where v √(A2+B+C2) is the distance between (abc) and (xyz). 7. The plane whose equation is A(x-a)+ &c. 0 may be called the plane (ABCabc), and the straight line just mentioned may be called the straight line (ABCabc). Throughout this article capitals are generally proportional to cosines of angles, and small letters are coordinates of points. The order of co-ordinates is xyz, and all letters connected with co-ordinates run in consecutive triplets, as ABC, PQR, &c. But when triplets of pairs are made, as AB, BC, CA, then AB particularly belongs to the co-ordinate to which C is attached, BC to that of A, and CA to that of B. 8. The angles made by the straight line (ABC, &c.) with the axes have for their cosines A÷√(A2 + B2 + C2), &c.; and the angle made by the two straight lines (ABC, &c.), (A'B'C', &c.), has for its cosine AA' + BB' × CC' ✔ (A2 + B2 + C2) √ (A'2 + B2 + C'2) When the lines are perpendicular, AA' + BB' + CC′ = 0; and when they are parallel, A, B, C are in the same proportion as A', B', C'. 9. The angles made by the plane (ABC, &c.) with the planes of yz, zx, and xy, are A ÷ √ (A2 + B2 + C2), &c.; the cosine of the angle made by the planes (ABC, &c.) and (A'B'C', &c.) with one another is as in the last, and also the conditions of perpendicularity and parallelism. 10. The plane (ABCabe) is at right angles to the line (ABCpqr), whatever a, b, c, p, q, r may be. And the plane (ABC, &c.) is at right angles to the line (A'B'C', &c.) whenever A, B, C, are proportional to A, B, C. But the plane (ABC, &c.) is parallel to the line (A'B'C', &c.) when AA'+ BB' + CC'≈ 0. 11. The straight line (ABCabc) lies entirely in the plane (PQRpqr) when 14. Two straight lines (ABCabc) and (A'B'C' a'b'') do not, generally speaking, intersect at all; their shortest distance is (BCCB') (a — a') + &c., divided by ✔{(BC — CB')2 + &c.}, and they meet when the numerator of this fraction is nothing. The plane (PQRpqr) is parallel to both straight lines when P, Q, R, are proportional to BC- CB', CA'— AC', AB' — BA'. 15. The equation of a plane which passes through the straight line (ABCabc) and is perpendicular to the plane (PQRpqr) is (BR — CQ) (x — a) + (CP — AR) (y — b) 16. The perpendicular distance from the point (abc) to the plane (PQRpqr) is P(a-p) + Q (b − q) + R (c —-r) divided by (P+Q2+ R2), independently of sign. And the perpendicular distance between the parallel planes (PQRpqr) and (PQRp'q'r') is P(p-p') + &c., divided by (P2 + &c.) 17. The perpendicular from the point (mn) upon the straight line (ABCabc) meets it in a point of which the co-ordinates are a+ Av, &c., where This is sufficient for a specimen of the method, and even for a summary of the most important propositions respecting the straight line and plane. On the good effect of symmetry it is hardly necessary to make much remark; not only are formulæ more easily remembered, since the whole can be formed from recollection of a part-and more easily used, since an unsymmetrical result is an indication of errorbut the actual expression can be shortened in type, of which the above is a sufficient proof. It would have been impossible safely to write down as many results in twice the space, if the ordinary plan of notation had been adopted. The best mode of treating the ordinary forms ALGORITHM, a corruption from the Arabic, the root being a word which means calculation, or at least refers to calculation or reckoning. When the Indian numerals were introduced from the East, this word came with them, and the new figures were denominated (by Chaucer for example) augrime (or algorithm) figures. The word is tolerably well naturalised among the French mathematicians, as meaning the system of notation: thus there is an algorithm of functions, and an algorithm of the differential calculus, &c. It has also been used by English writers, but our language does not want it; the word notation does just as well. Hard words sometimes lead to misconception; those who attempt to interpret them find them not only spelt in different ways, but with very different meanings. Daniel Fenning (Young Algebraist's Companion,' 1750) tells us that some writers are so short and intricate, that it is almost impossible to learn the algorithm from them, much less the algorism. In a note he informs us that the first of these hieroglyphics means the first principles, and the second their application to practice. Our old mathematical dictionaries define the word algorithm in probably its real imported sense, namely, as meaning the great rules of arithmetic. ALGUACIL, an officer in Spain, answering to the English bailiff. The name is from the Arabic el-vazil, or from the Hebrew verb gazal, which means to catch. The alguacil mayor is a superior officer, whose functions are the same as those of the common alguacil. The duty of an alguacil is at present confined to the apprehension of criminals; the office of executioner being discharged by the verdugo. ALIAS, a term used in legal proceedings to denote a second or further description of a person who has gone by two or more different names. If the same person is known by the name of John Smith as well as the name of John Thomson, he is described in legal language as John Smith, alias dictus (otherwise called) John Thomson. ALIBI, a Latin term signifying "in another place," of frequent offence committed at a certain time and place, shows that he was occurrence in criminal courts. Thus, where a person charged with an elsewhere at that time, he is said to prove an alibi. If true, this is obviously the best proof of innocence; but no kind of defence offers so ready an opportunity for false evidence: and the setting up an alibi is therefore, in practice, always regarded with suspicion. ALIEN. An alien is one who is born out of the legiance (allegiance) of the king. (Littleton, 198.) The word is derived from the Latin, alienus; but the word used by the English or other law writers in Latin is alienegena. The condition of an alien, according to this definition, is not determined by place, but by allegiance [ALLEGIANCE], for a man may be born out of the realm of England, or without the dominions of the king, and yet he may not be an alien. It is essential to