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NUE'CES, a river of Texas, rises in south-western Texas. lat. 30°. long, 101° w., and after a south-easterly course of 300 m., flows into Corpus Christi bay, and through the pass of the same name into the gulf of Mexico.

NUE'CES, a co, in s. Texas, on the gulf of Mexico, s. of the Nueces river, drained by the Santa Gertrudis river and others; 2,800 sq.m.; pop. '80, 7,669—4,410 of American birth, 628 colored. The surface is mostly level, and the soil a rich loam. There is not sufficient rain for agriculture, but the county is admirably adapted for cattle and sheep raising. Large quantities of wool are produced. Corpus Christi bay on the n.e., and numerous other inlets afford good tishing Co. seat, Corpus Christi.

NUEVA SPARTA. See MARGARITA.

NUEVO LEON, a Mexican state bounded n. by the Rio Grande, e. by Tamaulipas, s. by San Luis Potosi and Zacatecas, and w. by Coahuila; between 24° and 27° 30' n. Îat., and 99° and 100° 40' w. long.; about 20,000 sq.m.; pop. about 180,000. The surface is irregular and mountainous, and in the s. is made up of table-lands. The chief rivers are the Tigre and other branches of the Rio Grande. In the valleys are extensive forest and pasture lands, as well as good soil for cultivation. The soil would be very fertile were it well watered; maize (three crops), sugar cane, and wheat are the staples. There are mines of gold, silver, lead, copper, iron, and salt, but none fully developed. Marble, alabaster, and sulphur are also found. There are large manufactories of boots, shoes, leather, hats, and cotton cloth. The climate is hot and unhealthy, except in the higher districts. Nuevo Leon is divided into pine districts: Monterey, Cadereita, Villaldama, Salinas, Garcia, Victoria, Morelos, Doctor Arroyo, Linares, and Cerralvo. The capital is Monterey; Florida, Saltillo, Morelos, and Linares are important towns.

NUGGINA, a t. of British India, in the district of Bijnur, division of Rohilcund, n.w. provinces. It is 48 m. n. n.w. from Moradabad, on the route from Moradabad to Hurdwar. Nuggina is the Birmingham of upper India, and is famous in modern times for the manufacture not only of gun-barrels but of percussion-locks. Pop. '72, 19,696.

*NUISANCE is a legal term used to denote whatever is an annoyance to one's peighbors, or in a general sense to the public at large, in the exercise of their rights of property. The whole doctrine of nuisance is founded on the theory that every person is entitled to have the full use and enjoyment of his property, and of the right of passing to and fro on the highway without being interfered with or impeded by others, and whatever so impedes this full enjoyment of one's property and right of passage on the highway is a nuisance. Nuisances are thus capable of being divided into two kindsprivate and public. Thus, if a neighbor leave a heap of rubbish emitting noxious smells close to A's windows, or make loud noises in his house, these may be said to be private nuisances, for they annoy A in the enjoyment of the fresh air and quiet which are part of his right of property. On the other hand, if something is put of the same kind on a public highway, or so as to annoy divers people equally and in the same manner, then it is called a public nuisance. One of the leading incidents of a nuisance is that the party annoyed by it can in many cases, especially where the nuisance is injurious to health or life, take the law into his own hands and abate the nuisance without resorting to a court of law. The reason is that the matter is of too urgent importance to await the slow progress of a suit at law, and mischief may be done in the mean time which would be often irreparable owing to the delay. Another important qualification of the right of abating a nuisance is that the nuisance must be such that unless it is abated at once the party cannot exercise his legal rights; and hence if the nuisance is of such a kind that it does not directly interfere with the comfort or enjoyment of one's legal rights at the time, he has no right to abate it, but in that case is bound to resort to a court of law. This is best illustrated in the case of a nuisance on the highway, which is the class of cases in which the phrase a common nuisance is most familiarly known. Thus if while A is riding or driving along the highway his progress is interrupted by a fence or gate which nobody has a legal right to put there, it is obvious that unless A can knock down or demolish at once this obstruction he cannot proceed in the exercise of his legal right of using the highway. In such a case he has a right to demolish the gate and abate the nuisance, for it directly interferes with his own legal right. But if instead, a gate, a booth, or tent had been erected, not across the highway, but merely on one side of it, so as to leave room for passengers to pass, then, though such tent or booth would be as undoubted a nuisance as in the other case, yet inasmuch as A can pass without direct interference, he has no right to abate the nuisance by destroying the tent. He must, in this latter case, resort to the legal remedy only. The same rule applies to all kinds of nuisances.

