Ainger, Esq. COMMITTEE. Chairman-The Right Hon, LORD BROUGHAM, F.R.S., Memoer of the National Institute of France. William Allen, Esq., F.R. and R.A.S Captain Beaufort, R.N., F.R. and R.A.S., Hydrographer to the Admiralty. George Birkbeck, M. D. George Burrows, M.D. Peter Stafford Carey, Esq., A.M. John Conolly, M.D. William Coulson, Esq. R. 1). Craig, Esq. J. F. Davis, Esq., F.R.S. H. T. Dela Beche, Esq., F.R.S. The Right Hon. Lord Denman, Samuel Duckworth, Esq. The Right Rev. the Bishop of Durham, D.D. Sir Henry Ellis, Prin. Lib. Brit. Mus. T. F. Ellis, Esq., A.M., F.R.A.S. John Elliotson, M.D.. F.R.S. Thomas Falconer, Esq. I. L. Goldsmid, Esq., F.R. and R.A.S. LOCAL COMMITTEES. Lt. Col. C. Hamilton Smith, F.R.S. John Milford, Esq. (Coaver.) Alexander McGrigor, Esq. Liverpool Loc. As.-W. W. Currie, Esq. Ch. J. Mulleneux, Esq., Treasurer. Manchester Loc. As.-G. W. Wood, Esq., Sir Benjamin Heywood, Bt., Treasurer. Masham-Rev. George Waddington, M.A. T. Sopwith, Esq., F.G.S. Newport, Isle of Wight-Ab. Clarke, Esq. T. Cooke, Jun., Esq. R. G. Kirkpatrick, Esq. Presteign-A. W. Davis, M.D Ripon Rev. H.P. Hamilton, M.A.,F.R.S.,G.S. Ruthin-Rev. the Warden of Humphreys Jones, Esq. Ryde, I. of Wight-Sir Rd. Simeon, Lt. Tavistock-Rev. W. Evans, John Rundle, Esq., M.P. Yarmouth-C. E. Rumbold, Esq. Dawson Turner, Esq. THOMAS COATES, E Secretary, No, 59, Lincoln's Inn Fields John Phillips, Esq., F.R,8., F.G.8. Loclan: Printed by W CLows and Sox, Stamford-str. AUG 1 0 1921 19-20 THE PENNY CYCLOPÆDIA OF THE SOCIETY FOR THE DIFFUSION OF USEFUL KNOWLEDGE. PRI PRI PRIMATI'CCIO, FRANCESCO, was born at Bologna, in 1490. He was of a noble family, and his parents intended to have him brought up to the mercantile profession; but his natural genius leading him to the arts, he learned design and colouring from Innocenzio da Imola and Bagnacavallo, and having manifested extraordinary talent, he went to Mantua to study under Julio Romane, who was engaged on some great works in the palace Del Té at Mantua, many of which Primaticcio and others of his disciples executed after his designs. Frederic, duke of Mantua, recommended him in 1531 to Francis, king of France, who entrusted him with many works. A great jealousy arising between him and Rosso, who was likewise in high favour with Francis, the king sent Primaticcio to Rome to purchase antiques, a commission in which he was extremely successful. He was recalled from Rome to complete a large gallery left unfinished by the death of Rosso. The number of works which he executed in France is truly astonishing, especially in the palace of Fontainebleau, where, assisted by his pupil Nicolo Abate, he painted, besides other works, in the great gallery, which was 456 feet long and 18 wide, fifty-eight pictures, each 6 feet high and 8 feet wide, representing the principal scenes of the Odyssey; the roof, which was richly adorned with gilding and stucco, was decorated with fifteen large and sixty small pictures, chiefly subjects of heathen mythology. This great work was totally destroyed in 1738, when the great gallery was pulled down to erect apartments for some persons attached to the court. Francis II. gave him the abbey of St. Martin de Troyes, with a revenue of 8000 crowns, which he enjoyed till his death in 1570. Primaticcio's talents however were chiefly called into exercise under Henry II., most of the frescoes with which Francis intended to adorn Fontainebleau not being executed till after his death. The oil-paintings of Primaticcio are excessively rare in Italy. Fuseli mentions a Concert of three female figures in the Zambeccari gallery as an enchanting performance; and Dr. Waagen says that a picture at Castle Howard representing Penelope relating to Ulysses what has passed in his absence, is the finest work of this master that he had yet seen. PRIME. A number is said to be prime when it is not divisible without remainder by any less number than itself, except unity. Thus 1, 2, 3, are of necessity prime; 4 is not, being divisible by 2; 5 is prime, and so are 7, 11, 13, 17, 19, 23, 29, 31, &c. Large lists of prime numbers have been published TABLES], but they are seldom possessed by the elementary student. As it is however frequently desirable to know whether a number not exceeding 10,000 is prime or not, we shall give a table to that extent, the manner of using which is as follows:-If we wish to know whether 2897 be a prime number, under the heading 2 and in the column 8 we look for 97, which we find there: whence the table shows that 2897 is a prime number. Again, by the same means we find that 1457 is not a prime number, the adjacent prime Qumbers being 1453 and 1459. P. C., No. 1167. 