ether. It melts at 210°, and yields salts, most of which crystallize well. Several derivatives of this acid containing ethyl or methyl have been obtained, as also chloro, bromo, iodo, nitro, and amido derivatives. (Saytzeff, Ann. Chem. Pharm. exxvii. 129; Barth, Wien Akad. Ber. liv. [2] 633; Jour. Pr. Chem. c. 366; Graebe, Ann. Chem. Pharm. cxxxix. 134; Ladenburg, do. cxli. 241; Ladenburg and Fritz, do. 247; Beilstein and Kuhlberg, Zeits. Chem. v. 461, and Chem. Centr. 1870, 46; Peltzer, Ann. Chem. Pharm. cxlvi. 284; Zeits. Chem. v. 225.) PARAPH, the flourish after a signature. During the middle ages the paraph was the form of attestation of documents by notaries and other legal functionaries, and in some parts of Europe, as in Spain and at the French Palais de Justice, it is still a necessary legal formulary. Paraph is sometimes used as the designation for the mark or flourish at the bottom of a page or end of a line to prevent the introduction of additional words. 24 14 PARAPICOLINE, C12H1N2 (C22,H1N2), an oily base, isomeric with picoline, obtained by boiling the latter with metallic sodium. It has a density of 1077 and boils at about 300°. Most of its salts are uncrystallizable. (Anderson, Ann. Chem. Pharm. lx. 86.) PARATHIONIC ACID. The baric salt of this acid was obtained by Gerhardt on boiling a solution of baric ethylsulphate. It has since been proved to be identical with ethylsulphuric acid, and not merely isomeric. (Erlenmeyer, Ann. Chem. Pharm. clxii. 373; Scheibler, Deut. Chem. Ges. Ber. v. 446.) PARATOLUIDINE [TOLUIDINE, E. C. S.]. PARIAN, unglazed porcelain for statuettes and other delicate work, is sometimes called statuary biscuit. It was introduced about the year 1845 by Messrs. Minton, and has been brought to great perfection by them, Mr. Battam, Messrs. Copeland, and other firms. Cornish clay and Swedish or American felspar are the chief ingredients employed. When finely ground and mixed, the parian composition is cast in plaster moulds, and then subjected to other processes to produce a smooth surface. The firing is a very important part of the operation; and diversities in the management of it give rise to the differences between English and foreign parian, the former presenting a warm creamy tint, while much of the latter has a colder bluish tint. case at of baptisms with the names of the sponsors in every instance, The English use of parochial registers naturally commenced with the changed ideas in connection with religion. The monasteries had hitherto been the principal repositories of such registers, if indeed the irregular manner in which they occasionally noted down the birth, marriage, or death of any notable personage in their monastic registers or lieger-books may be so termed. How succession to patrimony was managed in disputed cases in the early medieval times is difficult to conceive; it was in all probability settled by the king's escheator, who on the death of any landholder held an inquiry, termed an "Inquisitio post mortem," to arrange the "relevium," or tax due to the king from the heir. Before such an heir could succeed he was bound to perform homage and pay the tax, he then received livery of his inheritance; but if he was a minor, or an attainder of treason, or felony had been suffered by the last tenant, the heir lost his inheritance; or, in the former case, waited until he attained his majority and made proof of his age. This inquiry, the records of which remain in tolerable numbers and afford valuable and interesting information connected with pedigrees and genealogical researches, was carried out by a responsible jury summoned to assist the escheator, and a transcript of the proceedings was sent into the exchequer. Four folio volumes of these returns, abridged, have been published by the Public Record Commissioners, and range over the period between 3 Henry III. or 1219, and 20 Charles I. or 1645. In 1538, Thomas Cromwell, afterwards Earl of Essex, and Vicar-general, issued a mandate for the keeping of registers of baptisms, marriages, and burials in each parish. He had probably become alive to the political value attaching to such records during his residence in the Spanish Netherlands. PARING AND BURNING. Improvements in the manufacture of artificial manure and in the management of grass lands render this old popular practice less needful than formerly. If grass lands are properly drained and aerated, and a suitable supply of manure from time to time applied, the meadows and pastures will increase in fertility. Some increase with very little manure; others require a much larger quantity. But if neglected in drainage, aeration, and manure, the finer grasses die out and are replaced by the coarser ones, generally stolo-to this protestation-"I shall keepe the register booke according niferous. Vegetable matter accumulates, which ultimately becomes effete, when paring and burning become necessary to get rid of it. Sandy and peaty soils require large dressings of clay and lime to keep them profitably in permanent pasture. At one time it was thought that