Benefactor.

BIOGRAPHY.-No. XX.

GIBBON.

BY J. R. BEARD, D.D.

EDWARD GIBBON, the last of England's historical triumvirate, was born on the 8th of May, 1737, at Putney in Surrey. Of a tender frame, he owed his preservation and his subsequent health to the delicate, thoughtful, loving and constant care of a good aunt. Studying in the Westminster School and the University of Oxford, Gibbon laid in an ample store of sound scholarship, and so prepared the way for his classical work, the "History of the Decline and Fall of the Roman Empire,' in which he has exhausted as well as adorned every direct and collateral topic connected with his grand and imposing subject. In a very charming composition, entitled "Memoirs of my Life and Writings,' Gibbon himself has given some particulars respecting his great production, which, as being specially interesting and instructive, we shall transcribe, runring them together. "My temper is not very susceptible of enthusiasm, and the enthusiasm which I do not feel I have ever scorned to affect; but at the distance of twentyfive years I can neither forget nor express the strong emotions which agitated my mind as I approached and entered the eternal city, after a sleepless night, and trod with a lofty step the ruins of the Forum; each memorable spot where Romulus stood or Tully spoke or Cæsar fell, was at once present to my eye; and several days of intoxication were lost or enjoyed before I could descend to a cool and minute investigation. It was at Rome, on the 15th of October, 1764, as I sat musing amidst the ruins of the Capitol, while the bare-footed friars were singing Vespers in the Temple of Jupiter, that the idea of writing the decline and fall of the city first started to my mind. But my original plan was circumscribed to the decay of the city rather than of the empire, and though my reading and reflections began to point towards that object, some years elapsed, and several avocations intervened, before I was seriously engaged in the execution of that laborious work. I began gradually to advance from the wish to the hope, from the hope to the design, from the design to the execution of my historical work, of whose limits and extent I had yet a very inadequate notion. The classics as low as Tacitus, the younger Pliny and Juvenal were my old and familiar companions. I reviewed again and again the immortal works of the French and English, the Latin and Italian classics. My Greek studies maintained and extended my knowledge of that incomparable idiom. Homer and Xeno phon were still my favourite authors, I insensibly plunged into the ocean of the Augustan History, and in the descending beries I investigated, with my pen almost always in my hand, the original records, both Greek and Latin, from Dion Cassius to Ammianus Marcellinus, from the reign of Trajan to the last of the Western Caesars. The subsidiary rays of medals and inscriptions, of geography and chronology, were thrown on their proper objects; and I applied the collections of Tillemont, whose inimitable accuracy almost assumes the character of genius, to fix and arrange within my reach the loose and scattered atoms of historical information. Through the darkness of the middle ages I explored my way in the "Annals and Antiquities of Italy" of the lea...ed Muratori, and diligently

