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where those unacquainted with their form be plainly visible to the naked eye : thas and habits may be easily gratified by a Galileo saw one of them in the year 1619; sight of them in various stages of growth, and Mr. Martin assures us, that he knew and bonnding before him with a vivacity two gentlemen that thus viewed them and elasticity highly entertaining. See several years ago; whence he concludes, Mammalia, Plate IX. fig. 3.

that these spots must therefore subtend, MACTRA, in patural history, a genus of at least, an angle of one minute. Now * the Vermes Testacea class and order. Ani. the diameter of the earth, if removed to the mal a tethys ; shell bivalve, uneqnal sided, sun, would subtend an angle of but 20''; SO equivalve ; middle tooth of the hinge com- that the diameter of a spot, just visible to plicated, with a small bollow on each side ; the naked eye, is, to the diameter of the lateral ones remote and inserted into each earth, as 60 to 20, or as 3 to 1 ; and, thereother. There are twenty-seven species. fore, the surface of the spot, if circular, to

MACULE, in astronomy, dark spots ap. a great circle of the earth, is as 9 to 1; but pearing on the luminous faces of the sun, 4 great circles are equal to the earth's sumoon, and even some of the planets ; in perficies ; whence the surface of the spot is, which sense they stand contradistinguished to the surface of the earth, as 9 to 4 ; or as from faculæ. See FACULÆ.

24 to 1. Gassendus says, he saw a spot These spots are most numerous and easily whose dianieter was equal to y of that of observed in the sun. It is not uncommon the sun, and therefore subtended an angle to see them in various forms, magnitudes, at the eye of 1' 30" ; its surface must have and numbers, moving over the sun's disk. been five times larger than the surface of the They were first of all discovered by astrono. whole earth. What these spots are, it is mer Galileo, in the year 1610, soon after he presumed, nobody can tell ; but they seem had finished his new-invented telescope. It to be rather thin substances than solid bohas been supposed that these spots adhere dies, because they lose the appearance of to, or tloat upon the surface of the son, for solidity in going off the disk of the sun : they the following reasons. 1. Many of them resemble something of the nature of scum are observed to break out near the middle or scoria, swimming on the surface, which of the sun's disk; others to decay and va are generated and dissolved by causes lilnish there, or at some distance from his tle known to us : but whatever these solar Jimb. 2. Their apparent velocities are always spots are, it is certain they are produced greatest over the middle of the disk, and from causes very inconstant and irregular; gradually slower from thence on each side for Scheiner says be frequently saw fifty at towards the limb. 3. The shape of the once, but for twenty years after scarce any spots varies according to their position on appeared. And in the last century the spots the several parts of the disk : those which were very frequent and numerous till the are ronnd and broad in the middle, grow year 1741, when, for three years succes. oblong and slender as they approach the sively, very few appeared, and now, since himb, according as they ought to appear the year 1744, they have again appeared as by the rules of optics.

usual. By comparing many observations of the These maculæ are not peculiar to the intervals of time in which the spots made sun, they have been observed in all the their revolution, by Galileo, Cassini, planets. Thus Venus was observed to have Scheiner, Hevelius, Dr. Halley, Dr. Der- several by Signior Blanchini, in the year ham, and others, it is found that 27 days, 1726. As in Venus, so in Mars, both dark 12 hours, 20 minutes, is the measure of one and bright spots have been observed, first of them at a mean ; but in this time the by Galileo, and afterwards by Cassini, &c. earth describes the angular motion of 26° Jupiter has had his spots observable ever 29", abont the sun's centre : therefore say, since the invention and use of large teles. as the angular motion of 360° + 26° 22', is copes. Saturn, by reason of his great disto 360°, so is 27 days, 12 hours, 20 mi. tance on one hand, and Mercury, by reason nutes, to 25 days, 15 hours, 16 minutes; of his smallness and vicinity to the sun on which, therefore, is the time of the sun's re- the other, have not as yet had any spots volution about its axis.

discovered on their surfaces, and couseAs to the magnitude of the spots, they quently nothing in relation to their diurnal are very considerable, as will appear if we motions and inclinations of their axis to the observe that some of them are so large as to planes of their orbits can be known, which

circumstances are determined in all the junction with the dearer reds, as cochineal : other planets, as well as in the sun, by means for demi-scarlets, and demi-crimsons. of these maculæ.