paring and burning destroyed insects, but this is more than doubtful, for it is now known that they are led by instinct to take up their winter quarters deep in the earth, at a safe distance below the effects of frost. Burning the surface sod may, however, deprive them of food when they rise to the surface, and thus starve them. The spread ashes are also destructive of insect life. By such means farmers may get rid of insects, but the process of burning the sods kills very few. Most artificial manures are destructive of insect life, and when grass lands are kept in the highest state of fertility by them, it is seldom that insects do much harm. As certain parasites only multiply on the body of the ox or horse, when the skin is in a dirty, unhealthy state, so something abnormal must be the matter with the swards of grass before insects will increase so as to do harm; and prevention by manure, drainage, and aeration will be found a safer cure than to kill by paring and burning. PARISH REGISTERS. The idea of keeping a record of births and deaths is by no means modern. Athens and Rome, from a very remote period in either case, kept such a public census, the one dating from the constitutions of Solon, the other from the semi-historical period of Servius Tullius; Ovid and Juvenal mention a very similar sort of registration, by them called "Libri actorum." But it was not until A.D. 1497 that parochial registers, in the modern acceptation of the word, began to be used in England, having been originally introduced on the continent by Cardinal Ximenes, who to remedy the then increasing evils of easy divorces, directed each parish to keep a list Although of late years they were regarded as an appendage of the state church rather than a beneficial institution, and so naturally suggested the principle of civil registration, in their early days no such objection was ever made to them. In the reign of Queen Elizabeth, among other ceremonies attaching to ecclesiastical institution, the minister was ordered to subscribe to the queene's majesties injunction." Consequent upon the irregularity which had crept in upon the proper keeping of such documents, a constitution of the province of Canterbury, 25th October, 1597, required the register book to be purchased by the parish, correct transcripts to be made into vellum books, each page to be certified correct by the incumbent and churchwardens, and such copies to be sent about Easter time to the registrar of the respective dioceses, that they might find a safe depository among the episcopal archives. The seventieth ecclesiastical canon of 1603 confirmed these regulations, and it has never been repealed, although it is not perhaps a matter of astonishment that disobedience of it has resulted in so many cases when we consider that the registration, transcription, and custody of these books entailed an unremunerative task upon so many individuals. The vellum register of Loughborough contains a notice under the date 1601 to the effect that John Dawson, master of the grammar school, at the age of seventy-one, made the copy from the old paper books. Many of the copies are known to have been abbreviated, by a careful collation with the originals. The custom of signing each page of the copy gave rise to ludicrous statements respecting the longevity of the clergymen of the 16th century. Duncombe, in his History of Herefordshire,' asserts that the vicar of Bromyard held his living for eighty-two years, and one of his churchwardens sixtyfour years, an error arising from the signatures appended to a transcript. Another example relates that the same person held the living of Keyham, in Leicestershire, for ninety-two years, being served by the same churchwardens for seventy years. The civil wars involved parish registers in the general confusion experienced by the Church; most parishes are deficient in regularity of their registration during the Commonwealth, the duty being commonly taken from the clergyman and deputed to some village tradesman. In 1644 the House of Commons referred the subject to the committee in charge of the "Directory for Public Worship," who, in the early days of the following year, among other changes, ordained that "a fair register book of velim should be provided by every parish, kept by the officiating minister, and shewn to all searchers." Entries of all births, baptisms, marriages, and burials were to be made. The registers themselves of this period contain remarkable notices of the confusion experienced in matters of church discipline; as for example that of Rotheby, co. Leic., "1643, bellum!; 1644, bellum!; 1645, bellum!, interruption!, persecution!, Seques"-that of St. Bridget's, Chester, "1643-1653 register defective, the tymes were such"-that of Everley, co. Wilts, records, under 1660, that William Eastman, a tinker, held the rectory for five years before he was driven out. tration! PARLIAMENT. 