"The first volume was now ready for the press. After the perilous adventure had been declined by my friend, Mr. Elmsley, I agreed upon easy terms with Mr. Thomas Cadell, a respectable bookseller, and Mr. William Strahan, an eminent printer; and they undertook the care and risk of the publication, which derived more credit from the name of the shop than from that of the author. The last revisal of the proofs was submitted to my vigilance, and many blemishes of style, which had been invisible in the manuscript, were discovered and corrected in the printed sheet. So moderate were our hopes, that the original impression had been stinted to 500, till the number was doubled by the prophetic taste of Mr. Strahan. During this awful interval I was neither elated by the ambition of fame, nor depressed by the apprehension of contempt. My diligence and accuracy were attested by my own conscience. History is the most popular species of writing, since it can adapt itself to the highest or the lowest capacity. I had chosen an illustrious subject. Rome is familiar to the schoolboy and the statesman, and my narrative was deduced from the last period of classical reading. I am at a loss how to describe the success of the work without betraying the vanity of the writer. The first impression was exhausted in a few days; a second and a third edition were scarcely adequate to the demand. My book was on every table and almost on every toilette; the historian was crowned by the taste or fashion of the day; nor was the general voice disturbed by the barking of any profane critic. The style of the first volume is, in my opinion, somewhat crude and elaborate; in the second and third it is ripened into ease, correctness and numbers; but in the three last I may have been seduced by the facility of my pen, and the constant habit of speaking one language and writing another may have infused some mixture of Gallic idioms. Happily for my eyes, I have always closed my studies with the day, and commonly with the morning; and a long but temperate labour has been accomplished without fatiguing either the mind or body. I have presumed to mark the moment of conception; I shall now commemorate the hour of my final deliverance. It was on the day, or rather night, of the 27th of June, 1787, between the hours of eleven and twelve, that I wrote the last line of the last page, in a summer-house in my garden. After laying down my pen, I took several turns in a berceau, or covered walk of acacias, which commands a prospect of the country, the lake and the mountains. The air was temperate, the sky was serene, the silver orb of the moon was reflected from the waters, and all nature was silent. I will not dissemble the first emotions of joy on the recovery of my freedom, and perhaps the establishment of my fame. But my pride was soon humbled, and a sober melancholy was spread over my mind by the idea that I had taken an everlasting leave of an old and agreeable companion, and that whatsoever might be the future date of my history, the life of the historian would be short and precarious. I will add two facts, which have seldom occurred in the composition of six or at least five quartoes: 1. My first rough manuscript, without any intermediate copy, has been sent to the press; 2. Not a sheet has been

own.

seen by any human eyes, excepting those of the author and the printer; the faults and the merits are exclusively my Gibbon died at his dwelling, St. James's-street, London, on the 16th of January, 1794. We hope that these particulars, combined with the ensuing extracts, will lead some of our readers to the diligent perusal of the history which is the everlasting monument of his fame.

spirit of fraud for enthusiasm, whose abode is not in the heavens but in the mind of the prophet. The faith which, under the name of Islam, he preached to his family and nation, is compounded of an eternal truth and a necessary fiction--that there is only one God, and that Mahomet is the apostle of God."

MAHOMET.

"According to the tradition of his companions, Mahomet was distinguished by the beauty of his person-an outward gift which is seldom despised, except by those to whom it has been refused. Before he spoke, the orator engaged on his side the affections of a public or a private audience. They applauded his commanding presence, his majestic aspect, his piercing eye, his gracious smile, his flowing beard, his countenance that painted every sensation of the soul, and his gestures that enforced each expression of the tongue. In the familiar offices of life he scrupulously adhered to the grave and ceremonious politeness of his country: his respectful attention to the rich and powerful was dignified by his condescension and affability to the poorest citizens of Mecca; the frankness of his manner concealed the artifice of his views; and the habits of courtesy were imputed to personal friendship or universal benevolence. His memory was capacious and retentive, his wit easy and social, his imagination sublime, his judgment clear, rapid and decisive. He possessed the courage both of thought and action; and although his designs might gradually expand with his success, the first idea which he entertained of his divine mission bears the stamp of an original and superior genius. The son of Abdallah was educated in the bosom of the noblest race, in the use of the purest dialect of Arabia; and the fluency of his speech was corrected and enhanced by the practice of discreet and reasonable silence. With these powers of eloquence, Mahomet was an illiterate barbarian; his youth had never been instructed in the arts of reading and writing; the common ignorance exempted him from shame or reproach, but he was reduced to a narrow circle of existence, and deprived of those faithful mirrors which reflect to our minds the minds of sages and heroes. Yet the book of nature and of man was open to his view; and some fancy has been indulged in the political and philosophical observations which are ascribed to the Arabian traveller. He compares the nations and religions of the earth; discovers the weakness of the Persian and Roman monarchies; beholds with pity and indignation the degeneracy of the times; and resolves to unite, under one God and one king, the invincible spirit and primitive virtues of the Arabs. Our more accurate inquiry will suggest, that instead of visiting the courts, the camps, the temples of the East, the two journeys of Mahomet into Syria were confined to the fairs of Bostra and Damascus; that he was only thirteen years of age when he accompanied the caravan of his uncle, and that his duty compelled him to return as soon as he had disposed of the merchandise of Cadijah. In these hasty and superficial excursions, the eye of genius might discern some objects invisible to his grosser companions; some seeds of knowledge might be cast upon a fruitful soil; but his ignorance of the Syriac language must have checked his curiosity; and I cannot perceive in the life or writings of Mahomet, that his prospect was far extended beyond the limits of the Arabian world. From every region of that solitary world the pilgrims of Mecca were annually assembled, by the calls of devotion and commerce: in the free concourse of multitudes, a simple citizen, in his native tongue, might study the political state and character of the tribes, the theory and practice of the Jews and Christians. Some useful strangers might be tempted or forced to implore the rites of hospitality; and the enemies of Mahomet have named the Jew, the Persian, and the Syrian monk, whom they accuse of lending their secret aid to the composition of the Koran. Conversation enriches the understanding, but solitude is the school of genius; and the uniformity of a work denotes the hand of a single artist. From his earliest youth Mahomet was addicted to religious contemplation: each year, during the month of Ramazan, he withdrew from the world and from the arms of Cadijah: in the cave of Hera, three miles from Mecca, he consulted the

