Mi ! BQ rABl 



MAGNA CHART V 



Md in 



tan** will prennl UM fcot of felling mow. The Und- 

 ttkibtted by UM other lantern i* a winter MOM : but before UM 

 vwttider i* oau*d into action, darknn* U made to come over the 

 hnfcmn by Dean* of a piece of black crape held over the aperture. 

 JUthTUoUrn invert* the image*, and the slider* are put in with what 

 may b* called the wrong aid* up, *o by winding the silk from the 

 bottom roller on to the top one, the ascending hole* appear to form a 

 ^w4,i> .K/.WJJ M l)w> iiiiimi ** 



MAGIC SQUARE. Thi* term U applied to a nt of numbers 

 arranged in a quare in *uch a manner that the vertical, horizontal, and 

 diagonal outurnn* ihall give UM aame nun*. Such arrangement* were 

 known very early to the Hindu*. Egyptian*, and Chinese, among whom, 

 a* aku among the European* of the middle ages, a belief existed that 

 poch iquan* had astrological and divinatory qualities. Emanuel 

 Moechopulu*.* of Constantinople, wrote on them hi Greek in the 

 middle of UM 15th century. Other* who have written on the subject 

 are Leibnite, Frank)*, Sachet, U Hire, Saurin, ftc. (See Montucla's 

 HMtory.' voL L, p. 346; Encyclopedia Moth.,' article ' Quarres 

 magiqtMi ; ' Button'. ' Dictionary ; ' and the ' Mathematical Recreations ' 

 of the *ame author.) : 



Though UM question of magic squares be hi itself of no use, yet it 

 belong* to a claw of problems which call into action a beneficial species 

 of investigation. Without laying down any rules for their construction, 

 we shall content ounelve* with destroying their magic quality, and 

 showing that the non-existence of such squares would be much more 

 urpriang than (heir existence. 



Take any wt of numbers in arithmetical progression, and such 

 that their number ahall be a square number, say the first sixteen 

 number* 



12345678 

 10 16 14 13 12 11 10 9 



any of then in the first half, with it* corresponding number in the 

 ' half, make* up 17. Write the numbers in the following 



1 



5 



9 



13 



2 

 6 



10 

 14 



8 



7 



11 



15 



4 



8 

 12 

 16 



Take four of then in such a manner as to take one out of each 

 row, and one out of each column, and it will be found, and may easily 

 be proved, that the *um of numbers in every such set must consist of 

 two pairs of corresponding numbers, so that their sum must be twice 

 17, or 34. The different ways in which this can be done are in 

 number 4 x 3 x 2 x 1, or 24, as follows. 



Out of then subdivision* a nt may be taken from each, so that no 

 number shall be repeated, in 24 different ways, as in the following 

 ample, which show* the four way* that begin with 1611 16. 



1 6 11 16 

 6 14 3 12 

 9 2 16 8 



1 6 11 6 



5 2 15 12 



9 14 7 4 



13 10 S 8 



1 6 11 16 



6 2 15 12 



9 14 3 8 



13 10 7 4 



1 6 11 16 

 5 10 15 4 

 9 14 3 8 

 13 2 7 12 



18 10 7 4 



Now in each of then 24 quare*, every horizontal row can be 

 hi 24 order* [COMBINATIONS], and in putting the different 

 ther, each aquare admiU of 



order* together, 



24x24x24x24, or 331,776 



. without altering the horizontal row*, but only the order 

 of UM figures in each row. But the order of the horizontal row* can 

 . varMd24 



be 



have Ml .776 



way* in each *quare, and there are 24 squara ; so that we 

 I x 24 x 24, or 191,102,976 squares, no one of which repeats 

 any number more than once, and in every one of which the mm of any 

 horizontal row U 34, made by two pair* of number* which give 17 

 *nli Bat UM Dumber of way* of forming 84 out of four of the first 

 I number* U Dot yet exhausted : for, taking any one set, say 



! 



10 



11 



in which 1 and 6 correspond to 16 and 11, we may write 2 and 5, or 3 

 and 4, for 1 and 6,ao that we have not included in the preceding list 



16 

 18 



11 

 11 



with all their variation* of order ; and *imilar one* for all the rest of 

 UM li*(. It would be almoot Impossible to doubt that in many of this 

 oormnu* number of squares, the vertical column* will sometime* be 

 on* of Am* D*w nt* : aad it would be something short of magic if 

 POM (boiild not ah have diagonal column* which fulfil the came condi- 

 tion, la Uct, Krnicl* ha* shown 880 methods of making thee ^uare* 



MM ttiak tab work WM wrlttn by Ennntnl Motchopalu* UM elder, a 

 Cntea, ha U*W at Ik* *ad of Ike INk natarr. 