alienage that the birth of the individual occurred in a situation and under circumstances which gave to the sovereign of this country no claim to his allegiance. The following instances will serve to illustrate the description of an alien. The native subject of a foreign country continues to be an alien, though the country afterwards becomes a part of the British dominions. Thus, persons born in Scotland before the accession of James I., were aliens in England even after that event; but those who were born afterwards were adjudged to be natural-born subjects. This question was the subject of solemn discussion in the reign of that prince; and the reported judgment of the court has guided lawyers in all similar controversies. Persons born in those parts of France which formerly belonged to the crown of England, as Normandy, Guienne, and Gascony, were not considered as aliens so long as they continued so annexed; and, upon the same principle, persons born at this day in any of our colonial possessions are considered native subjects. A man, born and settled at Calais whilst it was in the possession of the English, fled to Flanders with his wife, then pregnant; and there, after the capture of Calais by the French, had a son; the issue was held to be no alien. If, however, enemies invade the kingdom, and a child is born among them, the child is an alien. The children of ambassadors, and other official residents in foreign states, have always been held natives of the country which they represent and in whose service they are. This rule prevailed even at a time when the law was stricter than it now is. It has been since so far extended by various enactments, that all children born abroad, whose fathers, or grandfathers on the father's side, were natural subjects, are now deemed to be themselves natural-born subjects, unless their fathers were liable to the penalties of treason or felony, or were in the service of a prince at war with this country. (25 Ed. III. st. 2; 7 Anne, c. 5; 4 Geo. II. c. 21; 13 Geo. III. c. 21.) The children of a British mother by an alien, though aliens if born out of the king's allegiance, are now enabled to take property by devise, purchase, or succession. (7 & 8 Vict. c. 66.) The children of aliens born in England are, as a general rule, the same as natural-born subjects; they are entitled to the same rights and owe the same allegiance. It follows from the general principles of our law that a man may be subject to a double and conflicting allegiance; for, though he may become a citizen of another state (the United States of America, foi instance), or the subject of another king, he cannot divest himself of An alien can bring an action or suit in the English courts in respect of personal property or contracts; and may dispose of his property by will. The droit d'aubaine, or right of succeeding to the effects of a deceased alien, formerly claimed by the crown of France, never prevailed in this country. Nor was it customary to enforce it even in France, except as against the natives of a state in which a similar right was exercised. For some time previous to its abolition by the first | Constituent Assembly in 1791, it was generally stipulated by foreign countries in their treaties with France, that their subjects should be exempt from the law. [AUBAINE.] This doctrine of reciprocity was adopted by the French Code (Code Civil,' art. 726), but was abrogated in 1819, so far as the right of succession is concerned: so that aliens are now on the same footing in this respect with native Frenchmen throughout that kingdom. Aliens who are subject to any criminal proceeding in our courts of justice are in most cases entitled to trial by a jury de medietate linguæ. The disabilities of aliens may be partially removed by letters-patent constituting the party a free denizen. From the date of the grant he is entitled to hold land, and transmit it to his after-born children, and to enjoy many other privileges of a native subject. The partial effect of Letters of Denization give rise to the practice of obtaining naturalisation by act of parliament, which conferred on the alien every right of a natural-born subject, except the capacity of sitting in parliament or the privy council, or of holding grants and offices of trust under the crown; an exclusion originally dictated by the jealous policy of the legislature on the accession of the House of Orange. A temporary naturalisation may now, however, be obtained by the order of the Home Secretary. [DENIZEN.] The rights of aliens, enumerated above, must be understood to apply only to alien friends. Alien enemies, or subjects of a foreign state at war with this country, are in a very different condition, and may be said to possess very few rights here. As examples of the policy which has at different times been pursued in this country with reference to aliens, the following historical notices may be interesting : Magna Charta stipulates, in the article already cited, for the free access of foreign merchants for the purposes of trade, and its provisions were enforced and extended under the reigns of succeeding princes. In the 18th year of Edward I. the parliament rolls contain a petition from the citizens of London, "that foreign merchants should be expelled from the city, because they get rich, to the impoverishment of the citizens;" to which the king replies, that "they are beneficial and useful, and he has no intention to expel them." In the reign of Edward III. several beneficial privileges were conferred on aliens for the encouragement of foreign trade. Under Richard II. and his successor, statutes were made imposing various restraints on aliens trading within the realm, and especially prohibiting internal traffic with one another. Similar restrictions were introduced in the reign of Richard III., chiefly with a view to exclude them from retail trade; and in that of Henry VIII. violent insurrections against aliens were followed by repeated statutes, reciting the mischievous consequences attributed to the influx of foreigners, and laying greater impediments in the way of their settlement within the realm. Several Acts of this description are still in force, though they