Italy to be a crystallized lava, and as seen there, by giants, and thence call serts, that the antique basaltes is in every them Trollahland and Trollkonugardur, respect exactly similar to the compact and the latter term their magnificent lavas of Vesuvius and Monte Albano, causeway, the Giant's. The pillars of the which are used by statuaries to restore Icelandic basaltes have generally from mutilated statues made of this material. three to seven sides; they vary in thick
The Egyptian basaltes contain a small ness from four to six feet, and soine are proportion, in some of the varieties, of the of thirty-six, and others even forty.cight white garnet like short crystallizations feet in length, without horizontal divi. and lamellas common in the Italian lavas, sions ; but such are the capricious opera.. a circumstance that seems to prove to tions of nature, that pillars are sometimes,
found not more than six or twelve inches vessel employed to take him to Iceland long; those, however, are invariably very to anchor on the night of the twelfth of regular, and are made use of for doors August, in the sound between the Isle of and windows ; at others they appear in Mull and Morvern on the continent, and the utmost confusion, broken, and over- precisely opposite to Drumnen, the seat turned ; in particular instances they just of Mr. Maclean, by whom the Doctor and appear above the surface of the moun. his friends were immediately invited on tains, amongst lava and tufa, and there are shore to breakfast, with the characterisplaces where they extend three miles tic hospitality of the Highlanders. Mr. together without interruption. The ba. Banks, now Sir Joseph, being of the party salt pillars of Glockenberg in Snefalds- intending to visit Iceland, eagerly acceptnas, exhibit a very different appearance ed, with the Doctor, and others, the offer from those of any other part of Iceland, of Mr. Maclean to conduct them to Stafta, as the pillars on the summit of tbat moun. to which they were conveyed by the tain lie horizontally, those on the sides ship's long boat the same evening, about incline, and the lowest stand erect. In nine o'clock. “It was impossible," says some places they are found as if bent, the Doctor “for our surprise to be inwhen heated, into a semicircular form, an creased, or our curiosity to be fuller gra. effect which seems to confirm the idea tified than they were the next morning, that violent fires have prevailed, either at when we beheld the no less than beautitheir formation, or subsequently.
ful spectacle which nature presented to The substance of the pillars of this our view. If we even with admiration island resemble those of Staffa in some behold art, according to the rules preparts of it, but in others they are more scribed to it, observing a certain kind of porous, and incline more to a grey colour. order, which not only strikes the eye, but This circumstance induced the Doctor to also pleases it, what must be the effect think it would be an easy matter to trace produced upon us when we behold nature all the gradations between the most per- displaying, as it were, a regularity, which fect basalt pillar and the coarsest descrip- far surpasses every thing that art ever tion of lava, and he even saw some at Vic produced ? An attentive spectator will dey, of a fine grain, extremely solid, of a find as much occasion for wonder and asblackish grey, and consisting of many tonishment, when he observes how infi. joints; some porous glassy kind of stone, nitely short human wisdom appears, when which he found at Laugarnas, near the we attempt to imitate nature in this as sea, was so indistinctly divided, that he well as any other of her grand and awwas undecided whether to class it with ful productions; and though we acknowthe layas or basalt pillars ; but the opinion ledge nature to be the mistress of all the of his friends determined him in favour arts, and ascribe a greater degree of perof the latter.
fection to them, the nearer they approach We have been the more particular in and imitate it, yet we sometimes imagine noticing the peculiarities of the basaltes that she might be improved, according to of Iceland, as that island is situated in the the rules of architecture. How magnifivicinity of Staffa, to which we shall now cent are the remains which we have of turn our attention. The gentleman we the porticoes of the ancients, and with have just mentioned was one of the first what admiration do we behold the colonpersons who had the good fortune to ex- nades that adorn the principal buildings amine the latter with any degree of accu- of our times; and yet every one who comracy; nor indeed had the public been in- pares them with Fingal's cave, formed formed before of the distinguishing marks by nature in the Isle of Staffa, must reawhich render it so bighly interesting, dily acknowledge, that this piece of naBuchanan being then the only author that ture's architecture far surpasses every had noticed this beautiful work of nature, thing that invention, luxury, and taste, though very slightly. Mr. Pennant, who ever produced among the Greeks." possessed every requisite talent for in. A small cave on the west side of the forming the world, was disappointed by island affords a convenient landing place, an adverse wind, from visiting Staffa in but there are no regular basalt pillars to the year that proved more favourable to be met with in its immediate vicinity. Dr. Von Troil, who would have been ex. On the south side of it are some narrow actly in the same situation, in all probabi. pillars, which are inclined, and resemble lity, had not the tide, which flows with the springs of the ribs of an arch; beyond great strength between the western isles those is a small grotto, on the right hand, of Scotland, compelled the captain of the not composed of pillars, though they ap.