, a few of which an a* follow* (' Divers Ouvrages, Sx. Pan* 

 1698) : 



1 16 11 6 

 13 4 7 10 



8 9 14 3 

 12 5 2 15 



8 12 5 9 



11 1 16 



18 7 10 4 



2 14 3 15 



In Frenicle's list of 880, only those squares are included which are 

 essentially different : thus the following four, which may be made by 

 turning the hut square into different positions, count only as one. 



10 11 5 8 



15 2 16 1 



6 7 9 12 



3 14 4 13 



8 1 12 13 

 5 16 9 4 



11 '2 7 14 

 10 15 6 3 



13 4 14 3 



12 9 7 6 



1 16 2 15 



8 6 11 10 



3 6 15 10 

 14 7 2 11 



4 9 16 5 

 13 12 1 8 



The methods which have been given for the formation of magic 

 squares are divided into different rules, according as the number in 

 each side is odd, evenly even, or oddly even. A general method which 

 shall apply to all cases is yet wanting. For a full account of these 

 rules see Mutton's ' Mathematical Recreations.' 



MAOISTERY. The term used by alchemists to denote precipitation 

 of metallic solutions by water ; thus, the basic nitrate of bismuth, pre- 

 cipitated on diluting the neutral nitrate, was termed magistery of 

 bismuth, 



MAOISTERY OF BISMUTH. [BISMUTH, Moiumitrate of.] 



MAGISTRAL. Roasted copper pyrites employed in the extraction 

 of mercury from its ores by amalgamation. 



MAGISTRATE, a word derived from the Latin magittratus, which 

 contains the same element as magma and mayitter, and signifies both a 

 person and an office. A Roman magistrates is denned to be one who 

 presides in a court and declares the law, that is, a judge. The kings of 

 Rome were probably the sole magistrates originally, and on their 

 expulsion the two consuls were the magistrates. In course of time 

 other offices, as thoee of Praetor and .'Kdilc, were created ; and those 

 who filled these offices were elected in the forms prescribed by the 

 constitution, and they had jurisdictio. [JURISDICTION.] The original 

 notion of a magistrates, then, is one who is elected to an office, and 

 has jurisdiction. 



In England the term magistrate is usually applied to justices of the 

 peace in the country, and to those called police or stipendiary magis- 

 trates, such as there are in London. It has also been applied in other 

 ways ; for instance, people have sometimes said that the sovereign is 

 the chief magistrate in the state. But these applications of the term 

 do not agree with its proper sense. 



MAGNA CHARTA. The terms of the compact between the feudal 

 chief and his dependants underwent frequent changes in the middle 

 ages, the consequence for the most part of resistance made by the 

 tenants, and struggles to regain liberties which had been originally 

 surrendered or taken from them by the force and power of the chief. 

 When a material alteration was made in the terms of the compact, 

 a record was made of it in writing. These records are called charters, 

 in the restricted use of a term which is popularly applied to almost 

 every species of early diplomas. The tenant* of the various honours, 

 or great tenancies in capite, are seldom without one or more charters 

 which have been granted to them by their lords, by which exemptions 

 or privileges are given, base services are commuted for payments in 

 money, and the mode is settled in which justice shall be administered 

 among them. And even in some of the inferior manors there are 

 charters of a similar kind by which certain liberties are guaranteed by 

 the lord to bis tenants. These charters run in the form of letters, 

 " Omititnu," &c., from the person granting ; they set forth the thing 

 granted, and end with the names of penons who were present when 

 the lord's seal was affixed, often ten, twelve, or more, with the date of 

 place and time of the grant. 



Such a charter is that called the Magna Charta granted by King 

 John, but acting in his twofold character of the lord of a body of 

 feudatories, and the sovereign of the realm. This charter is often 

 regarded as the constitutional bads of English liberties, but in many 

 of it* provisions it seems to have been only a declaration of rights 

 which had been enjoyed in England before the Conquest, and which are 

 said to have been granted by King Henry I. on his accession. However, 

 if it did not properly found the liberties which the English nation enjoys, 

 or if it were not the original of those privileges and franchises which 

 the barons (or the chief tenants of the crown, for the names are here 

 equivalent), ecclesiastical persons, citizens, burgesses, and merchants, 

 enjoy, it recalled into existence, it defined, it settled them, it formed 

 hi iu written state a document to which appeal might be made, under 

 whose protection any person who had any interest in it might find 

 belter, and which served, a* if it were a portion of the common law of 

 the land, to guide the judge* to the decisions they pronounced in all 

 question* between the king and any portion of the people. 



Beside the great charter there was granted at the same time a charter 



