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. Between 0 and 10 10 and 20 No. of Primes. Between 150 and 200 200 and 250 No. of Primes. 4135 4061 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 r÷ (log x 108366), 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 (A log æ— B), but no reason has yet been given why A is 1, and B is 108366. Using the common logarithm, we find that the number of primes less than 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. It thus appears that we might name a succession of numbers beginning with one so high, that a million, or any other number however great, of numbers should pass without containing one prime number. Nevertheless there cannot be an end to the prime numbers; for if so, let p be prime number, and let N be the product of all the hers 2, 3, 5, ....., p. Now every number is either 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+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 No 1 or No+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 (M+1): N and (N2+1) : M are both whole numbers. But if x and y be not both odd, then either (My-1): N and (N+1): M are both whole numbers, or else (My+1) : N and (N-1): M are both whole numbers. This theorem is of considerable importance in the theory of numbers, and has been termed the law of reciprocity of prime numbers. 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 3 x 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 Ax 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. 244-236.) PRI'M NOA, 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. Primula veris. 3 2 1 1, a corolla laid open ; 2, a section of a capsule; 3, a section of a seed. 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 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, senatus in the Roman State. He seems to have been origior disposes of absolutely. nally 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 members of sovereign houses, as Prince Leopold, Prince Albert, both younger members of one branch of the sovereign house 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 have 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 narcotic, but the order is of no known utility. 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 wile. 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 popu lation 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 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 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. 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 Bruns-built with broad streets intersecting each other at right wick, 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. Ship-building is carried on in this island, and a considerable number of vessels, from one hundred to six hundred tons, are built for the British market: but the principal 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 rate, and weasels. The bears, which formerly destroyed A great number of cattle, sheep, and hogs, have been nearly minated. 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 govern ment is conducted by a lieutenant-governor and a council, which also acts in a legislative capacity; and there is a House of Assembly, which consists of eighteen members. The English law is administered by a chief-justice, and there are district courts for the recovery of small debts. (MacGregor's British America; Bouchette's British Dominions in North America.) PRINCE WILLIAM'S SOUND is a wide bay on the north-west coast of North America, extending, with several branches, between 60° and 61° N. lat. and between 146° and 148° 30′ W. long. It is called by the Russians Tshongathkaia. It opens to the south, and the entrance contains two large islands, of which the eastern is called Rose Island, and the western Montague Island. In both islands there are good harbours, and the largest vessels may enter the bay on both sides of Montague Island. Rose Island contains Port Etches, where the Russians have a factory, and a wooden fort, called Fort Constantine. The islands are rocky and mountainous, but the mountains do not rise so high as on the continent. The country abounds in pinetrees, some of which are very large; there is also a great quantity of alder and hazel trees. Wild berries, as strawberries, raspberries, and alderberries, are plentiful. Seaotters and foxes are still frequently met with, and other fur-bearing animals are abundant in the forests. The natives, who are few in number, and called Oogaliakhmutes, live mostly on the produce of their fishing. They are short in stature, and seem to be a cross between the Esquimaux and the other Indians. (Portlock's Voyage Round the World.) PRINCE OF WALES'S ISLAND. [PENANG.] PRINCE'S METAL, or Prince Rupert's Metal, an alloy of copper and zinc, which contains more copper than brass does, and is prepared by adding this metal to the alloy. PRINCIPAL, the name of a stop or row of metal pipes in an organ, tuned an octave higher than the diapason, an octave lower than the fifteenth, and serving to blend the two, as well as to augment the volume of sound. PRINCIPAL. [AGENT.] PRINCIPATO CITRA. [SALERNO, Province.] PRINCIPATO ULTRA, called also Provincia di Avellino,' is a province of the kingdom of Naples, bounded on the north by the provinces of Sannio and Capitanata, from which it is divided by the central ridge of the Apennines, on the east by Capitanata, on the south by Basilicata and the province of Salerno, and