have fallen into practical disuse; but the courts of law have always put on them a construction the most favourable to foreign commerce, agreeably to the opinion of Lord Chief Justice Hale, that "the law of | England hath always been very gentle in the construction of the disability, and rather contracting than extending it severely." (Ventris's 'Reports,' vol. i. p. 427.) In the reign of James I. the king was strongly petitioned to adopt exclusive measures against the aliens, who had flocked into the kingdom from the Low Countries; but James, though he acquiesced to a certain extent in the object of the petitioners, seems by no means to have participated in their feelings of enmity to aliens; for he professes his intention "to keep a due temperament between the interests of the petitioners and the foreigners;" and he especially commends "their industrious and sedulous courses, whereof he wished his own people would take example." In the reign of Charles II. aliens were invited to settle in this country, and to engage in certain trades, by an offer of the privileges of native subjects. (15 Charles II. c. 15.) This statute was repealed by 12 & 13 Wm. III. c. 2; but there is an unrepealed Act of 6 Anne, which naturalises all foreigners who shall serve for two years on board any ship of her majesty's navy or a British merchant-ship. In the early part of the last century (1708) a bill was brought into parliament for the general naturalisation of all foreign Protestants, upon their taking certain oaths and receiving the sacrament in any Protestant church, and it passed notwithstanding the strenuous opposition of the city of London, who represented that they would sustain loss by being obliged to remit certain dues which aliens were obliged to pay. After remaining in operation for three years, it was repealed on a suggestion of its injurious effects upon the interests of natural-born subjects; but a previous bill for effecting this object was rejected by the Lords. The reasons for and against the measure will be found in the fourth volume of Chandler's Commons' Debates,' p. 119-122. In 1748 and 1751, a measure similar to the Act of 1708 was brought forward, and in 1751 it was read a second time, but was dropped in consequence of the death of the Prince of Wales, which disarranged the public business. Upon a review of the history of our policy, the inference seems to be, that although the maxims prevalent in our courts of law have been generally favourable to aliens, and although the government appear to have been at all times sensible of the advantages resulting from a liberal reception of foreign settlers engaged in trade, yet popular prejudices have been on the whole successfully exerted in impressing upon the legislature a more jealous and exclusive system. The Alien Acts (33 Geo. III. c. 4; 34 Geo. III. c. 43, 67, and others) were passed entirely from political motives, and were mainly enacted on account of the great number of foreigners who came to England in 1792 and 1793. There is reason to believe that the crown has always had the power of banishing aliens from the realm, which these acts, however, expressly gave to it: at all events, the power has undoubtedly been often exerted; and it seems almost to be included in the ampler prerogative of declaring war against the whole, or any part, of a foreign state. However, either from want of recent authentic precedents, or from a desire to accompany the measure with provisions not within the ordinary exercise of the prerogative, this power has not been exercised of late years without the sanction of parliament. In 1827 a measure was introduced (7 Geo. IV. c. 54) for the general registration of all aliens visiting this country, and every foreigner was required to present himself at the Alien office. This Act was repealed by 6 & 7 Wm. IV. c. 11, but new provisions of a similar character were introduced. Masters of vessels arriving from foreign parts are to declare what aliens (mariners navigating the vessel excepted) are on board or have landed, under a penalty, for omission or for false declaration, of 201., and 101. for each alien omitted. Every foreigner on landing is required immediately to exhibit any passport in his possession to the chief officer of customs at the port of debarkation, and to state to him, either verbally, or in writing, his name, birth-place, and the country he has come from, under a penalty, for neglect or refusal, of 21. The officer of customs is to register this declaration, deliver a certificate to the alien, and transmit a copy of the declaration to the secretary of state. On leaving the country the alien is required to transmit to the secretary of state the certificate granted him on landing. The act does not affect foreign ministers or their servants, nor aliens under fourteen years. The proof of non-alienage lies on the person alleged to be an alien. Under the former act aliens were required to present themselves at the Alien-office; but this is no longer necessary. The registration clause, it may be added, is generally disregarded by foreigners, and is never enforced, for there is no provision in the Act for recovering the penalty. ('Blackst. Comm.,' Mr. Kerr's ed., v. i. pp. 254, 308, 367, et seq.) The same classes of persons who are aliens according to the law of England, are aliens according to that of Scotland, and the statute law on the subject extends to that part of the empire. When an alien resident in Scotland wishes to acquire the privileges of a British subject, the same forms which, as above described, are applicable to England, are gone through with the same effect. They are consistent with the constitutional doctrine of the separate kingdom of Scotland, in which, anterior to the Union, it appears that letters of denization could give a portion, but an Act of Parliament only could communicate the whole of the privileges of a born subject of the crown. The institutional writers maintain that an alien cannot hold any kind of heritable property in Scotland, but in the books there are only two cases on the subject, and in one the general question was evaded; in the other an alien was found not to have a sufficient title to