16:0 Sarcasm, libel, and malice glitter in many of the pages of these registers; epithets, such as:-"Old Virgin," Queen of Hell," "insipiens," "Redshanks," "Vagabonds, commonly called Egyptians, or "going after the manner of roguish Egyptians," are of constant occurrence. Many notices of executions, witch trials, plagues and pestilences, whippings, duckings, with the 'cukkinge stolle,' may be noticed, as also a remarkable formula mentioned by Waters for the reconciliation of a man with his wife, when by reason of his long absence she had taken another husband. (Sims, Manual; R. E. C. Waters, Parish Registers, reprinted with additions from the Home and Foreign Review, 1870; J. S. Burn, History of Parish Registers, 1862; Report of Com. of the H. of C. on Parochial Registration; Bigland, Observations on Parish Registers, 1764; from which books, as well as various county histories, Gentleman's Magazine, and Notes and Queries, much additional information may be acquired. For those in the British Museum see the New Classed Catalogue of Manuscripts, Biography, vol. i.) 38 64 Forsaken filius meretricis, scape begotten, filius scorti, Fliefornication the base son of C. Andrews, filia adulterina, a byeblow, a merry begot, lovebegot; to these may be added the term nothus, which occurs three or four times in the original register of Alderbury, co. Wilts, in the British Musuem, and the common expression 'a love-child.' Foundlings were usually designated by a name expressive of the circumstances or place of their discovery, such as:-Nameless, Godsend, Relictus, Subpoena, Mary Porch; and other names derived from the patron saint of their respective parishes :-Clement for those of St. Clement Danes, Temple for those found in the Temple; hence the appellation of Friday given to the new-found slave of Robinson Crusoe is by no means a forced instance, and Dickens's account of the circumstances attending the naming of Oliver Twist, is perfectly compatible with facts of constant occurrence. Registrars were appointed by act of parliament in 1653 to be The adoption of two or more Christian names, instead of the chosen from among the parishioners; they held office for three old practice which limited the name to one, appears to be of years and were allowed to charge a small fee for entries. In comparatively modern origin; and although rare instances 1695 a tax upon marriages, &c., was levied, and every clergy-occur, it does not seem to have become general until the reign man was bound to keep a register under penalty of a hundred of George III. pounds. In 1711, in consequence of the daily increase of clandestine marriages [FLEET MARRIAGES, E. C. S. col. 1016] further stringent rules were enforced respecting the proper keeping of the parish registers; other enactments were passed in 1781, and in 1812, tending to perfect the information to be afforded by these records; but fire, damp, and theft have at various periods contributed to the gradual destruction, or, at least, mutilation of a series of archives, which in their entirety would have formed a valuable index to the state of the population and the genealogies of the people at large. Many parishes have no early registers, few have them earlier than the reign of Elizabeth, and registers themselves vary very much in the information they afford. Mr. R. Sims, in his invaluable work, entitled 'A Manual for the Genealogist,' &c., has given a detailed list of "Transcripts of Parochial Registers in the Archives of the several bishops;" "Catalogues of Parochial Registers," compiled from the collections in the College of Arms, the British Museum, Society of Antiquaries, as well as those mentioned or abridged in Nichols' "Collectanea" and "Topographer;" an account of "Marriage Dispensations of Licenses," as well as great store of information respecting non-parochial registration [REGISTERS, E. C. S.]. In the British Museum is a very complete series of papers descriptive of the State of all Parochial Register-books extant in 1831. (Add. MS. 9355-9360.) As examples of the curious and interesting information to be acquired from these popular archives we may examine the list of Puritan names, such as Repente Kytchens, Freegift Mabbe, Restore Weeks, Constant Semar, Faintnot Kennard, which contrast with the names of the famous Sussex jury (Sussex Archæologia, xiv. 246) who rejoiced in the Christian names of Accepted, Redeemed, Makepeace, GodReward, Kill-Sin, Fight-the-good-Fight-of-Faith, More-Fruit, Weep-not, &c. We may also derive some knowledge of the working of the statute which, in 1666, was passed for "burying in woollen," with the object of protecting and encouraging the woollen manufactures. An affidavit was required from one of the mourners that the deceased had not been "put in, wrapt up, or wound up, or buried, in any shirt, shift, sheet, or shroud, made or mingled with flax, hemp, silk, hair, gold, or silver, or other than what is made with sheep's wool only, or in any coffin lined or faced with any cloth, &c." This was afterwards commuted into a penalty or tax, and gradually falling into disuse was finally repealed in 1814 (54 Geo. III. c. 108). Sometimes, to save the tax, which had been imposed in 1695, the person who kept