DA 000 oo oo oo ovo
pear above it, disposed in the manner of to Dr. Von Froil for the following particuthe interior parts of the timbers of a ship. lars : At a few yards distance, and opposite to
Ft. In. the grotto, extends the peninsula of Bo. The length from the furthest of scha-la, consisting of regular, but smaller the basalt pillars, which from pillars, which are all of a conical figure. the shore formed a canal to the Some of these diverge as from a centre, cave, 121 ft. 6 in.; from the some incline, and others, and by far the commencement of the vault greater number, are perpendicular. The to the end of the cave, 250 ft. 371 6 island itself, opposite to Bo-scha-la, is The breadth of its entrance - 53 composed of thick columns, which ex. Of the interior end ... 20 tend into the sea as far as the eye is able The height of the vault at the to penetrate, but are not very high, and entrance of the cave .. gradually decrease as they approach the Of ditto at the interior end ... 70 water. Their relative connection is so The height of the outermost pil. admirably preserved, that a person may lar in one corner - - - walk upon their ends as conveniently as the height of another in the if ascending or descending the steps of a north-west corner . . . .. staircase; these lead to Fingal's, or Finhn the depth of the water at Mac Coul's cave or grotto, which is exca. entrance - - - - - - vated out of that mountain from north-east of the inside end · · · · · to east.
From the water to the foot of The cave is formed by regular pillars,
the pillars · · · · · · · extending to a great distance on each
Height of the pillars . . . . side, which support an arch composed of
Height of the arch, or vault, the obtuse points of others, placed very
above the top of the pillars. close together; unfortunately the floor of
The stratum above ... 34 this wonderful place is covered by a body of clear fresh water, several feet in depth,
The western corner of Fingal's cave. through which may be seen an incredible number of fragments of pillars. The co
From the water to the foot of the lour of the columns is grey, inclining to
pillars . - - - - - - - 12 10 black, and the joints are distinguishable
Height of the pillars . . . . 37 3
The stratum above them by the intervention of a yellow stalactic
. . 66 quarry rind, that exhales, and serves to
Further west-the stratum be. make the separations more distinct, at the
neath the pillars - - - same time that it produces an agreeable
Height of the pillars - - - effect by many different gradations of co
The stratum above - - - lour.
Still more westward-stratum
beneath the pillars · · · A sufficient degree of light enters the Height of the pillars · · · · cave to illuminate it to the extremity, The stratum above them · · where the ranges of pillars are perfectly
More west-stratum beneath the discernible, and the ebbing and flowing
pillars . . . . . . . . 19 8 of the tide constantly conveying and dis. Height of the pillars . . . . charging air from within it, is at all times
The stratum above . . . . 54 7 fit for respiration, and by no means noxious. This circumstance may still further
The stratum beneath the pillars was originate from the passage of the water
considered by the party to be no other through a fissure in the rocks, rather low
than tufa, which being heated at the perier than the surface, which occasions a
od when this phenomenon was produced, rushing sound upon each rise of the tide,
received into its depths fragments of bathat contributes to render the effect of the
salt ; that above them tinged with red, ap. whole still more singular and impressive.
pears to be lava, containing other fragA boat is certainly the most convenient
ments scattered in various unequal direc. for visiting Fingal's cave, but it is possible
tions; although it is evident the most vioto walk into it, upon the points of some of
lent heat must bave acted upon it, yet the pillars which are higher than the level
there are not the least traces in its exteri. of the water.