on the west by Terra di Lavoro. The province of Principato Ultra lies almost entirely in the Apennines, and between the western lower ridge of those mountains, including Monte Taburno, Tifata, and Monteforte, which divides the basin of the river Calore, an affluent of the Volturno, from the plains of Campania, and the central ridge, which forms the watershed between the streams that flow into the Mediterranean and into the Adriatic. The Calore and its affluents the Tamaro and Sabbato are the principal rivers of the province. A small part of Principato Ultra however extends along the eastern slope of the central ridge, where the river Ŏfanto (Aufidus) has its source in the neighbourhood of Conza and Nusca. Owing to the local situation of the province and its elevation above the sea, the temperature is considerably lower upon the whole than that of the plains of Campania, although in some of the valleys the summer heats are occasionally very great. Some places in the valley of the Calore are subject to the malaria in consequence of stagnant waters. The country produces corn, fruits in abundance, silk, some wine, and has excellent pasture for cattle. By the last census the population of the whole province was 390,000, exclusive of Benevento and its territory, which belongs to the pope, although geographically included within the boundaries of Principato Ultra. [BENEVENTO.] The area is reckoned at 1960 square miles. (Neigebaur; Serristori.) The principal towns of the province are, Avellino, Ariano, Montesarchio with 6000 inhabitants, Montefusco, with 3000, and Sant' Angelo dei Lombardi. The province is divided, for administrative purposes, into three districts: Avellino, Ariano, and Montefusco. The province of Principato Ultra occupies the country of the antient Hirpini, one of the nations of the Samnite confederation. PRINCIPIA, the contracted title of the Philosophia Naturalis Principia Mathematica,' the great work of Newton, the publication of which is the most remarkable epoch in the history of science. The title-page of the first edition is: Philosophia Naturalis Principia Mathematica. Au tore Is. Newton, Trin. Coll. Cantab., Soc. Matheseos Professore Lucasiano, et Societatis Regalis Sodali. Imprimatur. S. Pepys, Reg. Soc. Præses, Julii 5, 1686. Londini, Jussu Societatis Regiæ ac Typis Josephi Streater. Prostat apud plures Bibliopolas. Anno MDCLXXXVII. The object of this article is to describe the publication and the contents of the Principia, with a brief notice of the principal commentaries. The first head, the publication, we should have left untouched, referring to the article NEWTON, if it had not been for the work which the late Professor Rigaud published a short time before his death, entitled Historical Essay on the First Publication of Sir Isaac Newton's Principia,' Oxford, 1838. A slight account of this publication, embodying Mr. Rigaud's conclusions, may be usefully appended to the article cited. Mr. Rigaud appears to receive the common story of the fall of an apple. [NEWTON, p. 201.] It was communicated by Newton's niece to Voltaire, and by her husband, Mr. Conduit, to Fontenelle. It is clear however that Newton first thought on the subject in 1666. With reference to the story of his laying by the theory until Picard's measure of the earth was brought to his notice in 1682 [p. 199], Mr. R. states the fact that Picard's Mésure de la Terre' was published in 1671, and much discussed at the Royal Society in the years following.* Moreover Dr. Pemberton, who derived his information from Newton himself, states most explicitly (in his preface) that a letter from Hooke gave occasion to his resuming his old thoughts, and that he then used Picard's measure. This letter from Hooke, the subject of which was the curve in which a falling body descends to the earth, taking into account the earth's motion, is clearly made out to have been written in 1679, which is therefore the date of Newton's resumption of his attempt, not 1682, as generally stated. The new attempt, as every one knows, was more successful, but Newton did not write any treatise nor contemplate any publication; he traced out the foundation of his system, and threw aside his papers. In January,+ 1684, Halley had concluded, from Kepler's third law, that the centripetal force on the pla ets (supposed to move in circles) was as the inverse square of the distance. Not being able to proceed further, he applied to Hooke and Wren, the former of whom professed to have solved the whole problem, but would communicate nothing; the latter declared that he had long given over the question from inability to succeed. In August following, Halley paid a visit to Newton at Cambridge, who informed him that he had solved the problem, but was not able to lay his hand on the papers which contained his solution, so completely had he thrown the subject aside. After Halley's departure, he worked the theorems out again, and transmitted them to Halley through Mr. Paget, the mathematical master at Christ's Hospital. On receipt of this communication, in November, Halley immediately paid another visit to Cambridge, to gain more information, and to induce Newton to pursue the inquiry. December 10, 1684, Halley stated at the Royal Society that he had lately seen Mr. Newton at Cambridge, and that he had shown him a curious treatise De Motu, which, upon his desire, he said was promised to be sent to the Society to be entered upon their register.' Halley and Paget were accordingly