Another rule is that in abating a nuisance the party is not to do unnecessary damage to property, i.e., more than simply abate the nuisance to such an extent as to enable himself to exercise bis legal right, and no further. If he go beyond the immediate occasion, and cause unnecessary destruction to property, then he subjects himself to an action of damages. Hence it is often a difficult thing to know when one is justified in abating a Quisance and taking the law into his own hands.

.Where the nuisance is sought to be removed by legal means, then the remedy is in some cases two-fold, and in some cases not so. Where the nuisance is of a privato nature, an action of damages is in general the only remedy given by the common law. But where the nuisance is public, and affects all the public equally, or nearly so, then in general either an action may be brought, or an indictment will lie. Thus in case of a nuisance on a highway, as this affects all the lieges alike, an indictment is the proper remedy, though if an individual suffered special damage over and above what he suffers as one of the public, then he may bring an action. In Scotland, instead of an indictment, an action in the nature of a public action is raised, which is substantially similar in its results to an indictment.

As will be seen from what has preceded, the legal remedy in cases of nuisances has long been felt to be insufficient. T'o add to the other defects, there is great difficulty in determining whether a particular mode of using one's premises is in the nature of a nuisance or not; for if the line is drawn too narrowly, the rights of property and the natural freedom of the subject may be interfered with. On the other hand, things which formerly were considered no nuisances are now treated as such, owing to the spread of more enlightened views of public health and habits of cleanliness. These considerations recently induced the legislature to alter the common law in an important degree, and substitute a new code under the name of the public health and nuisances removal acts, 11 and 12 Vict. c. 63; 18 and 19 Vict. c. 116; 35 and 36 Vict. c. 79. The general scheme of these acts is to enable districts to appoint local boards, with extensive powers of selfgovernment, and to undertake and execute sanitary improvements, such as drainage and water supply on a large scale, paying for the expense thereof by a local rate or assessment.

As regards the power of removing nuisances, a statute was passed in 1855 for England, called the nuisances removal act, which has been amended by two subsequent acts. By these acts, some sanitary authority, called rural or urban, under 35 and 36 Vict. c. 79, is appointed the local authority for carrying out the provisions of the act, and these are of an extensive kind. The act defines a nuisance to include any premises in such a state as to be a nuisance or injurious to health; any pool, ditch, gutter, water-course, privy, urinal, cess-pool, drain, or ashpit, so foul as be a nuisance or injurious to health; any animal so kept as to be a nuisance, or injurious to health; and any accumulation or deposit, overcrowding, foul condition, or smoke. The local authority is to appoint a sanitary inspector at a proper salary. Any person aggrieved may give notice to the local board, or the sanitary inspector may do so. The local board has extensive powers; it can authorize its inspector, on reasonable complaint, to demand an entrance into any private premises so as to inspect their condition, and may order the removal of nuisances found to exist there. The local board, on finding a nuisance exists, direct their officer to go before a justice of the peace and procure an order directing the private party to abate the nuisance. If he refuse to do so, the local board may remove the nuisance at the expense of the party on whose premises it exists, and sue him for such expenses. If any candle-house, melting-house, soap-house, slaughter-house, or place for boiling offal, blood, bones, etc., be certified by the medical officer, or any two medical practitioners, to be a nuisance, or injurious to the health of the inhabitants of the neighbor. hood, the local board may cause the person carrying on such trade to appear before a justice of the peace, and if it is not satisfactorily proved that he does not use the best practicable means for preventing or counteracting the effluvia, he is fined. So if houses are overcrowded, this may be stopped. Provisions are also enacted with a view to prevent the spread of diseases in times of epidemics, and to prevent common lodging-houses being kept in a foul state. Another important provision relates to the seizure of diseased ment and provisions exposed to sale, and the medical officer of health, or inspector of nuisances, has at all times power to inspect any animal, carcase, meat, poultry, game, flesh, fish, fruit, vegetables, corn, bread, or flour; and if found unfit for food, or dis