or, the pillars having been removed by it, The party already mentioned measured for the whole enormous mass rests upon the dimensions of this beautiful grotto, them. and we acknowledge ourselves indebted On the north side of the island is ano
ther cave, called Corvoranti, where the The angles are as sharp and well de. stratum is raised, and the pillars conse. fined as those of the pillars of the Giant's quently appear shortened; those are to Causeway in Ireland, and their colour is lerably distinct, and continue so till the generally black, the inclination to yellow intervention of a bay, that extends some being confined to the external sides, distance inland, and there the pillars are which are exposed to, and in some dediscontinued. The mountains in this gree bleached by, the action of the sun, neighbourhood are composed of dark rain, and wind. The texture of their brown stone, which may or may not be substance much resembles, and is probalava : but there is no sort of regularity bly he same as the Icelandic agate. Proobservable in its texture. On passing fessor Bergman was divided in opinion, further, and on the south-east side of the whether these pillars were produced by Island, the basalt columnar appearance first acting upon particular substances, or commences, though almost impercepti. whether subterraneous fires, sending bly; hence they gradually assume their forth vapour, may have softened the sucharacteristic form, till at last the specta. perincumbent earth, which becoming tor finds himself on the spot where they soft, and yielding to the force below, asare in full perfection.
cended in this peculiar form, and became The shape of the columns vary from gradually petrified. This latter suppothree to seven sides, though the majority sition met the ideas of Von Troil, who have five and six; the former are so nu. illustrates it by saying, he has observed merous, that a heptagonal pillar is sur. the distinct and regular appearance allud. rounded with seven others, which join ed to in dried clay, snd even starch, closely to its seven sides. In some in. when dried in a basin. “For,” adds stances inconsiderable fissures may be the latter, " it may be demonstated, that perceived, but those are generally filled they are not crystals formed by nature, with quartz, and in one particular place by their not being produced, as all other that had penetrated through several pil. crystals are, by external apposition (per lars, without interrupting the regularity appositionem, nor in any other matrix, of their arrangement; one of the greatest as is common among crystals." He furwonders attending this operation of na. ther observes, « The following may, ture, is, the separation of each pillar into however, serve as a proof that I did not, pieces, which are so closely jointed, that without due foundation, believe them to it is almost impossible to introduce a be a kind of lava, which burst in growing knife between the interstices. Upon an cold and hard. First, you find both in the attentive examination of many of those Island of Staffa, and many other places, pieces, it was found that the uppermost that the pillars stand on lava or tufa, and was generally concave, in some cases flat, are surrounded by this matter. Secondbut very rarely convex. When the upper ly, at Staffa there was a large stratum surface was flat, the lowest joint was the above the pillars, in which there were same ; but when it was excavated, the many pieces of those pillars irregularly lower one was rounded and reversed. thrown one among another, which leaves
The sides of the pillars are of unequal us to conjecture that they must have been dimensions, to prove which, we shall give more in number, and higher, after an old the measurement of two, extracted from eruption of fire ; but that a subsequent the Letters on Iceland, containing Dr. eruption had overthrown them, and misVon Troil's communication on this sub. ed ihem with the whole mass." ject.
STAIRCASE, in architecture, an asOne with four sides.
cent inclosed between walls, or a balus
Ft. In. trade, consisting of stairs, or steps, with First side . . . . . 1 5 landing-places and rails, serving to make Second ...... 11 a communication between the several Third . . . . . . 1 6 stories of a house. The construction of Fourth - - - - - - 1 1 a complete staircase is one of the most With seven sides.
curious works in architecture.
STAKE, the name of a small anvil, First side - -
used by smiths; sometimes it stands on a Second - - - - - - 2 4 broad iron foot on the work-bench, to be Third
moved up and down occasionally ; and Fourth · · ·
sometimes it hath a strong iron spike at Fifth . . .
the bottom, by which it is fixed to some Sixth - - - - -
place on the work-bench. Its use is to sit Seventh - -
small and cold work straight, by hammer