pursue a reduction of a conveyance of an estate. If the rule that aliens cannot hold heritage were strictly interpreted, it would affect property which all classes of persons are in the practice of holding in Scotland without molestation, but in the general case it would be difficult to find a form in which an alien's title could be brought in question. It is questioned whether an alien in Scotland who holds the statutory qualification may vote for a member of the House of Commons. The sheriffs, who are judges in the registration courts, have given conflicting judgments on this point. The following are the laws as to aliens in France and the United States of North America, two countries with which Englishmen are more closely connected than any other : A child born in France, of foreign parents, may, within one year after he has attained the age of twenty-one, claim to be a Frenchman; if he is not then resident in France, he must declare his intention to reside there, and he must fix his residence there within one year after such declaration. An alien enjoys in France the same civil rights as those which Frenchmen enjoy in the country to which the alien belongs; but he enjoys the right of succession in France, although this right may not be granted to French citizens in his own country. An alien is allowed by the king's permission (ordonnance du roi) to establish his domicile in France; and so long as he continues to reside there, he enjoys all civil but not political rights; but this enjoyment ceases immediately the domicile is lost. After an uninterrupted residence | during ten years, by permission of the king an alien may become naturalised. (Code Civil,' liv. 1, tit. i. s. 9.) A foreigner can buy and hold land in France without obtaining any permission from the crown or legislature. Upon the recognition of the independence of the United States of North America by the treaty of Paris, 1783, the natural-born subjects of the king of England who adhered to the United States became aliens in England; and it was decided that they became incapable of inheriting lands in England. It had been previously decided in America that natives of Great Britain were aliens there, and incapable of inheriting lands in the United States. Kent defines an alien to be "a person born out of the jurisdiction of the United States; " but this definition is not sufficiently strict, for the son of an alien, which son is born in the United States, is also an alien. Congress has several times altered the law respecting naturalisation, but chiefly as to the period of previous residence. In 1790, only two years' residence was required; in 1795 the term was prolonged to five years; and in 1798, to fourteen years. In 1802, the period of five years was again adopted, and no alteration in this respect has taken place. The benefits of naturalisation have always been confined to "free white persons; " persons of mixed blood are excluded, as well as the African and other pure races, whether black or copper-coloured. At what point a person of mixed blood could claim naturalisation is doubtful. By an old law of Virginia, which was not repealed up to a recent period, a person with one-fourth of negro blood is deemed a mulatto. An alien in the United States cannot have full and secure enjoyment of freehold of land; and if he does, the inheritance escheats. He can neither vote at elections nor hold public offices. Two years at least before he can obtain the privileges of a natural-born citizen he must appear in one of certain courts, or before certain officers, and declare on oath his intention to become a citizen of the United States, and to renounce his allegiance to his own state or prince. When the two years have expired, and if the country to which the alien belongs is at peace with the United States, he is next required to prove to the court, by his oath as well as otherwise, that he has resided five years at least in the United States, and one year in the state where the court is held; and he must show that he is attached to the principles and constitution of the United States, and is of good moral character. The court then requires that he should take an oath of fidelity to the constitution, and likewise an oath by which he renounces his native allegiance. He must also renounce any title or order of nobility, if he has any. The children of persons naturalised according to this form, if they were minors at the time, are deemed citizens if they are then dwelling in the United States. If an alien dies in the interval between having taken the preliminary steps towards his naturalisation and the time of his admission, his widow and children become citizens. If an alien resided in the United States previously to the 18th of June, 1812, the preliminary notice of two years is not necessary, nor if he be a ARTS AND SCI. DIV. VOL. I. minor under twenty-one and has resided in the United States during the three years preceding his majority. In the case of an alien who has arrived in the United States after the peace of 1815, it is required that he should not at any time have left the territory during the five years preceding his admission to citizenship. A naturalised alien immediately acquires all the rights of a natural-born citizen, except eligibility to the office of President of the United States, and of governor in some of the states. A residence of seven years, after naturalisation, is necessary to qualify him to be a member of Congress. (Kent's Commentaries,' vol. ii. p. 50-75.) In 1804 Congress passed an Act supplementary to the Act of 1802, which contains a clause respecting the children of American citizens born abroad, but it applies only to the children of persons who then were or had been citizens; and Kent remarks (' Commentaries,' vol. ii. p. 53) that the rights of the children of American citizens born abroad are left in a precarious state; and in the lapse of time there will soon be no statute which will be available, in which case the English common law will be the only principle applicable to the subject. Before the adoption of the present constitution of the United States, the several states had each the privilege of conferring