deputed to keep Newton in mind of his promise (a singular proceeding, showing how well the Society knew Newton's indifference about communicating), and the consequence was, that about the middle of February, 1685, a communication (that previously made to Halley, enlarged), entitled 'Isaaci Newtoni Propositiones de Motu,' was sent and registered: it contains what were afterwards the main theorems of the early sections of the Principia, direct and inverse, relating to centripetal forces. No Principia as yet existed, and even this basis had only recently been written down satisfactorily. Newton writes to Mr. Aston, Sec. R. S., in acknowledging the news of the above entry, 'I designed them for you before now, but the examining several things has taken a greater part of my time than I expected, and a great deal of it to no purpose. And now I am to go into Lincolnshire for a month or six weeks. Afterwards I intend to finish it as soon as I can conveniently.' (February 23, 1685.) On this Mr. Rigaud well • Mr. R. mentions that Newton must have been acquainted with the measures of Snell and Norwood, the result of the former of which appears in his and as to the former, we have shown [MILE] that in this very edition of Va own edition of Varenius. The latter, there can be no doubt, he did not trust; renius, he had allowed gross errors to pass as to the measures of his own coun try. It may be inferred that he had not much to do with the details of it. TION.] All the following dates are for a year beginning in January. That is, what we call 1684; Halley writes 1683-4. [PERIODS OF REVOLU remarks, The Principia was not a protracted compilation from memoranda which might have been written down under the impression of different trains of thought: it had the incalculable advantage of being composed by one continued effort, during which the mutual bearing of the several parts was vividly present to the author's mind.' On the 21st of April, 1686, Halley announced to the Royal Society that Mr. Newton had an incomparable Treatise on Motion almost ready for the press;' and on the 28th of the same month Dr. Vincent* presented the manuscript of the first book to the Society, who referred the question of printing to the Council, and the production of a report upon the contents to Halley. May 19, the Society decided that the work should be printed forthwith in quarto, &c.; and hence it has always been supposed that the Society paid the expenses of printing, though the title-page only bears jussu Societatis,' &c., and not jussu et sumptibus,' as usual where it bore the expenses. But Mr. Rigaud quotes the minute of the Council of the Society of the 2nd of June, confirming the vote of the Society to the extent of resolving that Mr. Newton's book be printed,' but adding that E. Halley shall undertake the business of looking after it, and printing it at his own charge, which he engaged to do. The fact was, that when the Council came to consider the Society's vote of the 19th of May, they found there was no money; a work of Francis Willughby, De Historia Piscium,' published 'jussu et sumptibus,' in 1686, had so reduced their funds, that they were obliged to pay their officers in copies of this very book about fishes. vying your happiness, that endeavour to disturb your quiet enjoyment; which, when you consider, I hope you will see cause to alter your resolution of suppressing your third book, there being nothing which you can have compiled therein, which the learned world will not be concerned to have concealed. Those gentlemen of the Society to whom I have communicated it, are very much troubled at it, and that this unlucky business should have happened to give trouble, having a just sentiment of the author thereof. According to your desire in your former, I waited upon Sir Christopher Wren, to inquire of him, if he had the first notion of the reciprocal duplicate proportion from Mr. Hooke. His answer was, that he himself very many years since had had his thoughts upon the making out the planets' motions by a composition of a descent towards the sun, and an impressed motion; but that at length he gave it over, not finding the means of doing it. Since which time Mr. Hooke had frequently told him, that he had done it, and attempted to make it out to him; but that he never was satisfied that his demonstrations were cogent. And this I know to be true, that in January, 1683-4, I, having, from the considerations of the sesquialter proportion of Kepler, concluded that the centripetal force decreased in the proportion of the squares o. the distances reciprocally, came on Wednesday to town, where I met with Sir Christopher Wren and Mr. Hooke, and falling in discourse about it, Mr. Hooke affirmed, that upon that principle all the laws of the celestial motions were to be demonstrated, and that he himself had done it. I declared the ill-success of my own attempts; and Sir ChristoIn the meanwhile arose a controversy with Hooke, the pher, to encourage the inquiry, said that he would give Mr. universal claimant, who, when the first part of the manu- Hooke, or me, two months' time to bring him a convincing script was presented by Vincent, asserted that he had dis- demonstration thereof; and, besides the honour, he of us, that covered the law of the inverse squares, and had communi- did it, should have from him a present of a book of forty cated that and other discoveries to Newton. The heads of shillings. Mr. Hooke then said, that he had it, but he would