THE RELIGION OF THE ANCIENT GERMANS.

"The religious system of the Germans (if the wild opinions of savages can deserve that name) was dictated by their wants, their fears and their ignorance. They adored the great visible objects and agents of nature, the sun and the moon, the fire and the earth; together with those imaginary deities who were supposed to preside over the most important occupations of human life. They were persuaded that, by some ridiculous arts of divination, they could discover the will of the superior beings, and that human sacrifices were the most precious and acceptable offering to their altars. Some applause has been hastily bestowed on the sublime notion entertained by that people of the Deity, whom they neither confined within the walls of a temple, nor represented by any human figure; but when we recollect that the Germans were unskilled in architecture, and totally unacquainted with the art of sculpture, we shall readily assign the true reason of a scruple, which arose not so much from a superiority of reason, as from a want of ingenuity. The only temples in Germany were dark and ancient groves, consecrated by the reverence of succeeding generations. Their secret gloom, the imagined residence of an invisible power, by presenting no distinct object of fear or worship, impressed the mind with a still deeper sense of religious horror; and the priests, rude and illiterate as they were, had been taught by experience the use of every artifice that could preserve and fortify impressions so well suited to their own interest.

"The same ignorance, which renders barbarians incapable of conceiving or embracing the useful restraints of laws, exposed them naked and unarmed to the blind terrors of superstition. The German priests, improving this favourable temper of their countrymen, had assumed a jurisdiction, even in temporal concerns, which the magistrate could not venture to exercise; and the haughty warrior patiently submitted to the lash of correction, when it was inflicted, not by any human power, but by the immediate order of the god of war. The defects of civil policy were sometimes supplied by the interposition of ecclesiastical authority. The latter was constantly exerted to maintain silence and decency in the popular assemblies; and was sometimes extended to a more enlarged concern for the national welfare. A solemn procession was occasionally celebrated in the present countries of Mecklinburgh and Pomerania. The unknown symbol of the Earth, covered with a thick veil, was placed on a carriage drawn by cows; and in this manner the goddess, whose common residence was in the island of Rugen, visited several adjacent tribes of her worshippers. During her progress the sound of war was hushed, quarrels were suspended, arms laid aside, and the restless Germans had an opportunity of tasting the blessings of peace and harmony. The truce of God, so often and so ineffectually proclaimed by the clergy of the eleventh century, was an obvious imitation of this ancient custom.

"But the influence of religion was far more powerful to inflame, than to moderate, the fierce passions of the Germans. Interest and fanaticism often prompted its ministers to sanctify the most daring and the most unjust enterprises, by the approbation of Heaven and full assurances of success. The consecrated standards, long revered in the groves of superstition, were placed in the front of the battle; and the hostile army was devoted with dire execrations to the gods of war and of thunder. In the faith of soldiers (and such were the Germans) cowardice is the most unpardonable of sins. A brave man was the worthy favourite of their martial deities: the wretch who had lost his shield was alike banished from the religious and the civil assemblies of his countrymen. Some tribes of the north seem to have embraced the doctrine of transmigration, others imagined a gross paradise of immortal drunkenness. All agreed, that a life spent in arms, and a glorious death in battle, were the best preparations for a happy futurity, either in this or in another world."