naturalisation. Each state can still grant local privileges. There is a considerable diversity in the laws of different states respecting aliens. By a permanent provision in the state of New York, an alien is enabled to take and hold lands in fee, and to sell, mortgage, and devise (but not to demise and lease the same), provided he has taken an oath that he is a resident of the state, and has taken the preliminary steps towards becoming a citizen of the United States. There are similar provisions in several of the other states. In New York resident aliens holding real property are liable to be enrolled in the militia, but they are not qualified to vote at any election, of being elected to any office, or of serving on a jury. In North Carolina and Vermont the constitution provides that every person of good character who comes into the state and settles, and takes an oath of allegiance, may hold land, and after one year's residence he becomes entitled to most of the privileges of a natural-born citizen. In Connecticut the superior court, on the petition of any alien who has resided in the state six months, has the power of conferring upon him the same privileges in regard to holding land, as if he were a natural-born citizen. In Pennsylvania aliens may purchase lands not exceeding 5000 acres, and hold and dispose of the same as freely as citizens. In Georgia aliens can hold land, provided they register their names in the Superior Court. No alien can act as executor or administrator in this state. In Kentucky, after a residence of two years, an alien can hold land. In Indiana, Missouri, and Maryland the disqualification of an alien holding land is done away with on his giving notice of an intention to become a citizen. Most, if not all, of the state legislatures are in the habit of granting to particular aliens, by name, the privilege of holding real property. ('Law relating to Aliens in the United States,' in Boston Almanac,' 1835.) In the States generally, perhaps in all, as in England, the alienage of a woman does not bar her right of dower. The following information is abstracted from evidence given by Harvey Gem, Esq., before the Select Committee on aliens, in 1843, and the information was stated to have been obtained from the ambassadors or ministers of the different Powers in London : In Prussia, from the moment when an alien becomes a resident and places himself under the protection of the laws, he enjoys the same rights as a natural-born subject, and not only has he a right to vote in the election of members to the Provincial States, but he is also eligible himself as a member. In Saxony, by a law passed in 1834, an alien may acquire the privileges of a natural-born subject by right of domicile, granted by the local authorities of each district, or by the purchase of real property, and in towns by obtaining the freedom of the corporation. In the two latter cases, the alien must have been in possession of his real property or of his freedom for five years, during which period he must have resided in the place where the property is, or in the town of which he has obtained the freedom. The right of voting, eligibility as a representative of the Chambers of the Kingdom, &c., depend upon the nature and value of the real property acquired, whether a manor, a house in a town, &c. In Bavaria aliens can possess landed property, without the condition of residence, but they are liable to the duties which attach to the property. Naturalisation is obtained either by marriage of a foreign woman with a Bavarian, by domicile and renouncing foreign allegiance, or by royal decree; but a residence of six years is necessary before the full citizenship can be obtained. The privileges of an alien in Bavaria depend in some degree on the policy of the state of which he is a subject towards foreigners in general or Bavarians in particular. In Würtemberg an alien who wishes to be naturalised, first purchases landed property in or near the place where he intends to settle, by which he obtains the consent of the local authorities to reside among them (bürger-recht). These conditions having been fulfilled and the sanction of government obtained, the alien acquires the Staatsbürger-recht, which gives him all the privileges of a natural-born subject, and with them its obligations, as liability to the military con P scription, &c. The burger-recht may give an alien all the municipal rights of a citizen in a town, while, as respects the Staatsbürger-recht, which makes him a citizen of the state, he may still be an alien. In Hanover naturalisation is acquired in one or other of the follow ing ways: by marriage of a foreign woman with a Hanoverian subject; by the adoption by a Hanoverian of a foreigner as his child; by holding any office under the government; by becoming a member of a commune; by the purchase of a residence or freehold in any commune; by the authority of the State, independently of the will of the commune; and by a residence of five consecutive years in any commune with the express approbation of the bailiff or mayor-the conditions in the two last cases being the possession of sufficient means of subsistence and an irreproachable character. marriage, and consequently to be entirely dependent upon him for her future maintenance. Upon this principle it is considered reasonable that if a separation is decreed, the wife should have a portion of her husband's estate allotted for her subsistence; and this allowance is termed in law "alimony." The right of the wife to this provision depends upon the fact whether she has or has not sufficient means, independently of her husband, to support her in her appropriate station in life. Where the wife has a sufficient income beyond the husband's control, she is not entitled to alimony. Alimony, as incidental to questions relative to or arising from marriage, fell until recently under the exclusive cognisance of the ecclesiastical courts; but the jurisdiction of these tribunals has now been transferred to the Court for Divorce and Matrimonial Causes; which is, however, directed to act on the principles of the ecclesiastical courts in matrimonial causes. The giving of alimony is necessarily incidental