the register put down no names for years. This practice fell away with the repeal of the tax in 1836. From the baptismal registers many interesting items may be gleaned, as in addition to the name and parentage of the child, other items have been occasionally added by the humour or caprice of the registrar; such as astrological signs, names of obsolete professions and trades :-Virginall-master, spurrer, comfit-maker, French-hood-maker, wood-monger, bowyer, fletcher, furbisher. Waters has given, in addition, notices of the "Creaturæ Christi," ""children of God," or "creatures," a term constantly applied to those who survived just long enough to be baptized; and of the "chrysoms," who died within a month of their birth. This term derived its name from the chrisom of white cloth placed upon the head when the baptismal ceremony was performed. The same writer has collected the terms employed to denote illegitimate children, some of which, as well as the actual names appropriated to them, are by no means complimentary, such as:-incerti patris, filia vulgi, filius terra, ARTS AND SCI. DIV.-SUP. PARISTYPHNIN, [CgHoO18? (C76H61036 ?), a bitter uncrystallizable substance contained along with paridin in Paris quadrifolia. By boiling with water, it is resolved into glucose and paridin [E. C. vol. vi. col. 297]. (Walz, N. Jahr. Pharm. xiii. 353.) PARLIAMENT. [COMMONS, HOUSE OF, E. C. vol. iii. col. 86; E. C. S. col. 602; ELECTION OF MEMBERS, E. C. vol. iii. col. 780; E. C. S. col. 845; PARLIAMENT, IMPERIAL, E. C. vol. vi. col. 302.] Corrupt Practices at Elections. In the year 1868 the British Parliament, desirous of more effectually suppressing corrupt practices at elections, surrendered the power hitherto retained in the hands of the House of Commons of inquiring into and deciding both questions of law and fact in respect of controverted elections. By the 31 & 32 Vict. c. 125, the trial of election petitions is to be conducted before a puisne judge of one of Her Majesty's superior courts of common law at Westminster or Dublin, sitting in the borough or the county respectively, where the disputed election takes place, with power, however, to the judge, whenever it shall seem desirable, to change the venue to a more suitable place. The judge is to be judge both of the law and the fact, except where it is deemed desirable to reserve some question of law, and in that case the said question is to be referred to the Court of Common Pleas. At the conclusion of the trial the presiding judge is to determine whether the member, whose return or election is complained of, or any and what other person was duly returned or elected, or whether the election was void,. and is forthwith to certify in writing such determination to the Speaker of the House of Commons; and upon such certificate being given, his determination is final to all intents and purposes. Where any charge is made in an election petition of any corrupt practice having been committed at the election to which the petition refers, the judge shall, in addition to such certificate and at the same time, report in writing to the Speaker as follows: - (a.) Whether any corrupt practice has or has not been proved to have been committed by or with the knowledge and consent of any candidate at such election, and the nature of such corrupt practice. (b.) The names of all persons, if any, who have been proved at the trial to have been guilty of any corrupt practice. 5 N (c.) Whether corrupt practices have, or whether there is reason to believe that corrupt practices have extensively prevailed at the election to which the petition relates, Such report of the judge is to be communicated by the Speaker to the House of Commons, and the House may make such order thereon, confirming or altering the return, or for the issue of a writ for a new election, or for referring the question of corrupt practices in the said borough or county to commissioners to be appointed, under the 15 & 16 Vict. c. 57, to inquire into the same, as to the House may seem fit. The petition against the return is to be presented to the Court of Common Pleas at Westminster or Dublin, as the case may be, and any elector or candidate may be such petitioner. Witnesses on the trial of such petition may, in addition to those produced on behalf of the parties, be summoned by the judge himself, if he think fit, and witnesses who have themselves been guilty of corrupt practices may, to serve the ends of justice, receive a certificate of indemnity under the hand of the judge. Where it is found, by the report of the judge upon an election petition under this Act, that bribery has been committed by or with the knowledge and consent of any candidate at an election, such candidate shall be deemed to have been personally guilty of bribery at such election, and his election, if he has been elected, shall be void, and he shall be incapable of being elected to and of sitting in the House of Commons during the seven years next after the date of his being found guilty; and he shall further be incapable during the said