MADREPORA, in natural history, a The spots, or maculæ, observable on the genus of the Vermes Zoophyta class and moon's surface, seem to be only cavities or order. Animal resembling a medusa ; colarge caverns, on which the sun shining ral with lamellate star-shaped cavities. This very obliquely, and touching only their is a very numerous genus, comprehending upper edge with his light, the deeper places about 120 species, separated into distinct remain without light; but as the sun rises divisions. A. composed of a single star. higher upon them, they receive more light, B. with numerous separate stars, and conand the shadow, or dark parts, grow smaller tinued gills. C. with numerous united and shorter, till the sun comes at last to stars. D. aggregate, undivided, with disshine directly upon them, and then the tinct stars and pornlous tuberculous promiwhole cavity will be illustrated : but the nent undulations. E. branched, with disdark dusky spots, which continue always tinct stars and tuberculous porulous undula. the same, are supposed to proceed from a tions. M. verrucaria, star orbicular, flatkind of matter or soil which reflects less tish, sessile, with a convex disk full of tubnlight than that of the other regions. Seelar pores and radiate border : it inhabits Moon.

the European, Mediterranean, and Red MADDER is a plant, with rough narrow Seas, adhering to marine vegetables and leaves, set in form of a star, at the joints of the softer zoophytes ; size of a split-pea, the stalk. The root, which is the only part and appears an intermediate species bemade use of, is long, slender, of a red co- tween the madrepore, tubipore, and mille. lour, both on the outside and within, ex- · pore; white or yellowish, with aggregate cepting a whitish pith, which runs along the tubes on the disk like the florets of a commiddle. For cultivating this plant, the posite flower, and a flattened striate border ground is plougbed deep in autumn, and like the rays of these flowers. A. ananas, again in March ; and then laid up in ridges, with angular convex stars, which are coneighteen inches asunder, and about a foot cave on the disk, inhabits the Mediterra. high. About the beginning of April, they nean and South American Sea, and is fre. open the ground where old roots are quently found fossile; gibbous, and when planted, and take off all the side shoots, dissected transversely, resembling a white which extend themselves horizontally; net with hexangular spots, including a these they transplant immediately upon the white ring, and striate between the net new ridges, at about a foot distance, where and ring. See ZOOPHYTA. they remain two seasons; and at Michael. MADREPORITE, a mineral found in mas, when the tops of the plants are decay- the valley of Russback, in Salzburg, and so ed, they take up the roots. It is to be ob- called from its external resemblance to served, that this method of planting in madrepore. It is found in large masses, ridges is only necessary in wet land, and is brittle and moderately heavy. Its com. that the rows are sometimes planted three ponent parts are, feet, and the plants in the rows eighteen . Carbonate of lime..........93.00 inches asupder. If all the horizontal roots

Carbonate of magnesia.... 0.50 are destroyed from time to time, it will

Carbonate of iron.........., 2.25 cause the large, downright roots, to be much

Charcoal ...................... 0.50 bigger, in which the goodness of this commo

Silica ........

............ 4.50 dity chiefly consists. Madder gives out its

99.75 colour, both to water and rectified spirit :

Loss........ the watery tincture is of a dark dull red;

25 the spirituous of a deep bright one. It im

100 parts to woollen cloth, prepared with alum and tartar, a very durable, though not a MADRIER, in the military art, a long very beautiful red dye. As it is the cheapest and broad plank of wood, used for supof all the red drugs, that give a durable co. porting the earth in mining and carrying on lour, it is the principal one commonly made a sap, and in making coffers, caponiers, use of for ordinary stuffs. Sometimes its dye galleries, and for many other uses at a is heightened by the addition of Brazil- siege. Madriers are also used to cover wood, and sometimes it is employed in con- the mouths of petards, after they are load.

ed, and are fixed with the petards to the masdes, or the good God; as darkness is the gates or other places designed to be forced truest symbol of Arimanius, or the evil god. open.

This religion was reformed by Zoroaster, MADRIGAL, in the Italian, Spanish, who maintained that there was one supreme and French poetry, is a short amorous poem, independent being; and under him two composed of a number of free and unequal principles or angels, one the angel of goodverses, neither confined to the regularity of ness and light, and the other of evil and a sonnet, nor to the point of an epigram, darkness : that there is a perpetual struggle but only consisting of some tender and de. between them, which shall last to the licate thought, expressed with a beautiful, end of the world; that then the angel of noble, and elegant simplicity. The madrigal darkness and his disciples shall go into a is usually considered as the shortest of all world of their own, where they shall be pu. the lesser kinds of poetry, except the epi. nished in everlasting darkness; and the gram : it will admit of fewer verses than ei- angel of light and his disciples shall also go ther the sonnet or the roundelay; no other into a world of their own, where they shall rule is regarded in mingling the rhymes, and be rewarded in everlasting light. The priests the different kinds of verse, but the fancy of the magi were the most skilful mathemaand convenience of the author : however, ticians and philosophers of the ages in which this poem allows of less licence than many they lived, insomuch that a learned man others, both with respect to rhyme, mea and a magian became equivalent terms. The sure, and delicacy of expression.