7 0123456789 (01 03 07 07 11 07 03 03 13.09 29 3 37 43 51 77 59 8961 59 177 79 69 61 81 91 81 71 93 83 99 91 83 83 991 8 93 99 91 193 prime or divisible by a prime; but N + 1 is not divisible by 2, 3, 5, or p, since it leaves a remainder 1 in every such division. It is therefore prime, or there is a prime number N+1, greater than the greatest prime number p, which is absurd. The following are among the properties of prime numbers. (1.) Every prime number (except 2) is odd, or of the form 2x+1. (2.) Every prime is of the form 4x + 1 or 4x + 3, and a prime of the form 4x + 1 is always the sum of two squares. (3.) Every prime is of the form 6x+1 or 6x + 5. (4.) No algebraical formula can always represent a prime number; but some formulæ show a long succession of primes: thus + x + 41 is prime from x = 0 to x 39, both inclusive. (5.) If 2x + 1 be a prime number, and N any number which it does not divide, either N-1 or N+ 1 must. be divisible by 2x+1. (6.) If M and N be two prime numbers, and if M = 2x+1, N = 2y+1, then if x and y be both odd numbers, either (M-1): N and (N-1): M are both whole numbers, or (My+1) N and (N+1): M are both whole numbers. But if x and y be not both odd, then either (My-1): N 01 03 03 11 03 11 01 19 03 01 and (N+1): M are both whole numbers, or else (My+1) 21 07 This theo: N and (N-1): M are both whole numbers. 23 rem is of considerable importance in the theory of numbers, and has been termed the law of reciprocity of prime numbers. 31 21 41 51 13 33 27 29 55 39 69 69 53 49 71 81 81 79 63 97 89 83 99 93 193 23 39 29 29 91 83 The distribution of the prime numbers does not follow any discoverable law, but it begins to be evident from the preceding table, that in a given interval the number of primes is generally less, the higher the beginning of the interval is taken. The following table will set this in a clearer light: the numbers in the first column mean thousands, and in the second column are found the numbers of primes which lie in the interval specified in the first column. Thus between 10 thousand and 20 thousand lie 1033 primes. In the first 10,000 numbers, upwards of 12 per cent. are primes; but between 900 thousand and a million, only 7 per cent. are primes. The preceding enumerations are taken from Legendre's Theory of Numbers, and were made from the large tables of primes given by Vega, Chernac, and Burkhardt. The only thing known relative to the proportions of prime numbers to others is that if a be a very large number, the number of primes contained between 0 and x is nearly ÷ (log x 1.08366), log x being the Naperean logarithm. This very curious theorem was discovered empirically, that is, by looking for a formula which should nearly represent the results of tables. Legendre, in the work cited, gave proof that such a formula must have the form x (A log x B), but no reason has yet been given why A is 1, and B is 1'08366. Using the common logarithm, we find that the number of primes less than x is such a proportion of x as 4342945 is of log x 470628, nearly. Thus, of all numbers less than a million of million of millions, only one out of 40 is prime, while the number of primes under the square of that number is one out of 82. Two numbers are said to be prime to one another, when they have not any common measure except unity: as 36 and 55. ... The prime factors of a number are those prime numbers which divide it. Thus 360 being 23 X 3X 5, its prime factors are 2, 3, 5, of which the first enters three times, the second twice, and the third once. If A, B, C, ... be the prime factors of a number, and a, b, c, the number of times which they severally enter, the number is Aax Box Cex ....., and the number of divisors which it admits of (unity and itself included) is (a+1) × (b+ 1) × (c+1) × .... . Call this number N: then the number of numbers less than N, and prime to N, is PRIME AND ULTIMATE RATIOS. [RATIOS, PRIME AND ULTIMATE; DIFFERENTIAL CALCULUS. PRIME'RO, a game at cards, so called from a situation in the game. He who holds the prime (primero), that is, a sequence of the best cards and a good trump, is sure to be successful over his adversaries; hence its denomination Primero, Prime, and Primavista were one and the same game. Primero appears to have been one of the earliest games at cards played in England, and continued to be the most fashionable game throughout the reigns of Henry VIII., Edward VI., Mary, Elizabeth, and James. In the earl of Northumberland's letters relating