period of seven years(1.) Of being registered as a voter and voting at any election in the United Kingdom; and (2.) Of holding any office under the Act of the session of the fifth and sixth years of the reign of his Majesty King William the Fourth, chapter seventy-six, or of the session of the third and fourth years of the reign of her present Majesty, chapter one hundred and eight, or any municipal office; and (3.) Of holding any judicial office, and of being appointed and of acting as a justice of the peace. If on the trial of any election petition under this Act any candidate is proved to have personally engaged at the election to which such petition relates as a canvasser or agent for the management of the election, any person knowing that such person has within seven years previous to such engagement been found guilty of any corrupt practice by any competent legal tribunal, or been reported guilty of any corrupt practice by a committee of the House of Commons, or by the report of the judge upon an election petition under this Act, or by the report of commissioners appointed in pursuance of the Act of the session of the fifteenth and sixteenth years of the reign of her present Majesty, chapter fifty-seven, the election of such candidate shall be void. Any person, other than a candidate, found guilty of bribery in any proceeding in which after notice of the charge he has had an opportunity of being heard, shall, during the seven years next after the time at which he is so found guilty, be incapable of being elected to and sitting in Parliament; and also be incapable (1.) Of being registered as a voter and voting at any election in the United Kingdom; and (2.) Of holding any office under the Act of the session of the fifth and sixth years of the reign of his Majesty King William the Fourth, chapter seventy-six, or of the session of the third and fourth years of the reign of her present Majesty, chapter one hundred and eight, or any municipal office; and (3.) Of holding any judicial office, and of being appointed and of acting as a justice of the peace. The Act applies to England, Scotland, and Ireland, special provisions being introduced to adapt the practice under it to the Scotch Courts. the election there are no more candidates so nominated than vacancies, the returning officer is forthwith to declare such candidates elected; if otherwise, he is to adjourn the election and take a poll in the manner subscribed by the Act. A candidate may during the time appointed for the election, but not afterwards, withdraw from his candidature by giving a notice to that effect signed by him to the returning officer; or the proposer of a candidate nominated in his absence out of the United Kingdom may withdraw him upon a similar notice with a written declaration of such absence. In the case of a poll at an election, the votes are to be given by ballot. The ballot of each voter shall consist of a paper (in this Act called a ballot paper) showing the names and description of the candidates. Each ballot paper shall have a number printed on the back, and shall have attached a counterfoil with the same number printed on the face. At the time of voting, the ballot-paper shall be marked on both sides with an official mark, and delivered to the voter within the polling station, and the number of such voter on the register of voters shall be marked on the counterfoil, and the voter having secretly marked his vote on the paper, and folded it up so as to conceal his vote, shall place it in a closed box in the presence of the officer presiding at the polling station (in this Act called "the presiding officer "), after having shown to him the official mark on the back. Any ballot paper which has not on its back the official mark, or on which votes are given to more candidates than the voter is entitled to vote for, or on which anything, except the said number on the back, is written or marked by which the voter can be identified, shall be void and not counted. After the close of the poll the ballot boxes shall be sealed up, so as to prevent the introduction of additional ballot-papers, and shall be taken charge of by the returning officer, and that officer shall, in the presence of such agents, if any, of the candidates as may be in attendance, open the ballot boxes, and ascertain the result of the poll by counting the votes given to each candidate, and shall forthwith declare to be elected the candidates or candidate to whom the majority of votes have been given, and return their names to the Clerk of the Crown in Chancery. The decision of the returning officer as to any question arising in respect of any ballot paper shall be final, subject to reversal on petition questioning the election or return. Where an equality of votes is found to exist between any candidates at an election for a county or borough, and the addition of a vote would entitle any of such candidates to be declared elected, the returning officer, if a registered elector of such county or borough, may give such additional vote, but shall not in any