shopkeeper fined. The local authority may also order owners of houses to supply proper water-closets, and to cleanse gutters and cess-pools which are foul. Besides the above provisions as to nuisances generally, there are separate statutes for the English metropolis and the river Thames; thus furnaces in mills, factories, bake-houses, etc., in London, must consume their own smoke. These statutes are the 16 and 17 Vict. c. 128, and 19 and 20 Vict. c. 107. The public health act, 1875 (39 and 40 Vict. c. 55), practically codifies the law on all such matters. The rivers pollution act, 1876 (39 and 40 Vict. c. 75), deals with another important species of nuisance.

In Scotland, a nuisances removal statute was passed in 1856, and was re-enacted by the public health açt, 1867, 30 and 31 Vict. c. 101. By that act the town council, or police commissioners of the place, are constituted the local authority for enforcing the act, and in other places the parochial board. Besides dealing with the same class of nuisances as the English act, the Scotch act provided for checking all trades and businesses offensive and injurious to the health of the neighborhood. Similar powers were given to the local board to enter private houses and explore the causes of nuisances. Diseased and unwholesome meat and provisions may also be seized. Common lodginghouses were to be registered, and to be subject to rules and regulations to be made by the local authority. With regard to towns in Scotland, an extensive code of police laws was enacted in the general police and improvement acts, 25 and 26 Vict. c. 101, 31 and 32 Vict. c. 102. The acts may be adopted by burghs; and villages above 700 of population may, by vote of householders, be converted into burgbs for this purpose. A smoke nuisance act for Scotland was passed applicable to all burghs, 20 and 21 Vict. c. 73 ; 24 Vict. c. 17; 28 and 29 Vict. c. 102.

The above is the usual legal acceptation of the term nuisance, but the word is sometimes used popularly to denote that class of nuisances, caused by disorderly houses or brotbels, which are familiarly described as common nuisances. In the law of England those who keep a brothel are liable to be indicted for a misdemeanor, but as there was often a difficulty in setting the law in motion in such cases, a statute of 25 Geo. II. c. 36, enacted that if any two inhabitants should give notice to a constable of such a house being kept, it should then be the duty of the constable under a penalty, to go with such inhabitants before a justice and engage to prosecute the keeper, and their expenses are paid by the parish out of the poor-rates. The same act provided that whoever in point of fact acted as the master or the mistress of the house, should be taken to be the keeper of the house. The punishment is fine and imprisonment. Of late an attempt has been made to convict a landlord under this statute when he knows of the character of his tenants, and refuses to give them notice to quit; but the courts have held that the mere fact of the landlord refusing to give notice to quit, and so to eject such tenants, was not enough to make him liable in any criminal punishment. In Scotland, the offense of keeping a brothel is punishable in a similar manner. But apart from the keeping of a brothel, there is no criminal offense committed in this country by those who frequent such houses for the purposes of prostitution unless where the circumstances amount to rape (q.v.), or abduction (q.v.), or an aggravated assault. See Supp., page 892.

NULLA BONA, a legal phrase in England, descriptive of the return made to a sheriff, who in executing process against a debtor finds he has no goods.

NULLIFICATION, in American politics, the doctrine of the extreme states' rights party, of the right of a state to declare a law of congress unconstitutional and void, and if the federal government attempted to enforce it to withdraw from the union. In 1832, during the presidency of gen. Jackson (q.v.), the free trade and states' rights party in South Carolina (q.v.), under the leadership of John C. Calhoun (q.v.), her senator in congress, asserted the doctrine of nullification in a state convention which declared the tariff acts of that year unconstitutional, and therefore null and void; that the duties should not be paid; and that any attempt on the part of the general government to enforce their payment would cause the withdrawal of South Carolina from the union, and the estab. fisinment of an independent government. President Jackson met this declaration with a vigorous proclamation, in which he declared that the laws must be executed, and that “the union must and shall be preserved.” South Carolina, standing alone, receded from her position under protest, and a “compromise bill,” introduced by Henry Clay (q.v.) in 1833, providing for a gradual reduction of duties, for the time settled the controversy.

