THE laws governing numbers are so perplexing to the uncultivated mind, and the results arrived at by calculation are so astonishing, that it cannot be matter of surprise if superstition has attached itself to numbers.

But even to those who are instructed in numeration, there is much that is mysterious and unaccountable, much that only an advanced mathematician can explain to his own satisfaction. The neophyte sees the numbers obedient to certain laws; but why they obey these laws he cannot understand; and the fact of his not being able so to do, tends to give to numbers an atmosphere of mystery which impresses him with awe.

For instance, the property of the number 9, discovered, I believe, by W. Green, who died in 1794, is inexplicable to any one but a mathematician. The property to which I allude is this, that when 9 is multiplied by 2, by 3, by 4, by 5, by 6, &c., it will be found that the digits composing the product, when added together, give 9. Thus:—

It will be noticed that 9 × 11 makes 99, the sum of the digits of which is 18 and not 9, but the sum of the digits 1 × 8 equals 9.

And so on to any extent.

M. de Maivan discovered another singular property of the same number. If the order of the digits expressing a number be changed, and this number be subtracted from the former, the remainder will be 9 or a multiple of 9, and, being a multiple, the sum of its digits will be 9. For instance, take the number 21, reverse the digits, and you have 12; subtract 12 from 21, and the remainder is 9. Take 63, reverse the digits, and subtract 36 from 63; you have 27, a multiple of 9, and 2 + 7 = 9. Once more, the number 13 is the reverse of 31; the difference between these numbers is 18, or twice 9.

Again, the same property found in two numbers thus changed, is discovered in the same numbers raised to any power.

Take 21 and 12 again. The square of 21 is 441, and the square of 12 is 144; subtract 144 from 441, and the remainder is 297, a multiple of 9; besides, the digits expressing these powers added together give 9. The cube of 21 is 9261, and that of 12 is 1728; their difference is 7533, also a multiple of 9.

The number 37 has also somewhat remarkable properties; when multiplied by 3 or a multiple of 3 up to 27, it gives in the product three digits exactly similar. From the knowledge of this the multiplication of 37 is greatly facilitated, the method to be adopted being to multiply merely the first cipher of the multiplicand by the first multiplier; it is then unnecessary to proceed with the multiplication, it being sufficient to write twice to the right hand the cipher obtained, so that the same digit will stand in the unit, tens, and hundreds places.

For instance, take the results of the following table:—

The singular property of numbers the most different, when added, to produce the same sum, originated the use of magical squares for talismans. Although the reason may be accounted for mathematically, yet numerous authors have written concerning them, as though there were something “uncanny” about them. But the most remarkable and exhaustive treatise on the subject is that by a mathematician of Dijon, which is entitled “TraitÉ complet des CarrÉs magiques, pairs et impairs, simple et composÉs, À Bordures, Compartiments, Croix, Chassis, Équerres, Bandes dÉtachÉes, &c.; suivi d’un TraitÉ des Cubes magiques et d’un Essai sur les Cercles magiques; par M. Violle, GÉomÈtre, Chevalier de St. Louis, avec Atlas de 54 grandes Feuilles, comprenant 400 figures.” Paris, 1837. 2 vols. 8vo., the first of 593 pages, the second of 616. Price 36 fr.

I give three examples of magical squares:—

These nine ciphers are disposed in three horizontal lines; add the three ciphers of each line, and the sum is 15; add the three ciphers in each column, the sum is 15; add the three ciphers forming diagonals, and the sum is 15.

But the connection of certain numbers with the dogmas of religion was sufficient, besides their marvellous properties, to make superstition attach itself to them. Because there were thirteen at the table when the Last Supper was celebrated, and one of the number betrayed his Master, and then hung himself, it is looked upon through Christendom as unlucky to sit down thirteen at table, the consequence being that one of the number will die before the year is out. “When I see,” said Vouvenargues, “men of genius not daring to sit down thirteen at table, there is no error, ancient or modern, which astonishes me.”

Nine, having been consecrated by Buddhism, is regarded with great veneration by the Moguls and Chinese: the latter bow nine times on entering the presence of their Emperor.

Three is sacred among Brahminical and Christian people, because of the Trinity of the Godhead.