to a decree of judicial separation or divorce, and may be temporary or permanent. While the proceedings in the suit are pendthe continuance of the litigation. When a decree has been obtained, a permanent provision will be given to her. In both cases it is an annual allowance proportionate to the estate of the husband. In Austria a residence of ten years is sufficient in all cases to obtain naturalisation. Whoever holds any office, either civil or military, under the crown, is thereby naturalised. Merchants or manufacturers who come to settle in the country with their families can obtain naturalisation at once, if they are of good reputation and not in needying, the court will, generally speaking, allot alimony to the wife during circumstances. Naturalisation confers, without any exception, all the rights and privileges of natural-born subjects. The Act of the German Confederation, Art. 18, gives to every German the right of holding civil and military offices in the different states of the Confederation. In Denmark, every foreigner who settles there with the intention of remaining, and who owns land of the value of 30,000 crowns, or houses in the towns of the value of 10,000 crowns, or a capital of 20,000 crowns in trade, acquires by that alone the right of demanding letters of naturalisation. Children born in Denmark of foreign parents, and persons naturalised, are eligible to all public offices, with one exception, which is this, a naturalised foreigner does not become eligible as a deputy of the provincial States until he has resided for five years in the European dominions of Denmark, and renounced his foreign allegiance. In the Hanseatic towns naturalisation is acquired in the following manner :-In Lübeck and its territory, any person of respectability, especially after a prolonged residence, is admitted as a citizen without difficulty, on showing, if required, that he has sufficient means of subsistence. Letters of naturalisation confer all the rights which natural-born subjects enjoy. In Hamburg an alien cannot hold landed property, but any persons taking up their bonâ-fide residence there may obtain letters of naturalisation on payment of a moderate sum (a few pounds, it is stated), upon which they enjoy all the rights of native citizens, with the exception of not being eligible to the order of the bürgerschaft; but the restrictions in this case apply only to age and some other qualifications, which are equally applicable to native citizens. No business can be transacted by foreigners until they have obtained the privilege of citizenship, and become members of some one of the guilds. Any foreigner may become a citizen by purchase. Jews cannot become citizens. In Bremen an alien obtains the rights of citizenship for a money payment, and by becoming a member of a commune. In Frankfort naturalisation is obtained by gift for public services, by marriage, or by purchase, if the person desirous of becoming a citizen can give satisfactory references as to character, station, and property. In Sardinia the power of conferring naturalisation rests entirely with the king, and is never refused on any bonâ fide application: a naturalised person enjoys all the privileges of a natural-born subject. In Portugal an alien of not less than twenty-five years of age can obtain letters of naturalisation after two years' residence, and provided he has the means of subsistence. The two years' residence is dispensed with if the alien has married a Portuguese woman; or has opened or improved a public road; embarked money in trade; improved any branch of arts; introduced any new trade or manufacture; or otherwise performed some service of public utility. In Belgium an alien cannot purchase or hold land. There are two kinds of naturalisation, the petite naturalisation and the grande naturalisation. The first gives the alien some advantages, as the right to sue, &c.; and the second, which is an act of the legislature, confers political privileges, in addition. In Switzerland naturalisation is conferred in some cantons by the legislature, and in others by the executive. In Tessin a naturalised foreigner can only enjoy the full rights of citizenship after five years have elapsed from the date of his naturalisation. In Thürgau no one can hold any office under the government unless he has been a burgess of the canton at least five years. In Berne, Zürich, Vaud, Geneva, and most of the cantons, an alien obtains the full citizenship from the date of his naturalisation. In Russia no foreigner, who does not become a "perpetual subject," can enjoy the rights and privileges attached to the guild of merchants. The commercial rights belonging to merchants are enjoyed in their character as guests, or as itinerant merchants. A foreigner who imports goods must sell them to Russians only. ALIMENT. [ALIMONY.] ALIMONY, from the Latin alimonium or alimonia, signifying "maintenance," or "support." By the law of England, a wife is presumed to have surrendered the whole of her property to her husband upon The amount of alimony depends wholly upon the discretion of the court, equitably exercised with a view to the circumstances of each particular case. After a separation on account of the husband's misconduct, the wife is alimented as if she were living with him as his wife. The court attends carefully to the nature as well as to the amount of the husband's means, drawing a distinction between substantial property and an income derived from personal exertion. The station in life of both parties, and the fortune brought by the wife, are also considered; and much stress is laid upon the disposal of the children and the expense of educating them. The conduct of the parties forms also a very material consideration. Where the wife has eloped from her husband, or where a sentence of divorce proceeds upon the ground of her adultery, alimony is not granted. Adultery in a wife involves a forfeiture of her dower. For the same reason the adulteress shall not partake of the husband's estate while living. In assigning alimony, it should be observed, that during the continuance of a suit it is always much less in amount than when permanently decreed. Thus in the