other case be entitled to vote at an election for which he is returning officer. Offences at Elections. Every person who— (1.) Forges or fraudulently defaces or fraudulently destroys any nomination paper, or delivers to the returning officer any nomination paper, knowing the same to be forged; or (2.) Forges or counterfeits or fraudulently defaces or fraudulently destroys any ballot paper or the official mark on any ballot paper; or, (3.) Without due authority supplies any ballot paper to any person; or (4.) Fraudulently puts into any ballot box any paper other than the ballot paper which he is authorised by law to put in; or (5.) Fraudulently takes out of the polling station any ballot paper; or (6.) Without due authority, destroys, takes, opens, or otherwise interferes with any ballot box or packet of ballot papers then in use for the purposes of the election ; Shall be guilty of a misdemeanour, and be liable, if he is a returning officer or an officer or clerk in attendance at a polling station, to imprisonment for any term not exceeding two years, with or without hard labour, and if he is any other person, to imprisonment for any term not exceeding six months, with or without hard labour. Any attempt to commit any offence specified in this section shall be punishable in the manner in which the offence itself is Three additional judges to the superior courts of common law at Westminster were created in consequence of this statute for the purpose of more conveniently carrying it into effect. Election by Ballot. In 1872, the 35 & 36 Vict. c. 33, was passed to amend the law relating to procedure at Parliamentary and Municipal elections. By this statute a candidate for election to serve in Parliament for a county or borough is now to be nominated in writing. This writing, subscribed by two regis-punishable. tered electors of such county or borough as proposer and seconder, and by eight other registered electors of the same county or borough as assenting to the nomination, is to be delivered during the time appointed for the election to the returning officer by the candidate himself, or his proposer or seconder. If at the expiration of one hour after the time appointed for Secrecy is enforced upon every officer, clerk, and agent in attendance at a polling station during the election, under pain upon summary conviction before two justices of the peace of imprisonment for a term not exceeding six months with or without hard labour. The same penalty is enacted against any person that shall directly or indirectly induce any voter to display his 1863 PARTITION OF NUMBERS. PARTITION OF NUMBERS. ballot paper after he shall have marked the same so as to make Assume that for (p) quantities, the required sum is : known the name of the candidate for or against whom he has so marked it. +..... m+p-1 + m+p-1 1651 (a1-ap) (a2-a1) (α-ag) + (ap By the rules prescribed in the schedule to the statute for the (a,-a ̧) (α, —αy) conduct of elections,-The returning officer is to appoint the time for the election, in the case of a county within two days after the day on which he receives the writ, and in the case of a borough on the same day that he receives it. The time so appointed may be any two hours between ten and three o'clock in the day, and the returning officer must attend during those two hours and for one hour after at the place of election. Let another element be added, and the required sum is: ap+1 ap+1 } The returning officer upon the nomination paper being delivered to him is in each case to placard the names of each candidate and of his proposer and seconder, outside the building or by hypothesis, appointed for the election. the sign Σ denoting the sum of terms obtained by the symmetrical interchange of letters. As to the poll-The returning officer is to provide a sufficient number of polling stations, each furnished with a number of compartments screened from observation in which the voters can mark their votes, and, with all the requisite materials for marking and stamping the ballot papers. Every ballot box is to be so constructed that the ballot papers can be introduced therein, but cannot be withdrawn therefrom, without the box being unlocked. The presiding officer at any polling station, just before the commencement of the poll, is to show the ballotbox open to all present in the station, so that they may see that it is empty, and is then to lock it up and place his seal upon it, and place the box in his view for the receipt of ballot papers. Immediately before a ballot is delivered to an elector, it paper is to be marked on both sides with the official mark; the number, name, and description of the elector is to be called out; and the number is to be marked on the counterfoil of, and the register so marked as to denote the delivery of a ballot-paper to that elector. The elector is then in one of the compartments to mark his ballot paper, fold it up so as to conceal his vote, and to place it in the ballot box. Voters unable to write, or to read and write, or who conscientiously object to write on the