NULLIFICATION (ante), in general, might be used to indicate any act of absolute invalidation or making void, but is almost exclusively applied to the doctrine first set forth by John C. Calhoun in a paper known as the South Carolina Exposition, which was presented by him in 1828 to the legislature of that state, and by them ordered printed. This doctrine asserted the right of any state to declare the unconstitutionality of any United States law, though it should have been passed in the proper manner, have received the assent of the president, and even have been tested as to its constitutionality before the U.S. supreme court. And it was further claimed that any attempt to enforce such law in a state which had refused to acknowledge its force was such an unconstitutional violation of the sovereign rights of that state as would justify her in at once leaving the union. The immediate cause of this remarkable assertion of power was the existing system of tariff laws, which, it was claimed, bore with great unfairness on the nonmanufacturing and raw material-producing southern states. The argument was in great measure based on language used by Jefferson in drawing up the Kentucky and Virginia resolutions of 1798-99 in regard to the sedition and alien laws. Here it was asserted that the general government was not “the final or exclusive judge of the extent of the powers delegated to itself, but that, as in all other cases of compact among powers having no common judge, each party has an equal right to judge for itself, as well of infractions as of the mode and measure of redress.” These resolutions further express the conviction that other states “returning to their natural rights in cases not made federal, will concur in declaring such laws void and of no force, and will each take measures of its own in providing that neither these acts nor any others of the general government not plainly and intentionally authorized by the constitution, shall be exercised wituin their respective territories.” Senator Havne of South Carolina was the first to advocate openly the destructive doctrine based on these expressions of Jefferson, and his speech on the subject in the senate called forth Webster's famous oration of Jan. 26, 1830. The theory rapidly gained ground among the extreme believers in state sovereignty, and toward the close of 1832 the governor of South Carolina, acting on the advice of Calhoun, summoned a convention to meet at Charleston. This convention reported for the action of the legislature an ordnance, declaring that the existing tariff law was “null and void, and no law,” authorizing the citizens of the state to refuse payment of any taxes under that law after Feb. 1, 1832, and denying the right of the U. S. supreme court to pass upon the validity of the ordinance itself. This bold declaration of independence from the authority of the general government was accompanied by the threat that if any steps were taken to enforce the collection of duties, the state would be justified in retiring from the union, and not a vote was cast against it in the convention. When congress met in 1832, Hayne was governor of South Carolina. Calhoun entered the senate, and the state legislature was on the point of enacting laws to carry out the nullification ordinance. The danger was averted partly by the adoption of the so-called Clay's compromise, a modification of the tariff law, but chiefly by the firm and wise action of Andrew Jackson, then serving his second term as president. His orders to the revenue officers of Charleston showed his intention to carry out the laws and maintain the authority of the general government; it was well known that he was not a man to be tritled with or intimidated, and his special message to congress on the subject is one of the ablest state-papers produced in the country's history. The authorship of the proclamation is generally attributed to Edward Livingston, the secretary of state. Jackson's position as a southern democrat and as a military hero also had much weight. Calhoun made an able and ingenious speech in the senate, Feb., 1833, sustaining his view of mllification, but the movement had lost its force, and though there was for some years a party of nullifiers under Calhoun's leadership, that form of the doctrine of state sovereignty was no longer a factor in politics, though undoubtedly the forerunner and logi cal parent of the doctrine of the right of secession.

NU'MA POMPILIUS, in the mythic history of Rome, was the successor of Romulus, the founder of the city. He was a native of Cures in the Sabine country, and was universally reverenced for his wisdom and piety. Unanimously elected king by the Roman people, he soon justified by his conduct the wisdom of their choice. After dividing the lands which Romulus had conquered, he proceeded, with the assistance of the sacred nymph Egeria, to draw up religious institutions for his subjects, and thus stands out in the primitive legend as the author of the Roman ceremonial law. His reign lasted for 39 years, and was a golden age of peace and happiness. The only feature in the myth of Numa Pompilius which we can regard as probably historical, is that which indicates the infusion of a Sabine religious element into Roman history at some remote period.