to the powder plot, we find that Josceline Percy was playing at primero on Sunday, when his uncle, the conspirator, called on him at Essexhouse. In the Sydney Papers, there is an account of a quarrel between Lord Southampton, the patron of Shakspere, and one Ambrose Willoughby, on account of the former persisting to play at primero with Sir Walter Raleigh and another, in the Presence Chamber, after the queen had retired to rest. Shakspere speaks of Henry VIII. playing at primero with the duke of Suffolk. One of the dialogues at the end of Minshew's Spanish Dictionary illustrates the method of playing this game; many of the terms of which are also detailed in one of Sir John Harington's epigrams, in which he describes 'the Story of Marcus's Life at Primero.' It is uncertain whether this game is of Spanish or Italian origin. Daines Barrington and Mr. Bowle (Archeologia, vol. viii., 133-151) were of opinion that it is of Spanish origin; but Berni's Capitolo del Gioco della Primeira affords proof that it was at least commonly played in Italy at the commencement of the sixteenth century. (Nares's Glossary; Singer's Researches into the History of Playing Cards, 4to., Lond., 1816, p. 244-256.) PRÍMNOA, a subdivision of the Linnæan genus Gorgonia. PRIMOGENITURE may be defined to be that rule of law by which a title of dignity or an estate in land comes to a person in respect of his being an eldest male. If a man dies seised of real estate, of which he had the absolute ownership, without having made any disposition of it by his last will, the whole descends to the heir at law or customary heir; and the heir at law is such by virtue of being the eldest male person of those who are in the same degree of kindred to the person dying, or the representative of such eldest male. [DESCENT.] This is a case in which primogeniture operates. A common example of primogeniture is where a father dies absolutely entitled to real estate, and without disposing of it by will, in which case his eldest son takes it all. If land is settled or entailed on a man and his male issue, the eldest son takes the land by two titles, first as being a male, and next as being the eldest son. The law of primogeniture then only applies in the case of land when the owner dies without having made any disposition of it by will, or where the land is settled on a man and his male issue. It does not apply when the interest in land is a chattel interest, or a term of years, whatever may be its du ration. 3 2 1 Primula veris. At present, those who are the absolute owners of large landed estates seldom die without making a disposition of them by will. In the case of lands which are settled, the person in possession is generally tenant for life, and the inheritance is entailed on the eldest son. When the eldest son is about to marry, it is usual for the father and son to take the usual legal steps (which they can do as soon as the son is of age) to unsettle the estate and obtain the absolute ownership. They then resettle the estate, making the father tenant for life as before the son, who was before tenant in tail, is also made only a tenant for life; and the 1, a corolla laid open; 2, a section of a capsule; 3, a section of a seed. inheritance is settled, as before, on the eldest son of the intended marriage. Such eldest son takes the estate, not as PRIMUM MO'BILE, the name given in the old astroheir, and therefore not by the law of primogeniture, but he nomy to the imaginary sphere by the motion of which takes it as the person designated by the deed of settlement. diurnal motion was given to the heavens. [PTOLEMAIC When a man happens to be tenant in tail, he usually SYSTEM.] takes the legal steps necessary (which he can do as soon as PRINCE is the Latin word princeps, which was origihe is of age) to acquire the absolute ownership of the pro-nally used to denote the person who was entitled princeps perty, which he then generally settles again by deed or will, or disposes of absolutely. It is usual in England to settle all large estates, and the object of the settlement is to keep the estates together, and to perpetuate them in one family; but there is a limit to this power of settlement. A man cannot, either by deed or will, settle his land, so as to prevent the absolute ownership of it from being obtained, for a longer period than a life or lives of persons in existence at the time when the settlement takes effect, and twenty-one years more. Lands in GAVELKIND and BOROUGH ENGLISH are an exception to the general rule of law as to the descent of land. The law of