CIRCUMCISION. 



CIRCUS. 



If the circulating part continued ad infnitnm be called S, it is plain 

 that 1000 S = 362 + S, or S=5^?, whence 



=--+ 



362 14x909 + 362 



100 99900 



Wallis ('Algebra/ ch. 89), Euler ('Algebra/ ch. 12, book i.), and 

 John Bernoulli the second (' Mem. Acad. Sci./ 1771), have treated this 

 subject We shall merely state some theorems to show the remark- 

 able character of the periods. 



1. Form the period of a prime number TO; its number of figures 

 will be either m 1 or one of its divisors. The period of 7 (being 



42857) has six figures; that of 13 (being 769230) has 6, the half of 

 13 1 figures. 



2. When the period of a prime number TO contains m 1 figures, 

 the last half may be formed from the first by taking each figure in the 

 first from 9. Thus the first and second halves of the period belonging 

 to 4" are- 

 First half 02127659574468085106382 



Second half 97872340425531914893617 



3. When the period of a prime number m has TO 1 figures, multi- 

 plication by any number under TO only changes the order of the 

 figures. Thus the period of 7 being 142857, we have here a number 

 which, being multiplied by 2, becomes 285714; by 3, 428571; by 

 4, 571428; by 5, 714285; and by 6, 857142: 



The following work may be useful to those who are curious on the 

 subject : ' A Table of the Circles arising from the division of a Unit, 

 fir any other whole number, by all the integers from 1 to 1024, being 

 all the pure decimal quotients that can arise from this source.' London, 

 Richardson, 1823. 



CIRCUMCISION, the operation of cutting off the prepuce or fore- 

 skin, is sometimes performed for a medical purpose ; but it is general 

 or universal among some nations as a religious rite, and among others 

 as a national custom. The practice of circumcision appears to be of 

 the highest antiquity. Abraham, as recorded in Genesis (xvii. 10-14), 

 by the command of God, circumcised himself and all the males of his 

 household; though circumcision is not there mentioned as being a 

 novelty, nor are any directions there given for the manner of per- 

 forming the ceremony. Abraham himself was ninety-nine years old 

 (Gen. xvii. 24) when he was circumcised. The rite of circumcision was 

 ordained to be an everlasting covenant between God and the seed of 

 Abraham ; and it was declared that " the uncircumcised man-child 

 whose flesh of his foreskin is uncircumcised/ that soul shall be cut off 

 from his people ; he hath broken my covenant." All the males that 

 left Egypt were circumcised, but during the forty years' wandering in 

 the wilderness the rite was not performed. Joshua, by the express 

 command of God, renewed it by circumcising all the males just after 

 the passage of the Jordan. (Joshua v.) Ever since the circumcision by 

 Joshua, it has been universally observed, both among the Jews and the 

 Ishmaelitish descendants of Abraham. Circumcision is not, properly 

 speaking, a rite of the Mohammedan religion ; it is not enjoined in the 

 Koran, but the Arabs, and Mohammed himself, were circumcised 

 before the religion of the Koran began to be preached, and their 

 descendants have continued the usage as one which had always pre- 

 vailed among them, arid have also communicated it to the Saracens, 

 the Turks, and the other nations who have become associated with 

 them in a common faith. In point of fact, circumcision is as universal 

 among the Mohammedans as it is among the Jews. 



A great deal has been written, both on the ceremonial of the Jewish 

 circumcision, and on the question as to the sacramentary efficacy which 

 has been sometimes attributed to the rite. On these matters the 

 reader may consult Burder's ' Oriental Literature/ Calmet's ' Diction- 

 ary of the Bible/ Simon's ' Dictionary of the Bible/ and especially 

 the able dissertation on circumcision in Michaelis's ' Commentaries on 

 the Laws of Moses,' book iv. chap. iii. part i., the English translation 

 by Dr. Smith, 4 vols. 8vo, 1814, and the authorities there referred to. 

 Michaelis is decidedly of opinion that circumcision was never intended 

 aa a sacrament. Among the ancient Jews, not only all proselytes were 

 circumcised, but also all bondmen or slaves, and their children. (Gen. 

 vii. 12, 13.) 



The prevalence of circumcision among various ancient nations is 

 mentioned by Herodotus (ii. 36, 37, 104), by Diodorus Siculus (i. 26 

 and 55, iii. 32), and others. Herodotus says that the Colchi, the 

 Egyptians, and the Ethiopians, were the only nations who had prac- 

 tised the custom from time immemorial, and that the Phoenicians and 

 the Syrians of Palestine (the Jews) admitted that they had acquired the 

 custom from the Egyptians. This notion, that the Jews had learned 

 circumcision from the Egyptians, has been taken up and maintained 

 in modern times by Sir John Marsham in his ' Chronicus Canon 

 yKgyptiacus/ by Jahn, and others. (See De Pauw's ' Recherches Philo- 

 pophiquea sur les Americains.') But supposing this opinion to be false, 

 it does not follow, on the other hand, as has been contended by some, 

 that all other nations among whom the custom prevails must have 

 derived it from the Jews. It has been supposed by some critics (but 

 in our opinion without good reason), that among the ancient Egyptians 

 it was only the priests, and those who desired to study the sciences of 



which they were the teachers, who were obliged to be circumcised. 