NUMANTIA, the chief t. of the Celtiberian people called Arevaci in ancient Spain, was situated on the Douro (Durius), in the neighborhood of the present Soria in old Cas. tile. The site is probably marked by the present Puente de Guarray. Numantia is celebrated for the heroic resistance which it made to the Romans, from 153 B.C., when its citizens first met a Roman army in battle, to 134 B.C., when it was taken and destroyed by Scipio the younger, after a siege of 15 months, in the course of which famine and the sword had left alive very few of its 8000 brave defenders. The besieging force under Scipio amounted to 60,000 men.

NUMBERS, THEORY OF, the most subtle and intricate, and at the same time one of the most extensive, branches of mathematical analysis. It treats primarily of the forms of numbers, and of the properties at once deducible from these forms; but its principal field is the theory of equations, in as far as equations are soluble in whole numbers or rational fractions, and more particularly that branch known as indeterminate equations. Closely allied to this branch are those problems which are usually grouped under the diophantine analysis (q.v.), a class of problems alike interesting and difficult; and or which the following are examples: 1. Find the numbers the sum of whose squares shall be a square number, a condition satisfied by 5 and 12, 8 and 15, 9 and 40, etc. 2. Find three square numbers in arithmetical progression; Answer, 1, 25, and 49; 4, 100, 196, etc.

Forms of numbers are certain algebraic formulas, which, by assigning to the letters successive numerical values from 0 upwards, are capable of producing all numbers with. out exception, e.g., by giving to m the successive values 0, 1, 2, 3, etc., in any of the following groups of formulas: 2m, 2m + 1; 3m, 3m + 1, 3m + 2; 4m, 4m + 1, 4m + 2, 4m + 3, we can produce the natural series of numbers. These formulas are based on the self-evident principle, that the remainder after division is less than the divisor, and that, consequently, every number can be represented in the form of the product of two factors + a number less than the smaller factor.

By means of these formulas, many properties of numbers can be demonstrated without difficulty. To give a few examples. . (1.) The product of two consecutive numbers is divisible by 2: Let 2m be one number, then the other is either 2m +1 or 2m - 1, and the product 2m (2m + 1) contains 2 as a factor, and is thus divisible by 2. (2.) The product of three consecutive numbers is divisible by 6: Let 3m be one of the numbers (as in every triad of consecutive numbers one must be a multiple of 3), then the others are either 3m – 2, 3m – 1; 3m – 1, 3m + 1; or 3m +1, 3m + 2. In the first and third cases, the proposition is manifest, as (3m – 2) (3m – 1), and (3m + 1) (3m + 2), are each divisible by 2, and therefore their product into 3m is divisible by 6(= 1.2.3). In the second case the product is 3m (3rn – 1) (3m + 1), or 3m (9m? – 1), where 3 is a factor, and it is necessary to show that m (9m – 1) is divisible by 2; if m be even, the thing is proved; but if odd, then mis odd, 9m? is odd, and 9m' - 1 is even; hence, in this case also the proposition is true. It can similarly be proved that the product of four consecutive numbers is divisible by 24 (= 1.2.3.4), of five consecutive numbers by 120 (= 1.2.3. 4.5), and so on generally. These propositions form the basis for proof of many proper. ties of numbers, such as that the difference of the squares of any two odd numbers is

Numerais.

divisible by 8. The difference between a number and its cube is the product of three consecutive numbers, and is consequently (see above) always divisible by 6. Any prime number which, when divided by 4, leaves a remainder unity, is the sum of two square numbers: thus, 41 = 25 + 16 = 5 + 4°, 233 = 169 + 64 = 13° + 8, etc.

Besides these, there are a great many interesting properties of numbers which defy classification; such as, that the sum of the odd numbers beginning with unity is a square number (the square of the number of terms added), i.e., 1 + 3 + 5 =9=39, 1+ 3+5+7+9= 25 = 5*, etc.; and, the sum of the cubes of the natural numbers is the square of the sum of the numbers, i.e., 13 + 2 + 33 = 1+8+ 27 = 36 = (1 + 2 +3), 13 + 23 + 33 X 48 = 100 = (1 + 2 +3 +4)', etc...