day in ques- and the result is therefore tion, as in the case of Jews on a Saturday, are to have their papers marked for them by the presiding officer in presence of the agents of the candidates, and then placed in the ballot box. At the close of the poll the ballot box is to be sealed up and delivered to the returning officer, who, in the presence of the agents of the candidates, is to proceed as soon as practicable with the counting of the votes. Municipal Elections. The Act and the rules appended relating to vote by ballot are applied with the necessary modifications to municipal elections. PARQUETRY (MARQUETRY AND PARQUETRY, E. C. vol. v. col. PARTITION OF NUMBERS. The principal discoveries on this subject are due to Professor Sylvester. The main theorem which we shall presently give will be found enunciated by him, with an intimation of the method of proof, in the Quarterly Journal of Pure and Applied Mathematics,' vol. i. p. 142. The demonstration we are about to give is due to Mr. Samuel Roberts, and will be found in the same journal, vol. iv. Let a ag as a, be given elements, positive whole integers, and let a + Aq Xq + + Ap x2 = N. When n is a positive whole number, required the number of the solutions of this equation in positive integers. a "+p + ... (ap+1 (a-ap-1) (ap+1-a) + (αp+1-αp) It will be observed that this demonstration depends upon the fact that the quotity of (n) with respect to a, a,... an is the sum of the homogeneous n-dimensional powers and products of the roots of the denominator of the generating function. PARTRIDGE WOOD, so named from a peculiar wavy pattern in the grain, is the produce of a tree growing in Brazil, and is used for walking-sticks, umbrella handles, and small articles in fancy and cabinet work. rhymed by Father Magus; again, in 1810, by Ottmar Weis, parish priest, and Rochus Dedler, schoolmaster of Oberammergauthe former correcting the text, the latter arranging the music; finally, in 1860, by Daisenberger, present priest of Oberammergau, as it was represented in that year and in 1870 and 1871. It is probable that as, in the first instance, the fathers of Ettal and the priests of Oberammergau were the arrangers of the play, the monks were the actors. The performance now is entirely managed by the peasants of the village, no outsider being admitted to take part. The village of Oberammergau is situated at about twenty-six miles from Weilheim, which village lies at a distance of two hours by rail from Munich; but after leaving Weilheim the road rises all the way, and finally becomes precipitous till it arrives at Ettal, which is situated on a table land within two miles of Oberammergau, which village is surrounded by high hills. Though the distance is not great, the nature of the road makes it a long day's journey from Munich. Many people attribute the preservation of the play in its religious integrity, to the isolation of the place and its inhabitants; but though isolated, it has never been unknown. An author of the last century calls the valley of Unter and Oberammergau the most beautiful in the Bavarian Alps, a place of historical interest, known in the time of the Romans. It was a high road for the products of the East by Venice to Augsburg, and so to northern countries. There PASSANT, in Heraldry, walking. Thus a lion represented with his face directed forwards is described as a Lion passant;" if with his face turned to the spectator, as "a Lion passant guar-were certain dues paid for free passage; this continued until dant;" if walking and looking backwards, as "passant regar- the Thirty Years' War, when the traffic, and consequent redant;" when two animals are blazoned walking in opposite venue, was destroyed, after which the art of wood carving, for directions, they are counter-passant, or passant-repassant. which the inhabitants had always been more or less celebrated, PASSING-BELL, or, as it was popularly called, the Soul-Bell became their chief employment and source of emolument. (A. S. Sawl-cnyll, Northumbrian sawl-cnul), the tolling of a The representation of the play takes place generally on church bell as a person was dying. In early times the custom was Sundays, once a week, from Whitsunday to the end of Septemgeneral in England, the object being to invite those who heard ber, usually in each tenth year; but in consequence of the war the bell to offer up a prayer for the passing, or departing, soul between Germany and France, which interrupted the perform(Monast. Angl.' ., xliv.). Thus Sir Thomas Browne writes ance after the third representation in 1870, men having been Religio Medici,' Pt. ii. § 6):-"I never hear the toll of a pass-drawn off for the war, many of them, the Christus, for instance, ing-bell, though in my mirth, without my prayers and best being amongst the principal performers, it was reproduced in wishes for the departing spirit." Some writers speak of it as 1871. The Christus, by special permission of the king, was intended also to scare away evil spirits who were about the sick exempted from serving on the battle field. He