Pythagoras taught that each number had its own peculiar character, virtue, and properties.

“The unit, or the monad,” he says, “is the principle and the end of all; it is this sublime knot which binds together the chain of causes; it is the symbol of identity, of equality, of existence, of conservation, and of general harmony. Having no parts, the monad represents Divinity; it announces also order, peace, and tranquillity, which are founded on unity of sentiments; consequently One is a good principle.

“The number Two, or the dyad, the origin of contrasts, is the symbol of diversity, or inequality, of division and of separation. Two is accordingly an evil principle, a number of bad augury, characterizing disorder, confusion, and change.

“Three, or the triad, is the first of unequals; it is the number containing the most sublime mysteries, for everything is composed of three substances; it represents God, the soul of the world, the spirit of man.” This number, which plays so great a part in the traditions of Asia, and in the Platonic philosophy, is the image of the attributes of God.

“Four, or the tetrad, as the first mathematical power, is also one of the chief elements; it represents the generating virtue, whence come all combinations; it is the most perfect of numbers; it is the root of all things. It is holy by nature, since it constitutes the Divine essence, by recalling His unity, His power, His goodness, and His wisdom, the four perfections which especially characterize God. Consequently, Pythagoricians swear by the quaternary number, which gives the human soul its eternal nature.

“The number Five, or the pentad, has a peculiar force in sacred expiations; it is everything; it stops the power of poisons, and is redoubted by evil spirits.

“The number Six, or the hexad, is a fortunate number, and it derives its merit from the first sculptors having divided the face into six portions; but, according to the Chaldeans, the reason is, because God created the world in six days.

“Seven, or the heptad, is a number very powerful for good or for evil. It belongs especially to sacred things.

“The number Eight, or the octad, is the first cube, that is to say, squared in all senses, as a die, proceeding from its base two, an even number; so is man four-square, or perfect.

“The number Nine, or the ennead, being the multiple of three, should be regarded as sacred.

“Finally, Ten, or the decad, is the measure of all, since it contains all the numeric relations and harmonies. As the reunion of the four first numbers, it plays an eminent part, since all the branches of science, all nomenclatures, emanate from, and retire into it.”

It is hardly necessary for me here to do more than mention the peculiar character given to different numbers by Christianity. One is the numeral indicating the Unity of the Godhead; Two points to the hypostatic union; Three to the Blessed Trinity; Four to the Evangelists; Five to the Sacred Wounds; Six is the number of sin; Seven that of the gifts of the Spirit; Eight, that of the Beatitudes; Ten is the number of the commandments; Eleven speaks of the Apostles after the loss of Judas; Twelve, of the complete apostolic college.

I shall now point out certain numbers which have been regarded with superstition, and certain events connected with numbers which are of curious interest.

The number 14 has often been observed as having singularly influenced the life of Henry IV. and other French princes. Let us take the history of Henry. On the 14th May, 1029, the first king of France named Henry was consecrated, and on the 14th May, 1610, the last Henry was assassinated.

Fourteen letters enter into the composition of the name of Henri de Bourbon, who was the 14th king bearing the titles of France and Navarre.

The 14th December, 1553, that is, 14 centuries, 14 decades, and 14 years after the birth of Christ, Henry IV. was born; the ciphers of the date 1553, when added together, giving the number 14.

The 14th May, 1554, Henry II. ordered the enlargement of the Rue de la Ferronnerie. The circumstance of this order not having been carried out, occasioned the murder of Henry IV. in that street, four times 14 years after.

The 14th May, 1552, was the date of the birth of MarguÉrite de Valois, first wife of Henry IV.

On the 14th May, 1588, the Parisians revolted against Henry III., at the instigation of the Duke of Guise.

On the 14th March, 1590, Henry IV. gained the battle of Ivry.

On the 14th May, 1590, Henry was repulsed from the Fauxbourgs of Paris. On the 14th November, 1590, the Sixteen took oath to die rather than serve Henry.

On the 14th November, 1592, the Parliament registered the Papal Bull giving power to the legate to nominate a king to the exclusion of Henry.

On the 14th December, 1599, the Duke of Savoy was reconciled to Henry IV.

On the 14th September, 1606, the Dauphin, afterwards Louis XIII., was baptized.