We shall close this article with a few general remarks on numbers themselves. Numbers are divided into prime and composite-prime numbers being those which contain no factor greater than unity; composite numbers those which are the product of two (not reckoning unity) or more factors. The number of primes is unlimited, and so consequently are the others. The product of any number of consecutive numbers is even, as also are the squares of all even numbers; while the product of two odd numbers, or the squares of odd numbers, are odd. Every composite number can be put under the form of a product of powers of numbers; thus, 144 = 24 x 3%, or, generally, n = ap.69.c", where a, b, and care prime numbers, and the number of the divisors of such a composite number is equal to the product (p + 1)(a + 1)(r + 1), unity and the number itself being included. In the case of 144, the number of divisors would be (4 + 1)(2+1), or 5 X 3, or 15, which we find by trial to be the case. Perfect numbers are those which are equal to the sum of their divisors (the number itself being of course excepted); thus, 6 = 1 + 2 + 3, 28 = 1+ 2+4+7+ 14, and 496, are perfect numbers. Amicable numbers are pairs of numbers, either one of the pair being equal to the sum of the divisors of the other; thus, 220(= 1+ 2+4+5+ 10 +11 +20 + 22 + 44+ 55+ 110 = 284), and 284 (=1+2 +4 + 71 + 142 = 220), are amicable numbers. For other series of numbers see FIGURATE NUMBERS.

The most ancient writer on the theory of numbers was Diophantus, who flourished in the 3d c., and the subject received no further development till the time of Vieta and Fermat (the latter being the author of several celebrated theorems, a discussion of which, however, is quite unsuited to this work), who greatly extended it. Euler next added his quota, and was followed by Lagrange, Legendre, and Gauss, who in turn successfully applied themselves to the study of numbers, and brought the theory to its present state. Cauchy, Libri, aud Gill (in America) have also devoted themselves to it with success. The chief authorities down to the present century are Barlow's Theory of Num. bers (1811); Legendre's Essai sur la Théorie des Nombres (3d ed., Paris, 1830); and Gauss's Disquisitiones Arithmetice (Brunswick, 1801; Fr. translation, 1807); and for the latest discoveries, the transactions of the various learned societies may be cousulted.

NUMBERS, BOOK OF (LXX. Arithmoi; Heb. Bamidbar), the fourth book of the Pen. tateuch, consists of 36 chapters, embracing the history of the march of the Israelites through the desert, together with the special laws given during this period as complementary to the Sinaitic legislation. Beginning with the census of the people (whence the name of the book), and the assigning of the special places to each tribe with reference to the sanctuary, the whole people is classified, and the tribe of Levi specially singled out. Ordinances on the purity to be maintained in the camp, the functions of the priests, and a description of the passover, follow. The second portion of the book describes the journey from Sinai to the borders of Canaan, the miraculous sustenance of the people, their dissatisfaction and consequent rejection, together with various special laws respecting sacrifices, etc., and the episode of Korah. The third part embraces the first ten months of the fortieth year of the wandering-an epoch hurried over with remarkable swiftness by the historian. In quick succession, the renewed strife of the people with their leaders, the message to the king of Moab, the death of Aaron, the defeat of the king of Arad, the punishment of the people by serpents, the march from Hor to Pisga, and the victorious battle against the kings of Sihon and Og, are recounted, and the extraordinary episode of Balaam follows. The further wiles employed by the alarmed Moabites and Midianites to avert the threatening invasion, and their result, together with the second census, are narrated. Moses is warned of his death, and the vital question of his succession is settled. Further laws and ordinances respecting sacrifices and vows, the conquest of the Midianites, and the partition of the country east of the Jordan among certain tribes, a recapitulation of the encampments in the desert, a detailed specification of the manner in which the promised land should be divided after its conquest, and the final ordinance of the marriages of heiresses among their own tribe only, so as to preserve the integrity of landed property, make up the remainder of the book.

The book of Numbers is, like the rest of the Pentateuch, supposed by the greater part of modern critics to consist of several documents written by Elohists and Jehovists respectively. See GENESIS, PENTATEUCH.

NU'MERALS, the general name given to figures or symbols by means of which numbers are expressed (for Roman and Greek numerals, see NoTATION); the distinctive name of Arabic numerals being given to the nine figures or digits and the zero that are now

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