was kept in the person's bed; and other reasons, more or less fanciful, have been war office, and allowed to retain his long hair. The influx of assigned, as may be seen in Brand ('Pop. Ant.' ii. 128-140), visitors was so great, that many predict the eventual spoiling but there can be no doubt that the true purpose was that above and subsequent suppression of the performance. It is a thorough stated. Many references to the passing-bell occur in our older representation rather than an acting of the Gospel narrative. poets and prose writers. For the passing-bell has been substi- The men are a remarkably handsome race, with great dignity: tuted the tolling of a bell after a death, with which every one is they are mostly what we should call in England yeomen, that familiar. is, they till their own land; but then they till it themselves, most of them not being rich enough to employ paid labour. The men who performed the parts of St. James and St. John on the 9th of July, 1871, returned from the field on Saturday night, on their own hay cart, with the hay they had made, and housed it under the roof of their cottage, which cottage was only superior to that of an English labourer, in its exquisite cleanliness. The man, Joseph Mair, who acted the part of the Christus, lives in a scarcely better cottage: he is a wood carver, especially celebrated for his crucifixes. The greater part have to labour with their own hands for their daily bread; some again have substantial stone houses, sometimes adorned with frescoes; these follow different callings; they are the grocers, dyers, &c., of the village. The village itself is like a great farmyard, with no regular streets, houses, great and small, dotted about, stacks of hay and wood and manure, cattle, cows, and sheep encountering the visitor. PASSION PLAY. The history of the religious drama to its decline in the Miracle Plays of England and the Continent is given at sufficient length under DRAMA, DRAMATIC LITERATURE, E. C. vol. iii. col. 634, &c. (see especially cols. 653-56). Here we propose to give a short account of almost the only surviving representation of the old scriptural drama, the Passion Play, still performed at Oberammergau, a mountain village of Bavaria. The Oberammergau Passion Play is acted once in ten years, according to the local tradition, in fulfilment of a vow made on the occasion of a fearful pestilence which devastated the neighbourhood in 1633. This, however (as shown by F. A. Daisenberger, parish priest of Oberammergau, in the account of the play which he published in 1850), was only the revival of a custom which had fallen into abeyance. Since the general prohibition of these plays in Bavaria, the peasants of Oberammergau have at various times received permission to perform theirs. Others were also revived for a time, but the Oberammergau play is the only one that still survives. Dubbers accounts for this in three ways: he says that the people are possessed of an innate artistic taste for representation, as shown in their talent for wood carving; that they are an earnestly religious people; and that there is an intrinsic worth and sacred character in the text. This text has, at each period of its reappearance, been carefully revised, altered, and adapted to altered times. The original MS., on which all later ones have been formed, is in the King's Library at Munich, and the compiler was Johannes Aelbl, parish priest of Weilheim, who died in 1609. It is interspersed with alternate action and tableaux vivants; but the latter are scenes also from the Passion, not as at present, Old Testament types. In 1750 and 1760 it was played (according to Deutinger) after a text arranged by Father Ferdinand, a Benedictine of Ettal, with tableaux from the Old Testament, with an angel as interpreter, the part now performed by the chorus. In 1770 and 1780 it was revised again and The scene of the performance is a large wooden structure, capable of accommodating 6,000 people. The better seats have a rough protection from the weather; but all the rest of the theatre, both for actors and spectators, is under the canopy of the sky. As was probably the case with all such performances in olden time the spectacle is preceded by masses, which begin from dawn and continue on till high mass at six o'clock, so giving every one an opportunity of assisting at one or other of the masses before he proceeds to the theatre for the instruction, which commences precisely at eight o'clock, and, with one hour's intermission, lasts for eight hours. As a gun fires, the chorus, nineteen in number, file in, headed by the choragus,-costume and gait, and all details of dress, are most minutely attended to. The singers are dressed in flowing robes, with flowing hair, golden crowns, and sandalled feet; their tread as they advance or retire is majestic; men and women are dressed exactly alike (except the choragus), and are only to be distinguished by their voices. The business of the chorus is to call attention to the scene about to be represented, to explain the meaning of the |