On the 14th May, 1610, the king was stopped in the Rue de la Ferronnerie, by his carriage becoming locked with a cart, on account of the narrowness of the street. Ravaillac took advantage of the occasion for stabbing him.

Henry IV. lived four times 14 years, 14 weeks, and four times 14 days; that is to say, 56 years and 5 months.

On the 14th May, 1643, died Louis XIII., son of Henry IV.; not only on the same day of the same month as his father, but the date, 1643, when its ciphers are added together, gives the number 14, just as the ciphers of the date of the birth of his father gave 14. Louis XIV. mounted the throne in 1643: 1 + 6 + 4 + 3 = 14.

He died in the year 1715: 1 + 7 + 1 + 5 = 14.

He lived 77 years, and 7 + 7 = 14.

Louis XV. mounted the throne in the same year; he died in 1774, which also bears the stamp of 14, the extremes being 14, and the sum of the means 7 + 7 making 14.

Louis XVI. had reigned 14 years when he convoked the States General, which was to bring about the Revolution.

The number of years between the assassination of Henry IV. and the dethronement of Louis XVI. is divisible by 14.

Louis XVII. died in 1794; the extreme digits of the date are 14, and the first two give his number.

The restoration of the Bourbons took place in 1814, also marked by the extremes being 14; also by the sum of the ciphers making 14.

The following are other curious calculations made respecting certain French kings.

Add the ciphers composing the year of the birth or of the death of some of the kings of the third race, and the result of each sum is the titular number of each prince. Thus:—

Louis IX. was born in 1215; add the four ciphers of this date, and you have IX.

Charles VII. was born in 1402; the sum of 1 + 4 + 2 gives VII.

Louis XII. was born in 1461; and 1 + 4 + 6 + 1 = XII.

Henry IV. died in 1610; and 1 + 6 + 1 = twice IV.

Louis XIV. was crowned in 1643; and these four ciphers give XIV. The same king died in 1715; and this date gives also XIV. He was aged 77 years, and again 7 + 7 = 14.

Louis XVIII. was born in 1755; add the digits, and you have XVIII.

What is remarkable is, that this number 18 is double the number of the king to whom the law first applies, and is triple the number of the kings to whom it has applied.

Here is another curious calculation:—

Robespierre fell in 1794;

Napoleon in 1815, and Charles X. in 1830.

Now, the remarkable fact in connection with these dates is, that the sum of the digits composing them, added to the dates, gives the date of the fall of the successor. Robespierre fell in 1794; 1 + 7 + 9 + 4 = 21, 1794 + 21 = 1815, the date of the fall of Napoleon; 1 + 8 + 1 + 5 = 15, and 1815 + 15 = 1830, the date of the fall of Charles X.

There is a singular rule which has been supposed to determine the length of the reigning Pope’s life, in the earlier half of a century. Add his number to that of his predecessor, to that add ten, and the result gives the year of his death.

Pius VII. succeeded Pius VI.; 6 + 7 = 13; add 10, and the sum is 23. Pius VII. died in 1823.

Leo XII. succeeded Pius VII.; 12 + 7 + 10 = 29; and Leo XII. died in 1829.

Pius VIII. succeeded Leo XII.; 8 + 12 + 10 = 30; and Pius VIII. died in 1830.

However, this calculation does not always apply.

Gregory XVI. ought to have died in 1834, but he did not actually vacate his see till 1846.

It is also well known that an ancient tradition forbids the hope of any of St. Peter’s successors, pervenire ad annos Petri; i.e., to reign 25 years. Those who sat longest are

There is one numerical curiosity of a very remarkable character, which I must not omit.

The ancient Chamber of Deputies, such as it existed in 1830, was composed of 402 members, and was divided into two parties. The one, numbering 221 members, declared itself strongly for the revolution of July; the other party, numbering 181, did not favor a change. The result was the constitutional monarchy, which re-established order after the three memorable days of July. The parties were known by the following nicknames. The larger was commonly called La queue de Robespierre, and the smaller, Les honnÊtes gens. Now, the remarkable fact is, that if we give to the letters of the alphabet their numerical values as they stand in their order, as 1 for A, 2 for B, 3 for C, and so on to Z, which is valued at 25, and then write vertically on the left hand the words, La queue de Robespierre, with the number equivalent to each letter opposite to it, and on the right hand, in like manner, Les honnÊtes gens, if each column of numbers be summed up, the result is the number of members who formed each party.

