NUKHA 



NUMBERS 



547 



cause unnecessary disturbance or destruction of pro- 

 perty. Where th'e nuisance is public an indictment 

 will lie. If a highway, for instance, is in a danger- 

 ous state for want of repair, an indictment lies 

 against the parties who are bound to repair it ; but 

 if an individual has suffered special damage, over 

 and above what he suffers as one of the public, he 

 may bring an action. These legal remedies are now 

 reinforced by the extensive powers conferred on 

 local authorities. The acts passed for the removal 

 of nuisances are now consolidated in the Public 

 Health Act, 1875. Sanitary authorities ( the guar- 

 dians in rural districts, and the council or local 

 board in towns) are empowered to appoint in- 

 spectors and medical officers, and to take measures 

 for the removal of nuisances. The act contains an 

 elaborate code of rules in regard to sewers, privies, 

 ditches, gas-works, cellars, common lodging-nouses, 

 offensive trades, sale of unsound meat, infectious 

 and epidemic diseases, &c. Bylaws may be made 

 by the local authority in regard to these matters ; 

 such bylaws require to be confirmed by the Local 

 Government Board. Besides the provisions of 

 the Public Health Act, which are too volumin- 

 ous to be even summarised within our present 

 limits, there are other acts whicli empower local 

 authorities to deal with alkali-works, chimneys 

 emitting black smoke, and other forms of nuis- 

 ance. The Kivers Pollution Act, 1876, was in- 

 tended to prevent the fouling of streams. Special 

 acts have been passed for the metropolitan district 

 and for the river Thames ; and the local acts which 

 have been obtained by town-councils and other 

 public bodies make numerous additions to the 

 already complicated rules of the general law. For 

 the enactments in regard to the suppression of 

 brothels, see PROSTITUTION. 



In Scotland the remedies provided in cases of 

 nuisance are sultstantially the same as in England ; 

 and the Public Health Act of 1867 consolidates 

 the statutory powers of local authorities. As to 

 Ireland, see 'the Public Health Act of 1878. The 

 United States law closely follows the English law ; 

 in the legislation of some states the term is used 

 in a narrower sense to denote houses of ill-fame, 

 &c. The powers of municipal authorities are de- 

 fined by the law of the state to which they belong. 



\uklia. a town of Russian Transcaucasia, in 

 Elizabethpol ; it is on the southern slope of Cau- 

 casus, and 120 miles E. of Tiflis. Pop. 24,994. 



Nullification, in the history of the United 

 States, refers especially to the action of the legis- 

 lature of .South Carolina in 1832, declaring certain 

 acts of congress unconstitutional and therefore 

 null and void. In 1828 congress passed what 

 became known as the ' tariff of abominations,' 

 whicli discriminated unfairly against the people of 

 the southern states. There cotton was the staple 

 product, and any step tending to impose restric- 

 tions on the commercial intercourse with Europe, 

 where its principal markets lay, was bitterly 

 opposed ; whereas in the north, with its manufac- 

 turing interests, a protectionist policy had steadily 

 grown in favour. In 1832 congress readjusted the 

 tariff, modifying some of the objectionable features, 

 but still leaving the southerners unjustly treated. 

 In November a state convention in South Carolina 

 passed an ordinance nullifying the tariff of 1828 

 and 1832, and declaring their right and intention, 

 in the event of any attempt at coercion, to with- 

 draw from the Union and organise a separate 

 government. In December President Jackson 

 (q.v.) issued a vigorous proclamation against the 

 ordinance, and the governor of South Carolina 

 replied with a counter-proclamation, and volun- 

 teers, in addition to the state militia, were organ- 

 iaed to resist the national government. But in 



February 1833 Clay, the 'great pacificator,' intro- 

 duced a Compromise Bill, providing for the gradual 

 reduction by the year 1842 of all higher duties to 

 20 per cent. ; congress passed this on March 2, and 

 on March 15 the South Carolina convention re- 

 pealed the ordinance of nullification and secession. 

 See CALHOUJJ ; and for the whole question out of 

 which this movement grew, see STATES' RIGHTS. 



Nlllliailtia. the chief town of the Celtiberian 

 people called Arevaci, in Hispania Tarraconensis, 

 was situated on a steep hill on the During (Douro), 

 in the neighliourhood of the present Soria in Old 

 Castile. The site is probably marked by the 

 present Puente de Guarray. Numantia is cele- 

 brated for the heroic resistance which it made to 

 the Romans. After a siege of fifteen months, in 

 the course of which famine and the sword had left 

 alive very few of its 8000 brave defenders, it was 

 taken and destroyed by Scipio the younger, 134 B.C. 

 Scipio's army numbered no fewer than 60,000 men. 



\llllia PompilillS, in the legendary history 

 of Rome, its second king, the successor of Romulus. 

 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 

 a.-sirttance of the nymph Egeria, who gave him 

 interviews in a grove near the city, 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 

 thirty-nine years, and was a golden age of peace 

 and happiness. 



Numbers. See PEXTATEUCH, BIBLE, APOCA- 

 LYPTIC NUMBER. 



Numbers. THEORY OF, the most subtle and) 

 intricate, and at the same time one of the most 

 extensive branches of mathematical analysis. Ik 

 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 branchi 

 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 of 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, &c. (2) find three square 

 numbers in arithmetical progression ; Answer, 1, 25, 

 and 49 ; 4, 100, 196, &c. 



Forms of Numbers are certain algebraic formulas, 

 which, by assigning to the letters successive 

 numerical values from upwards, are capable of 

 producing all numbers without exception e.g. by 

 giving to m the successive values 0, 1,2, 3, &c., 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 2? be 

 one number, then the other is either 2m -I- 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 