vulgar looked on their knowledge as more MAGAZINE, a place in which stores than natural, and imagined them inspired are kept, of arms, ammunition, provisions, by some supernatural power; and hence &c. Every fortified town ought to be fur those who practised wicked and mischievous nished with a large magazine, which should arts, taking upon themselves the name of contain stores of all kinds. sufficient to magians, drew on it that ill signification enable the garrison and inhabitants to hold which the word magician now bears among out a long siege, and in which smiths, car us. This sect still subsists in Persia, under penters, wheelwrights, &c. may be em- the denomination of gaurs, where they ployed, in making every thing belonging watch the sacred fire with the greatest care. to the artillery, as carriages, waggoms, &c. and never suffer it to be extinguished. See

MAGÁzine, powder, a place in which GAURS. powder is kept in large quantities, and MAGIC, originally signified only the which, on account of the nature of the sub- knowledge of the more sublime parts of stance preserved, should be arched and philsosophy; but as the magi likewise probomb-proof. According to the plan of fessed astrology, divination, and sorcery, Vauban, they are sixty feet long and twen.

the term magi became odious, being used to ty-five broad in the inside. The foundations

signify an unlawful diabolical kind of science, are eight or nine feet thick, and about as acquired by the assistance of the devil and many feet high from the foundation to the departed souls. See ASTROLOGY, NECROspring of the arch. As some inconveniences

MANCY, &c. have arisen from this structure, Dr. Hutton Natural magic is only the application of proposes to find an arch of equilibration, natural philosophy to the production of which he would have constructed to a span surprising but yet natural effects. The comof twenty feet, the pitch being ten feet: the mon natural magic, found in books, gives exterior walls at top forming an angle of us merely some childish and superstitions 113', and the height of the angular point traditions of the sympathies and antipathies above the top of the arch to be seven of things, or of their occult and peculiar profeet.

perties ; which are usually intermixed with MAGGOT. See Musca..

many trifling experiments, admired rather MAGI, or MAGIANS, an ancient religions for their disguise than for themselves. sect in Persia, and other eastern countries, Magic lantern. See LANTERN. who maintained, that there were two prin M aGic square, in arithmetic, a square ciples, the one the canse of all good, the figure made up of numbers in arithmetical other the canse of all evil; and abominating proportion, so disposed in parallel and equal the adoration of images, worshipped God ranks, that the sums of each row, taken eionly by fire, which they looked upon as the ther perpendicularly, horizontally, or diagobrightest and most glorious symbol of Oro- nally, are equal : thus,

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Natural square.

Magic square.

numbers in every row 15 : to Jupiter the square of 16 places, the side being 4, and the amount of each row 34 : to Mars the square of 25 places, the side being 5, and the amount of each row 65 : to the sun the square with 36 places, the side being 6, and the sum of cach row 111: to Venus the

square of 49 places, the side being 7, and Magic squares seem to have been so called, the amount of each row 175 : to Mercury from their being used in the construction of the square with 64 places, the side being 8, talismans.

and the sum of each row 260 : and to the Take another instance ;

moon the square of 81 places, the side being Natural square.

Magic square.

9, and the amount of each row 369. Finally, they attributed to imperfect matter, the square with 4 divisions, having 2 for its side ; and to God the square of only one cell, the side of which is also an unit, which multiplied by itself undergoes no change. To form a magic sqnáre of an odd number

of terms in the arithmetic progression 116117118

1, 2, 3, 4, &c. Place the least term 1 in

the cell immediately under the middle or 121 22 23 24 25

7 52119

central one ; and the rest of the terms, in

their natural order, in a descending diagonal where every row and diagonal in the magic direction, till they run off either at the square makes just the sum 65, being the same bottom, or on the side : when the number as the two diagonals of the natural square. runs off at the bottom, carry it to the up

It is probable that these magic squares permost cell, that is not occupied, of the were so called, both because of this proper- same column that it would bave fallen in ty it them, viz. that the ranks in every dibelow, and then proceed descending diagorection make the same sum, appeared ex. nalwise again as far as you can, or till the tremely surprising, especially in the more numbers either run off at bottom or side, ignorant ages, when mathematics passed for or are interrupted by coming at a cell alinagic, and because also of the superstitions ready filled: now when any number runs operations they were employed in, as the off at the right-hand side, then bring it to the construction of talismans, &c.; for, ac. furthest cell on the left-hand of the same cording to the childish philosophy of those row or line it would have fallen in towards days, wbich ascribed virtues to numbers, the right-hand : and when the progress what might not be expected from numbers diagonalwise is interrupted by meeting with 80 seemingly wonderful? The magic square a cell already occupied by some other pumwas held in great veneration among the ber, then descend diagonally to the left Egyptians, and the Pythagoreans their dis- from this cell till an empty one is met with, ciples, who, to add more efficacy and virtue where enter it ; and thence proceed as to this square, dedicated it to the then before. Thus, known seven planets divers ways, and en To make a magic square of the 49 num. graved it upon a plate of the metal that was

bers 1, 2, 3, 4, &c. esteemed in sympathy with the planet. The square, thus dedicated, was inclosed by a re 22 | 47 | 16

10 35 gular polygon, inscribed in a circle, which was divided into as many equal parts as

23 48 17 42 11 29 there were units in the side of the square ; with the names of the angels of the planet,

| 6 24 49 18 36 12 and the signs of the zodiac written upon the

13 31 7 | 23 43 19 37 void spaces between the polygon and the circumference of the circumscribed circle.

