SERASKIER 



SERIES 



321 



with many of the attributes of Osiris. The worship 

 of Serapis, introduced into Egypt by the Ptolemies, 

 subsequently became greatly extended in Asia 

 Minor; and'liis image, in alliance with that of Isis 

 and other deities, appears on many of the coins of 

 the imperial days of Rome. In 146 A. D. the worship 

 of the god was introduced into the city of Rome 

 by Antoninus Pius ; but it was not long after 

 abolished by the senate, on account of its licen- 

 tious character. A celebrated temple of Serapis 

 also existed at Puteoli (see PozzuOLl), near 

 Naples, and the remains of it are still seen. In 

 Egypt itself the worship of the deity subsisted 

 till the fall of paganism, the image at Alexandria 

 continuing to ne worshipped till destroyed, 398 

 A.D., by Theophiliis, archbishop of that city. 

 Busts of Serapis are found in most museums, and 

 his head or figure engraved on certain stones was 

 supposed to possess particular mystic virtues. 



Seraskier, the name given by the Turks to 

 the commander-in-chief of the army or to the 

 minister of war. 



Serbs. See SERVIA. 



Serenade (Ital. serenata), originally music 

 performed in a calm night ; hence an entertain- 

 ment of music given by a lover to his mistress 

 under her window especially in Spain and Italy. 

 A piece of music characterised by the soft repose 

 which is supposed to be in harmony with the still- 

 ness of ni^'ht is sometimes called a serenade, more 

 usually a Nocturne (see Music, Vol. VII. p. 358). 



Sereth, an affluent of the Danube, rises in the 

 south of the Austrian crown-land of Galicia, runs 

 southward through almost the whole length of 

 Moldavia, and joins the Danube just above Galatz, 

 after a course of nearly 300 miles. 



Serf (Lat. tervut, 'a slave'), the term usually 

 given to the villeins of mediaeval Europe, and 

 to the unfree peasants of Russia. The serf was 

 distinguished in a general way from the slave by 

 beinfj attached to the land and having certain 

 definite rights, whereas the slave was the absolute 

 chattel of his master. But serfdom falls to be 

 treated as part of the subject of Slavery (q.v.). 



Serge, a kind of twilled worsted cloth which 

 has a wide range of quality, strength, and thick- 

 ness. The surface of the fabric is not smooth like 

 that of a milled woollen cloth. Serges are gener- 

 ally dyed a dark blue or black, and good qualities 

 are very durable. Clothes made of serge have 

 been much worn both by men and women of late 

 years. 



Sergeants, or SERJEANTS (through the Fr., 

 from Eat. servient, 'serving'), are non-commis- 

 sioned officers of the army and marines in the 

 grade next above corporal. They overlook the 

 soldiers in barracks, and assist the officers in all 

 ways in the field. They also command small 

 liodiea of men as guards, escorts, &c. The daily 

 pay of a sergeant varies from 2s. 4d. in the infantry 

 to 3s. 4d. in the horse artillery (see also NON- 

 COMMISSIONED OFFICERS). There are three ser- 

 geants and one colour-sergeant in each company 

 of infantry. Each troop of line cavalry has also 

 three sergeants and one troop sergeant-major. In 

 the Household Cavalry the corresponding non-com- 

 missioned officers are called corporals of horse (four 

 per troop) and troop corporal -major. In the Royal 

 Horse Artillery there are six sergeants per battery 

 and one battery sergeant-major, whose pay is 

 4s. 4d. per day. A regimental sergeant-major is 

 a warrant officer on the staff of a battalion of 

 infantry, regiment of cavalry, or corresponding 

 body of troops. The daily rate of pay vanes from 

 6. in the horse artillery to 5s. in the infantry. 

 Unlike the sergeants, the sergeant-major does not 

 437 



command any particular portion of the corps, but 

 generally superintends the whole of it, and in 

 respect of discipline, &c. is the assistant of the 

 adjutant. There is a separate article on COLOUR- 

 SERGEANT. For the Quartermaster-sergeant, see 

 QUARTERMASTER ; for Sergeant-drummer and Ser- 

 geant-trumpeter, see BAND. In ancient times the 

 rank of sergeant was considerably more exalted. 

 In the 12th century the sergeants were gentlemen 

 of less than knightly rank, serving on horseback. 

 Later the sergeants-at-arms were the royal body- 

 guard of gentlemen armed cap-a-pie. 



Sergeanty. See GRAND SERGEANTY. 



Sergipe, a maritime state of Brazil, the 

 smallest in the republic, but the second in density 

 of population (31 per square mile), is bounded on 

 the N. by the Sao Francisco, which separates it 

 from Alagoas, and on the W. and S. by Bahia. 

 Area, 7370 so. m. ; pop. ( 1890) 461,307. The shores 

 are low and sandy, the interior mountainous. 

 The east part is fertile, well wooded, and produces 

 sugar and cotton ; the western plateaus are devoted 

 principally to the rearing of cattle. The capital is 

 Aracajii, with a small port and 5000 inhabitants. 



Sericite. See MICA. 



Series, in Algebra, is the sum of a set of terms 

 formed according to some definite law. For 

 example, let n be any integer, and <p(n) a definite 

 function of n. Then, by giving n the successive 

 values 1, 2, 3, &c., and forming the corresponding 

 functions <p( 1 ), 0(2), &c., we are able to construct 

 the series S = ^(1 ) + ^(2) + . , . + <p(m), where 

 m is the highest value of n that is to be involved. 

 If 41(11) is simply a multiple of n, we get an 

 Arithmetical Progression (q.v.), viz. a + 2o + 3a 

 + . . . Again, if <f>( n) is of the form a*, we get a 

 Geometrical Progression ( q. v. ), viz. o + a 2 + a 3 + . . . 

 These simplest cases of series are considered under 

 their special headings, and shall not be again 

 referred to except by way of illustration. 



It is evident that if a finite number of terms be 

 taken, and if no term has an infinite value, the 

 series itself will have a finite and determinate 

 value. We may suppose, however, that no limit 

 is to be assigned to tne number of terms that are 

 to be taken in other words, that the highest value 

 (m) of n is to be larger than any assignable 

 quantity. We thus get a series with an infinite 

 number of terms. But it does not follow that such 

 an Infinite Series, as it is called, has necessarily 

 an infinite value. Consider, for example, the 

 Geometrical Series 1 + J + J + J + ?, + . . . to in- 

 finity. Draw a line ABC equal in length to two 



units. AB ( = 1 ) will represent the first term of 

 the series ; the second term may be represented 

 by BD, the half of BC ; the third bj DE, the half 

 of DC ; and so on indefinitely. It is evident that, 

 however far we may go, we shall always fall 

 short of C by an amount equal to the last bit 

 added on. Thus 



But by taking n large enough we may make 1/2" as 

 small as we please. Hence the value of the Infinite 

 Series is 2. 



It will be seen that the terms in this series 

 approach zero indefinitely, while the sum ap- 

 proaches a definite limit. Any series in which 

 the latter condition is satisfied is called a Con- 

 vergent Series. In all convergent series the former 

 condition just stated must also be satisfied. But 

 it does not follow that a series whose successive 

 terms approach zero indefinitely is necessarily con- 

 vergent. For example, the series 1 + 4 + 4 + i + 