former case the proportion usually allowed is one-fifth of the net income of the husband; in the latter, a moiety of the whole income is not unfrequently given. No general rule can, however, be laid down upon this subject, as the amount granted must always depend upon the infinitely varied combinations of facts brought before the court. The assignment of alimony during the continuance of a suit does not discharge the husband from liability for his wife's contracts. When the court has allotted her a permanent maintenance, the wife is liable for her own contracts, and the husband is discharged from them. The equivalent in Scottish law for alimony, is Aliment. A wife is entitled to aliment when deserted by her husband, when judicially separated from him, and during a suit for a divorce whether at her own or at his instance, the aliment in this last case including what may be necessary for the expenses of the defence. She has no right to aliment in the case of a voluntary contract of separation. ALIQUOT PART. One number or fraction is said to be an aliquot part of a second number or fraction, when the first is contained an exact number of times in the second. Thus, 6, 3, 4, 2, 11, 1, 1, &c., are all aliquot parts of twelve, being contained in it respectively 2, 4, 3, 6, 8, 28, 96, &c. times. The word is principally used in the arithmetical rule called practice, and the convenience of using it is as follows: If we want to know how much 30 yards cost at 17. 15s. 6d. a yard, the direct process of common arithmetic would be to turn 30 yards into half yards, giving 61, and 17. 15s. 6d. into sixpences, giving 71. Then multiplying 61 by 71, and dividing the product by 2, we have the number of sixpences which 30 yards cost, which must then be reduced into pounds, shillings, and pence. But if we observe that 1. 15s. 6d. is made up of 1., 108. the half of one pound, 53. the half of 10s., and 6d. the tenth of 5s., we can proceed as follows: in which each line is derived from the preceding by simple division, on the obvious principle that at 6d. a yard we give the tenth part of what we give at 5s. a yard, and so on. The object therefore is, to be ready in dividing a sum of shillings and pence into parts, each of which shall be the aliquot part of a pound, or of one of the preceding parts. The following table contains the simple aliquot parts of a pound, arranged so that the aliquot part of an aliquot part shall be visible on inspection. Figures written by themselves are shillings, and the semicolons separate shillings from pence. useless. Half, 13 10 Half. Third. 84 Fourth. Fifth. Sixth. Eighth. Tenth. Twelfth. Twentieth. 42 3; 4 2; 6 2 13 Fortieth. 8888 ;3 ;4 ;2 ;3;1 ;2;1 5 3; 4 2; 6 1; 81; 3 Third, ;10 ;6 ;1 The aliquot parts omitted contain fractions of farthings, and are carbonates are likewise pungent. They exercise an immediate influence on the fluids of the mouth and alimentary canal, as far as they pass unchanged. They neutralise all acids they meet with in their course, and render the mucus, and perhaps some other secretions, thinner and more watery. That they are readily absorbed into the circulating mass, on which they have a marked influence, is certain; but they are for the most part speedily eliminated, the kidneys appearing to be the channels by which they are thrown out of the system. Many alkaline compounds, as well as the uncombined but diluted alkalies, increase the secretion of urine, and change its nature, if long persevered in, altering it from an acid to an alkaline state. This is particularly the case when the compound is one of carbonic acid, or of a vegetable acid with the base, all of which are decomposed in transitu, as first remarked by Sir Gilbert Blane, and produce on the urine, and the system gene;21;1; rally, ultimately the same effects as the pure alkalies. The alkalies possess a power of rendering albumen soluble: unboiled white of egg is an albuminate of soda. The albumen of the blood is rendered more fluid by alkalies; hence in excess they impair the plastic power of that fluid. These facts seem all that are requisite to form a correct estimate of their therapeutic powers and employment. Their caustic and rubefacient properties fit them for external use. Their internal employment is regulated by a variety of indications, but it is chiefly as antacids, or to counteract acidity in the stomach and primæ viæ, and as diuretics, and to dissolve calculi in the kidneys or bladder, and as refrigerant or cooling medicines in inflammatory diseases, that they are used. Many persons, soon after food has been taken into the stomach, are distressed with heartburn and other signs of indigestion, and either have the urinary secretion in an unhealthy state, or, if they be of a gouty disposition, have frequent attacks of gout. Such persons feel relief by taking some alkaline medicine after meals, or have recourse to them because others use them. When uric or lithic acid exists in the urine, such means may be proper; but this point should be ascertained before having recourse to measures which, when not appropriate, are far from being harmless. Some acid, either hydrochloric or acetic, is essential to sound digestion: to neutralise these is to retard and disturb that process. Other acids, especially lactic, in bilious persons and those who use sugar or saccharine fruits in excess, occur, and require to be obviated; but the proper time for taking, as well as the proper quantity to be taken, requires much judgment. Assuming that some alkali is proper, Sir B. Brodie thinks from three to four hours after each of the principal meals, especially dinner, the most suitable time. (Lectures on the Urinary Organs,' 3rd ed. p. 203; and Medical Gazette,' vol. xxiii. p. 151.) Dr. Prout makes a similar remark with respect to alkaline mineral waters. A variety of circumstances regulate the alkali to be selected. From their greater causticity, the pure alkalies can rarely be persevered in sufficiently long, even when taken in such bland vehicles as veal-broth. The alkaline carbonates are better borne, and bi-carbonate of potass more easily than carbonate of soda. Their unpleasant taste constitutes an objection with many: this