primogeniture then only operates in the cases already explained; and the system of settlements by which property is kept together in large masses is quite distinct in principle from the law of primogeniture. It is not the result of a law which favours primogeniture, but it is the result of the legal power which an owner of land has over it, and of the habits of the people. The various reasons which have laid the foundation of this habit, and which perpetuate it, are foreign to the consideration of primogeniture as a rule of law. In Virginia, after the Revolution, an act was passed for converting estates tail into fee simple, and at the same time the law of primogeniture was abolished. These laws have so far been in accordance with or bave acted on public opinion, that a parent by his will now generally makes the same disposition of his property as the law makes in case he dies intestate. (Tucker's Life of Jefferson, i. 96, &c.) (Remarks on Primogeniture and Entails, Hayes, Introduction to Conveyancing.) PRIMULA CEÆ are monopetalous Exogenous plants, peculiarly distinguished by the stamens being opposite to the lobes of the corolla, and a superior capsule with a free central placenta. In most respects they correspond indeed with the Myrsinaceous order, but the latter are known by their being trees or shrubs with an indehiscent fleshy fruit. The Primulaceous order consists of herbaceous plants inhabiting the temperate parts of the world, in moist situations, such as meadows, morasses, and alpine stations, or in the damp parts of woods, which they adorn with their lively flowers. The Primula, Anagallis, Soldanella, Cyclamen, and Lysimachia, of various species and under many forms, are the gayest of the genera, some of whose species are found in almost all gardens. The cowslip is slightly nareotic, but the order is of no known utility. senatus in the Roman State. He seems to have been originally the custos of the city, and his office was one of importance. Subsequently it became a title of dignity, and the princeps was named by the censors. (Liv., xxvii. 2.) In the senate he gave his opinion first after the magistratus. Augustus and his successors adopted the title of princeps, as a name that carried no odium with it; and this became henceforward the characteristic title of the master of the Roman world. Accordingly the constitutions of the emperors are called principum (Gaius, i. 2), or principales. The word princeps is formed similarly to anceps, municeps, &c., and contains the same element as primus. In the course of time the word prince, which is derived from princeps, has come to be applied to persons having personal preeminence, and especially to certain sovereigns of smaller states possessing either perfect independence of all others or enjoying under some superior high political rights. Of the first kind were the old sovereigns of Wales, who, under the name of princes, enjoyed the same right and power which belong to kings; and of the second, the heads of certain states of Germany comprehended in the great Germanic confederation. But the word seems not to have acquired so definite a sense as that which belongs to king, duke, marquis, earl, and some others of the class; but rather to denote persons of eminent rank in certain states, as in Prussia, Russia, Italy, and other continental states, when no sovereignty, properly so called, comes along with it, or persons who are junior mem bers of sovereign houses, as Prince Leopold, Prince Albert, both younger members of one branch of the sovereign house of Saxe. In England it has sometimes been the practice of the heralds to speak of a duke as the high and mighty prince; but the word seems rather to be restricted among us in its application to persons who are of the blood-royal, that is, a son, grandson, or nephew of a king; and it would probably be extended to the remote male posterity, though no such case has arisen in the course of the last three centuries; and in its application it is merely a term of common parlance, not being conferred, like the title of duke, in any formal manner; and even the precedence which is given to bloodroyal has respect to birth, and not to the enjoyment of this word as a title of honour. The king's eldest son is however made Prince of Wales by a special act of creation. PRINCE EDWARD'S ISLAND, a British island on the coast of North America, in the Gulf of St. Lawrence, is situated between 45° 58′ and 47° 7' N. lat. and between 62° and 64° 27' W. long It extends from east to west in a somewhat curved line 135 miles in length. The