 See the notes of Wesseling and Larcher on the passages of Herodotus 

 above referred to, the Commentary of Origen on the ' Epistle to the 

 Romans/ ch. ii. v. 13, and a curious note of M. Huet on Origen's Com- 

 mentary on Genesis. (Origenis Opera, a Car. de la Hue, 4 vols. fol., 

 Par., 1733, &c., vol. ii.) It is said that Pythagoras submitted to the 

 operation of circumcision in order to obtain instruction in the secret 

 doctrines of the Egyptian priests. 



Strabo (book xvii. 824) says by mistake that the Jews practised 

 excision on their female children ; but, although this never 'was a 

 custom of the Jews, it has prevailed, and still does, among other 

 nations, particularly the Abyssinians, Nubians, and the modem 



seems to have extended from south to north, and to have included 

 Ethiopia, Egypt, Judcca, Phoenicia, Syria, Cappadocia, the Macrones, 

 and the Colchians. 



It is remarkable that circumcision has been found to prevail, and in 

 some cases the excision of females also, among various savage or imper- 

 fectly civilised races. It is said that the rite was practised by the 

 Mexicans when the Spaniards first became acquainted with them. 

 Cook found an imperfect species of circumcision, consisting of the 

 splitting of the prepuce, in use among the natives of the Friendly 

 Islands. (Kerr's ' Voyages/ vol. xiii.) Long before, many of the old 

 voyagers had met with it among the islands of the Indian Archipelago, 

 among the tribes of the west coast of Africa, and elsewhere. In 

 Purchas's ' Collection/ Edmund Scot gives a long account of the cere- 

 monial of the circumcision of the king of Bantam in Java, at which he 

 was present, in 1605. Captain William Keeling, in 1608, states that 

 he found the people at the bay of St. Augustine, on the west coast of 

 Africa, circumcised ; and Captain Richard Jobson describes the cere- 

 mony, as he witnessed it at Batto, on the same coast, in 1621. An 

 abstract of these and other early accounts may be found in Prevost's 

 ' Histoire Ge'ne'rale des Voyages.' See the same work for a description 

 of the ceremony of circumcision as practised among the people of 

 Madagascar. Dampier, in his graphic manner, describes the mode of 

 circumcision as he witnessed it performed in 1686 at the Philippine 

 Islands. (' Voyages.') An account of what he calls the circumcision of 

 females as well as of males by some of the African tribes, is given by 

 Bosnian, in his ' Description of the Coast of Guinea/ English trans- 

 lation ; and it has been more recently ascertained to have long existed 

 among some of the Indians in South America, among the inhabitants 

 of Tahiti, and those of the Fiji islands. The principal distinction 

 between circumcision as practised by the Jews and by other nations, is 

 that the former, in obedience to the terms of the command given 

 to Abraham, always when it is practicable circumcise the child on 

 the eighth day after its birth ; whereas, among other nations it is 

 usually deferred to a much later period. Among the Mohammedans it 

 is commonly performed in the thirteenth year, because Ishmael, the 

 progenitor of the Arabs, was of that age when he underwent the 

 operation. (Gen. xvii. 25.) By some it has been contended that this 

 operation has been adopted from a notion that it was conducive to 

 health in hot climates. 



Kolben, in his ' Present State of the Cape of Good Hope ' (trans- 

 lated by Medley), gives an account of a very singular custom of the 

 Hottentots, which he conjectures 'may have been derived from the 

 Jewish circumcision ; and see Winer's ' Biblisches Realwbrterbuch/ 

 article ' Beschneidung/ Leipzig, 1847. 



CIRCUMFERENCE (eircum and fero), the line which goes round a 

 figure. We do not know why, but this word is always applied to a 

 curvilinear figure ; while the synonymous Greek word periphery (irepl, 

 tpfpto) is used for a rectilinear figure. 



CIRCUMFERENTOR. This instrument is a species of surveying- 

 compass, and its construction may be understood from a view of the 

 diagram in the article SPIRIT LEVEL, since, if the reader will imagine 

 the telescope of that instrument to be removed, and, for the supports, 

 called Y.s, sight- vanes or perforated plates to be substituted, the instru- 

 ment will be a complete circumferentor. 



Such an instrument being far inferior to a theodolite in respect 

 of the accuracy with which by its means a survey may be made, is not 

 much used in Europe ; but in the United States of America and in the 

 British colonies, where land is less valuable, it is, or was till lately, 

 almost the only instrument employed. 



In using the circumferentor for the survey of a line of road, or the 

 determination of the boundary of a tract of land, the instrument is set 

 up, on its stand, successively at the principal bends of the road or 

 boundary line ; and a staff being held up vertically at the next bend 

 which is visible from the place of the instrument, the sights of the 

 latter are directed to it ; then the bearing of each station-line from the 

 needle in the compass-box, that is, from the magnetic meridian, is ob- 

 served. Each station-line is measured by the chain, and the smaller 

 bends of the road or boundary are determined by " offsets " measured 

 perpendicularly to that line. [COMPASS, AZIMUTH ; SURVEYING.] 



CIRCUMFLEX. [ACCENT.] 



CIRCUS, a large enclosed space, adapted for chariot-races, an amuse- 

 ment to which the Romans were passionately attached. The name 

 Circus (of which circulus, a circle, is a diminutive) does not convey an 