38 14 32 1 26 Such a talisman or metal they vainly ima. gined would, upon occasion, befriend the

39 8 33 person who carried it about him. To Saturn they attributed the square of 9 places

934 31 or cells, the side being 3, and the sum of the

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First place the 1 next below the centre 256 little squares, in which all the numbers leell, and thence descend to the right till the from 1 to 256, or the square of 16, are 4 runs off at the bottom, which therefore placed, in 16 colnmns, which inay be taken carry to the top corner on the same column either horizontally or vertically. Their chief as it would have fallen in; but as that runs properties are as follow. 1. The sum of off at the side, bring it to the beginning of the 16 numbers in each column or row, verthe second line, and thence descend to the tical or horizontal, is- 2056. 2. Every half right till they arrive at the cell occupied column, vertical and horizontal, makes by 1; carry the 8 therefore to the next 1028, or just one half of the same stim 2056. diagonal cell to the left, and so proceed S. Half a diagonal ascending, added to half till 10 runs off at the bottom, which carry a diagonal descending, makes also the same therefore to the top of its column, and so sum 2056; taking these half diagonals from proceed till 18 runs off at the side, which the ends of any side of the square to the therefore bring to the beginning of the middle of it; and so reckoning them either same line, and thence proceed till 15 arupward or downward, or sideways from rives at the cell occupied by 8; from right to left, or from left to right. 4. The this therefore descend diagonally to the same with all the parallels to the half diago. left; but as 16 runs off at the bottom, nals, as many as can be drawn in the great carry it to the top of its proper column, square : for any two of them being directed and thence descend till 21 runs off at the upward and downward, from the place side, which is therefore brought to the be where they begin, to that where they end,.. ginning of its proper line ; but as 22 arrives their sums still make the same 2056. Also at the cell occupied by 15, descend diago- the same holds true downward and upward ; nally to the left, which brings it into the as well as if taken sideways to the middle, first column, but off at the bottom, and and back to the same side again. Oply one therefore it is carried to the top of that co- set of these half diagonals and their parallels, lumn ; thence descending till 29 runs off is drawn in the same square upward and both at bottom and side, which therefore downward; but another set may be drawn carry to the bigliest unoccupied cell in the from any of the other three sides. 5. The last column; and here, as 30 runs off at the four corner pumbers in the great square side, bring it to the beginning of its proper added to the four central numbers in it, column, and thence descend till 35 runs off make 1028, the half sum of any vertical or at the bottom, which therefore carry to horizontal column, which contains 16 numthe beginning or top of its own column; bers; and also eqnal to half a diagonal or and here, as 36 meets with the cell occu- its parallel. 6. If a square hole, equal in pied by 29, it is brought from thence dia breadth to four of the little squares or cells, gonally to the left; thence descending, 58 be cut in a paper, through which any of the runs off at the side, and therefore it is 16 little cells in the great sqnare may be bronght to the beginning of its proper line; seen, and the paper be laid upon the great thence descending 41 runs off at the bot. square; the sum of all the 16 numbers, tom, which therefore is carried to the be. seen through the hole, is always equal to ginning or top of its column ; from whence 2056, the sum of the 16 numbers in any hodescending, 43 arrives at the cell occupied rizontal or vertical column. by S6, and therefore it is brought down MAGISTERY, an old chemical term, from thence to the left; thence descending, very nearly synonymous with precipitate, 46 runs off at the side, which therefore is but is now rarely used except in the follow. brought to the beginning of its line; buting combinations : magistery of bismuth, here, as 47 runs off at the bottom, it is car which is the white oxide of this metal preci. ried to the beginning or top of its column, pitated from the nitrous solution by the adfrom whence descending with 48 and 49, dition of water; magistery of sulphur, which the square is completed, the sum of every is sulphur precipitated from its alkaline solurow and columu and diagonal making just tion by an acid. 175. Dr. Franklin carried this curious spe- MAGNA charta. See LIBERTY. culation further than any of his predecessors MAGNESIA, in chemistry, an earth, in the same way. He constructed both a the properties of which were not fully magic square of squares, and a magic circle known till Dr. Black, about the middle of of circles, the description of which is as fol- the last century, investigated its nature. lows.' The magic square of squares is In the pursuit, the Doctor was led to the formed by dividing the great square into important discovery of the carbonic acid

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