the paper on which he founds his claim are given at length conceal it for some time, that others trying and failing might in HOOKE, ROBERT, and they show that though he had (in know how to value it, when he should make it public. Howcommon with several others) some very correct notions on ever, I remember that Sir Christopher was little satisfied the subject, he had not even arrived at the knowledge of that he could do it; and though Mr. Hooke then promised the law of the inverse squares, though that had been pro- to show it him, I do not find that in that particular he has pounded by BOUILLAUD. Mr. Rigaud enters at great been so good as his word. The August following, when length into this question; if we were to do the same, we I did myself the honour to visit you, I then learnt the should take an advanced position, and before we attempted good news that you had brought this demonstration to perto show that Hooke did not write any part of the substance fection: and you were pleased to promise me a copy thereof, of the Principia, we should require reasonable proof that he which the November following I received with a great deal would have been able to read and understand the mathe- of satisfaction from Mr. Paget; and thereupon took another matical part of it when written: and not until this had been journey to Cambridge, on purpose to confer with you about given, which we are convinced could not be given from it, since which time it has been entered upon the Register Hooke's writings, should we consider it necessary to enter Books of the Society. As all this passed, Mr. Hooke was on the first point. Had it not been for Halley, this trum- acquainted with it, and according to the philosophically pery claim of Hooke's would have produced serious couse- ambitious temper he is of, he would, had he been master of quences. Newton, easily disgusted by controversy, and a like demonstration, no longer have concealed it, the reason having observed that physical questions generally gave rise he told Sir Christopher and me now ceasing. But now, he to it, proposed (in a letter to Halley, June 20, 1686) to omit says, this is but one small part of an excellent system of the third book altogether, which contains the actual ap- nature, which he has conceived, but has not yet completely plication of the first two books to the existing universe. made out, so that he thinks not fit to publish one part withHe says, 'The third I now design to suppress. Philo- out the other. But I have plainly told him, that unless sophy is such an impertinently litigious lady, that a man he produce another differing demonstration, and let the had as good be engaged in lawsuits as have to do with world judge of it, neither I nor any one else can believe it. her. I found it so formerly, and now I have no sooner As to the manner of Mr. Hooke's claiming the discovery, come near her again, but she gives me warning. The two I fear it has been represented in worse colours than it first books, without the third, will not so well bear the ought; for he neither made public application to the Society title of Philosophia Naturalis Principia Mathematica," for justice, nor pretended you had all from him. The truth and therefore I had altered it to this," De Motu Corporum is this: Sir John Hoskyns, his particular friend, being Libri Duo," but upon second thoughts, I retain the former in the chair when Dr. Vincent presented your book, the title. Twill help the sale of the work, which I ought not Doctor gave it its just encomium both as to the novelty to diminish now 'tis yours.' Halley had to soothe this irri- and dignity of the subject. It was replied by another tation, and prevent the consequences; and as the letter in gentleman, that you had carried the thing so far, that there which he did this is very curious, and has never been printed was no more to be added. To which the Vice-president realtogether, except by Mr. Rigaud, the surpassing interest plied, that it was so much the more to be prized, for which everything connected with the Principia excites that it was both invented and perfected at the same time will justify our giving it entire, particularly as it is the This gave Mr. Hooke offence, that Sir John did not, at original voucher for several of the most important circum- that time, make mention of what he had, as he said, disstances connected with the publication:covered to him; upon which they two, who till then were the most inseparable cronies, have since scarce seen one Sir, I am heartily sorry that in this matter, wherein another, and are utterly fallen out. After the breaking all mankind ought to acknowledge their obligations to you, Mr. Hooke did there endeavour to gain belief, that he had up of that meeting, being adjourned to the coffee-house, you should meet with anything that should give you disquiet; or that any disgust should make you think of desist-hint of this invention. But I found, that they were all of some such thing by him, and that he gave you the first ing in your pretensions to a lady whose favours you have so much reason to boast of. 'Tis not she, but your rivals, en London, 29 June, 1686. This gentleman is supposed to have been the husban 1 of a lady to whom Newton was attached in early life, opinion, that, nothing thereof appearing in print, nor on the books of the Society, you ought to be considered as the inventor. And if in truth he knew it before you, he ought not to blame any but himself, for having taken no more |