Some coincidences of dates are very remarkable.

On the 25th August, 1569, the Calvinists massacred the Catholic nobles and priests at BÉarn and Navarre.

On the same day of the same month, in 1572, the Calvinists were massacred in Paris and elsewhere.

On the 25th October, 1615, Louis XIII. married Anne of Austria, infanta of Spain, whereupon we may remark the following coincidences:—

The name Loys[36] de Bourbon contains 13 letters; so does the name Anne d’Austriche.

Louis was 13 years old when this marriage was decided on; Anne was the same age.

He was the thirteenth king of France bearing the name of Louis, and she was the thirteenth infanta of the name of Anne of Austria.

On the 23d April, 1616, died Shakspeare: on the same day of the same month, in the same year, died the great poet Cervantes.

On the 29th May, 1630, King Charles II. was born. On the 29th May, 1660, he was restored.

On the 29th May, 1672, the fleet was beaten by the Dutch.

On the 29th May, 1679, the rebellion of the Covenanters broke out in Scotland.

The Emperor Charles V. was born on February 24, 1500; on that day he won the battle of Pavia, in 1525, and on the same day was crowned in 1530.

On the 29th January, 1697, M. de Broquemar, president of the Parliament of Paris, died suddenly in that city; next day his brother, an officer, died suddenly at Bergue, where he was governor. The lives of these brothers present remarkable coincidences. One day the officer, being engaged in battle, was wounded in his leg by a sword-blow. On the same day, at the same moment, the president was afflicted with acute pain, which attacked him suddenly in the same leg as that of his brother which had been injured.

John Aubrey mentions the case of a friend of his who was born on the 15th November; his eldest son was born on the 15th November; and his second son’s first son on the same day of the same month. At the hour of prime, April 6, 1327, Petrarch first saw his mistress Laura, in the Church of St. Clara in Avignon. In the same city, same month, same hour, 1348, she died.

The deputation charged with offering the crown of Greece to Prince Otho, arrived in Munich on the 13th October, 1832; and it was on the 13th October, 1862, that King Otho left Athens, to return to it no more.

On the 21st April, 1770, Louis XVI. was married at Vienna, by the sending of the ring.

On the 21st June, in the same year, took place the fatal festivities of his marriage.

On the 21st January, 1781, was the fÊte at the HÔtel de Ville, for the birth of the Dauphin.

On the 21st June, 1791, took place the flight to Varennes.

On the 21st January, 1793, he died on the scaffold.

There is said to be a tradition of Norman-monkish origin, that the number 3 is stamped on the Royal line of England, so that there shall not be more than three princes in succession without a revolution. William I., William II., Henry I.; then followed the revolution of Stephen.

Henry II., Richard I., John; invasion of Louis, Dauphin of France, who claimed the throne.

Henry III., Edward I., Edward II., who was dethroned and put to death.

Edward III., Richard II., who was dethroned.

Henry IV., Henry V., Henry VI.; the crown passed to the house of York.

Edward IV., Edward V., Richard III.; the crown claimed and won by Henry Tudor.

Henry VII., Henry VIII., Edward VI.; usurpation of Lady Jane Grey.

Mary I., Elizabeth; the crown passed to the house of Stuart.

James I., Charles I.; Revolution.

Charles II., James II.; invasion of William of Orange.

William of Orange and Mary II., Anne; arrival of the house of Brunswick.

George I., George II., George III., George IV., William IV., Victoria. The law has proved faulty in the last case; but certainly there was a crisis in the reign of George IV. As I am on the subject of the English princes, I will add another singular coincidence, though it has nothing to do with the fatality of numbers.

It is that Saturday has been a day of ill omen to the later kings.

William of Orange died Saturday, 18th March, 1702.

Anne died Saturday, 1st August, 1704.

George I. died Saturday, 10th June, 1727.

George II. died Saturday, 25th October, 1760.

George III. died Saturday, 30th January, 1820.

George IV. died Saturday, 26th June, 1830.