width varies | valuable furs, have become scarce. Seals are found in the between 34 miles and one mile. The surface is calculated bays and along the shores in summer and autumn; and in to comprehend an area of 2157 square miles, or 1,380,480 summer immense numbers sometimes come down on the ice acres: it is about 45 square miles larger than the North from the northward. Among the birds, the partridges are Riding of Yorkshire. It is separated from Nova Scotia and distinguished by their size, and wild pigeons are numerous, New Brunswick by Northumberland Strait, which in the but only appear in summer. Wild geese make a stay of narrowest part is hardly more than ten miles wide. about six weeks in spring, and about as long in autumn. Fish as well as shell-fish are plentiful, and the oysters are considered the finest in America. Many cargoes are annually sent to Quebec and Halifax. The coast is so intersected by bays and creeks, that there is hardly a place which is more than eight miles from the shore. These bays and inlets form good harbours, and the larger ones contain several branches which have good anchorage. Only at the western extremity, between North Cape and West Cape, and again along the northern coast towards the eastern extremity, between St. Peter's Bay and East Cape, there is no harbour. The most remarkable of these bays is Hillsboro Bay, which enters the island from the south with a broad opening, but afterwards becomes so narrow that it appears like a river, and is accordingly called Hillsboro River: the tide ascends nearly to its extremity, 20 miles above Charlotte Town. Farther west are Halifax Bay and Richmond Bay, of which the former intersects the country from the south and the latter from the north, so as to leave between them only an isthmus one mile wide. Richmond Bay stretches ten miles from its entrance inland, and is nine miles wide, but the entrance is contracted by a long narrow island lying across it. No minerals have been found on the island except red and white clay, fit for bricks and pottery. The island is divided into three counties, King's County, Queen's County, and Prince's County. Queen's County occupies the central districts, King's County the east, and Prince's County comprehends the west. Queen's County contains 771 square miles, and is nearly equal to Nottinghamshire; King's County contains 650 square miles, and is not so large as Worcestershire; Prince's County has 736 square miles, or almost as many as Oxfordshire. The population chiefly consists of Scotch emigrants and their descendants, some families of English extraction, and a few Acadians, or Americans of French origin. Formerly there were several families of Micmac Indians, but it appears that they have all emigrated to Chaleurs Bay. In 1768 the number of families did not exceed 150. According to the census The surface of the island consists of gentle ascents and taken in 1827, the population consisted of about 36,000, descents. There is no plain of any extent, and the emi-and as the number of settlements was then rapidly innences do not deserve the name of hills, with the exception creasing, Bouchette estimated the population, in 1832, at perhaps of a series of heights which intersect the island 50,000. nearly in the middle, running from Disable Bay on the southern shores, to Grenville Bay on the north. The soil, though nowhere very fertile, is in general productive. There are a few swamps, some of which are dry and covered with shrubs and moss; others are wet, and produce dwarf alder, long grass, and a variety of shrubs. There are also barren tracts which produce nothing except dry moss or shrubs. But the swamps and barrens bear only a small proportion to the whole surface of the island. The climate of Prince Edward's Island is favourably distinguished from that of all the surrounding countries by being exempted from fogs and being much less subject to cold. A misty fog appears sometimes on a summer or autumnal morning, but it is soon dispersed. The winter is two months shorter than in Nova Scotia and New Brunswick, and the frost much less intense; snow however falls in considerable quantity. For three or four months the country is covered with it. In April spring begins, but the heat increases rapidly, and summer may be considered as beginning in May. In June, July, and August the heat is excessive, the thermometer commonly rising to 80° or 90°, and during this period thunder-storms are frequent. From September to November the season is pleasant, and in December the frost sets in. With the exception of the swamps