is in some degree obviated by giving them in the condensed form recently devised by Mr. Brockedon, or in an effervescing state with an excess of alkali, as recommended by Sir Gilbert Blane. If taken unnecessarily or persevered in too long, much evil is done: not only is an alkaline state of urine induced, with a deposition of the phosphates, as indicated by a white sabulous sediment, or an iridescent pellicle on the surface of the urine, but much general debility is caused. "Other ill consequences follow the too liberal use of alkalies: they alter the quality of the blood. After some time the patient is liable to petechiæ; he perspires too easily, becomes low-spirited, and less capable than when in health of physical exertion." (Brodie, l. c. p. 202.) As effervescing or saline draughts, made with a vegetable acid and some alkaline carbonate, are much used at the beginning of inflammatory diseases for their reducing and refrigerant effects, the same caution is requisite lest they be pushed too far. This is also needful in the case of soda-water (when it really contains soda, and not merely carbonic acid, as is frequently the case), citrated alkali, imperial, and other drinks much used in warm weather. Scrofulous persons can least of all bear up against the abuse of these, yet for such are they unfortunately most employed. Weak vegetable acids will be found more beneficial. ALIZARIC ACID. [MADDER.] ALIZARIN ACID. [MADDER.] ALKALIES. Although the term alkali (compounded of the Arabic prefix al, and kali the name of plant-ashes, from which potash is obtained) was formerly rather loosely applied to a variety of basic substances, yet its use is now generally restricted to three metallic oxides, namely, potash (KO), soda (NaO), and lithia (LiO), which from their non-volatility at a red heat are termed the fixed alkalies, and to ammonia, a compound of nitrogen, hydrogen, and oxygen (NH,O), which on account of its volatility, even at ordinary temperatures, is sometimes called the volatile alkali. The chemical properties of the alkalies are the following: their aqueous solutions turn vegetable blues green, and vegetable yellows reddish-brown; hence infusion of red cabbage and infusion of turmeric, or papers stained with them, are used as tests of the presence of an alkali. The alkalies restore the colour of vegetable blues-as of litmus, for instance--which have been reddened by acids, and, on the other hand, the acids restore vegetable colours which have been altered by the alkalies. These properties are also common to lime, baryta, and strontia. The alkalies have great affinity for, and readily combine with, acids, forming salts, and the power of both in altering vegetable colours, is then destroyed. The alkalies are separated at the negative pole of the voltaic decomposition cell. Potash and soda destroy the skin when applied to it in concentrated solution. These alkalies, together with lithia, are inodorous, but possess a peculiar acrid taste. Ammonia has a similar taste, and possesses a very pungent odour, like hartshorn, or smelling salts. All the alkalies are very soluble in water. For their preparation, special properties, and uses, see POTASH, SODA, LITHIA, and AMMONIA. ALKALIES, Medical Properties of. It is impossible to exclude magnesia and lime from consideration when treating of alkalies, but the remarks which follow are chiefly intended to apply to soda, potassa, and ammonia. The two former are termed fixed, the latter volatile: soda is likewise termed the mineral or fossil alkali; while potassa is termed the vegetable alkali, or sometimes merely kali. The salts formed with alkalies are apt to effloresce, and resolve the crystals into the state of powder, or to absorb water from the air, and deliquesce or become liquid. Alkalies in a pure state are extremely caustic, destroying the tissues with which they come in contact, and forming an eschar which is deep if the alkali be confined, extensive and superficial if allowed to spread. This seems to depend on their strong affinity for water: hence they act as violent corrosive poisons, and are never used in a pure state, save in surgery to open abscesses or to form caustic issues. Diluted with oils they constitute rubefacients, particularly ammonia. Their causticity is also greatly lessened by combination with carbonic acid, and is more subdued by an excess of the acid; hence bi-carbonates are less caustic than sesqui-carbonates, and these last than carbonates. Carbonate of ammonia will altogether disappear if not kept in a well stopped bottle; this tendency is one source of its utility when used as smelling salts. When suitably diluted with water or by combination with carbonic acid, so as to be safely applied to the tongue, alkalies have a taste peculiar, and to most persons unpleasant, which is designated alkaline, for want of anything similar to which to liken it. Ammonia and its ALKALIMETRY, a term applied to certain ready methods of estimating the commercial value of the alkalies, more especially of potash and soda, and of certain of their salts which possess an alkaline reaction. The most simple method of performing this operation consists in ascertaining the amount of a dilute acid of known strength required exactly to neutralise 100 grains of the sample of alkali. The alkalies and alkaline salts generally tested in this way are potash, soda, and their carbonates. For most of the purposes to which these materials are applied in the arts, their value depends upon the quantity of the alkali which they contain, either in a caustic state or in the condition of carbonate; other alkaline salts or compounds that may be present being useless, if not deleterious. As soda is much more largely used in the arts than potash, the standard acid, or test acid, as it is termed, is often made with reference to this alkali, and is graduated to such a strength that 1000 grain measures of it exactly neutralise 100 grains of anhydrous caustic soda (NaO); but the following method of preparing the test-acid, recommended by Faraday, is the most convenient and generally applicable, both to potash, soda, and their carbonates. The test-acid employed is measured from an instrument |