and barrens, the island was formerly entirely overgrown with high forest-trees, especially pine, the timber of which has been so largely exported to England, that at present there is no more than is required by the inhabitants for house and ship building and other purposes. The other trees are spruce-fir, hemlock, beech, birch, maple, poplar, and white cedar in abundance; oak, eim, ash, and larch are not plentiful, and the quality of the first is very inferior. At present about one half of the cultivable surface of the island is still wooded. The settlements are dispersed all.over the island. The coasts are more densely settled than the interior, with the exception of the western coast between North Cape and East Cape, which is almost entirely in its natural state, and is overgrown with forests. The northern coast has a greater number of settlements than the southern. Charlotte Town, the capital and seat of government, is situated in Queen's County, on the north side of Hillsboro River, near its confluence with the rivers Elliot and York. The harbour is considered one of the best in the Gulf of St. Lawrence. At the entrance it is little more than half a mile wide, but within it enlarges and forms a safe and spacious basin, which branches off into three beautiful and navigable rivers. The town stands on a gently rising ground, and is regularly built with broad streets intersecting each other at right angles. There is a court-house, an Episcopal church, a Scotch church, and a Roman Catholic and a Methodist chapel. In 1830 it contained about 350 dwelling-houses and 3400 inhabitants. In three or four places on the eastern and northern coast timber is shipped for England. Ship-building is carried on in this island, and a consider able number of vessels, from one hundred to six hundred tons, are built for the British market: but the principa. trade of the island consists in supplying Newfoundland with schooners for the seal and cod fisheries, with black cattle, sheep, hogs, poultry, oats, potatoes, turnips, &c.; the returns are chiefly made in money or West India produce. Wheat and other grain are sent to Miramichi and other settlements on the eastern coast of New Brunswick, where the population are chiefly engaged in preparing timber for the market. The same articles are sent to Halifax. Beef, pork, sheep. hams, cheese, oats, potatoes, flour, and fish are occasionally exported to Bermuda. Though the best fishing-banks within the Gulf of St. Lawrence lie in the immediate vici nity of the northern shores of this island, fishing is not car Soil and climate unite to make this island an agricultural country. All kinds of grain and vegetables raised in Eng-ried on to any great extent. land grow very well. Wheat, barley, and oats are extensively grown; and some winter-rye and buckwheat. Beans and peas are also raised. All the culinary vegetables common in England attain perfection. Indian-corn does not succeed well. Flax is raised only for home consumption, and is of excellent quality; hemp does not thrive well. The fruits are cherries, plums, damsons, and black, red, and white currants. Apples and pears require great attention, and are of inferior quality. The horses are small but hardy. The black cattle are of a smaller size than in England. Sheep and swine are plentiful, and the breed of the former has lately been much improved. The wild animals are bears, loup-cerviers, foxes, hares, otters, martens, musquashes, minks, squirrels, musk rats, and weasels. The bears, which formerly destroyed a great number of cattle, sheep, and hogs, have been nearly exterminated. Otters, martens, and musk-rats, which supply Prince Edward's Island was discovered by Cabot in 1497, on St. John's day, and hence it obtained the name of St. John's Island, which it preserved up to 1799, when it was changed into its present name in honour of the late duke of Kent. It was taken possession of by the French after the settlement of Canada, but no permanent establishment seems to have been formed in it before the peace of Utrecht (1713), when some families from Cape Breton settled there. In 1758 it was taken by the English, who retained possession of it at the peace of Paris (1763). In 1770 a separate constitution was granted to it, and the first House of Assembly met in 1773. Prince Edward's Island is in the diocese of Nova Scotia. There are two schools supported by the government in Charlotte Town; and there are also schools for elemen tary instruction in most of the settlements. The government is conducted by a lieutenant-governor and a counei, |