S. If 55 tons of hemp cost £660, what will 220 tons cost at

ANALYSIS.

THE term Analysis, in physical science, signifies the resolving of a compound body into its elements, or component parts. ANALYSIS, in arithmetic, signifies the resolving of numbers into the factors of which they are composed, and the tracing of the relations which they bear to each other.

In the preceding lessons the student has become acquainted with the method of analysing particular examples and combinations of numbers, and thence deducing general principles and rules. But analysis may be applied with advantage not only to the development of mathematical truths, but also to the solution of a great variety of problems, both in arithmetic and practical life. Indeed, it is the method by which business men generally solve practical questions. A little practice will give the student great facility in its application.

No specific directions can be given for solving examples by analysis. None, in fact, are requisite. The judgment, from the "onditions of the question, will suggest the process. Hence lysis may, with propriety, be called the COMMON SENSE

RULE.

In solving questions analytically, it may be remarked in general that we reason from the given number to 1, then from 1 to the number required.

Ex. 1. If 60 yards of cloth cost 240 crowns, what will 85 yards cost?

Analytic Solution.-Since 60 yds. cost 240 crowns, 1 yd. will cost of 240 crowns; and of 240 crowns is 4 crowns, or £1. Now, if 1 yd. costs 4 crowns, 85 yds. will cost 85 times As much; and 4 crowns X 85-340 crowns, or £85. Ans.

Or, we may reason thus: 85 yds. are of 60 yds.; therefore, 85 yds. will cost of 240 crowns (the cost of 60 yds.), and of 240 crowns is 240 crowns X-340 crowns, or £85, the same as before.

Other solutions of this example might be given; but our present object is to show how this and similar questions may be solved by analysis. The former method is the simplest and most strictly analytic, though not so short as the latter. It contains two steps:

First, we separate the given price of 60 yds. (240 crowns) into 60 equal parts, to find the value of 1 part, or the cost of 1 yd., which is 4 crowns.

Second, we multiply the price of one yd. (4 crowns) by 85, the number of yds. whose cost is required, and the product is the answer sought.

This and similar questions are usually placed under the rule of Simple Proportion, or the Rule of Three.

The operation of solving a question by analysis, is called an analytic solution. In working the following examples, each one should be analysed, and the reason for every step given in full. 2. A man bought a horse, and paid £45 down, which was of the price of it: what did he give for the horse?

Analysis. Since £45 is of the price, the question resolves itself into this: £45 is of what sum? If £45 is of a certain sum,is of £45; and of £45 is £9. Now, if £9 is 1 seventh, 7 sevenths are 7 times as much; and £9×7=£63. Ans. £63.

PROOF. of £63 £9, and 5 sevenths are 5 times as much, which is £45, the sum he paid down for the horse.

In solving examples of this kind, the learner is often perplexed in finding the value of, etc. This difficulty arises from supposing that if of a certain number is 45, of it must be of 45. This mistake will be easily avoided by substituting in his mind the word parts for the given denominator. Thus, if 5 parts cost £45, 1 part will cost of £45, which is £9. But this part is a seventh. Now, if 1 seventh cost £9, then 7 sevenths will cost 7 times as much.

3. If 40 bales of wool cost £120, how much will 100 bales cost? 4. Bought 35 tons of hay for £70: how much will 16 tons cost?

5. What is the cost of 37 gallons of rum, at £21 a hogshead? -6. What is the cost of 1,500 pounds of rice, at £14 per ton? 7. What is the cost of 18 quarts of chestnuts, at 3 crowns a bushel?

9. If 165 bushels of apples cost £32, how much will 31 bushels cost?

10. If 72 bushels of peas cost 253 crowns, what will a pint cost at the same rate?

11. If 150 acres of land cost £7,000, what will a square rood cost?

12. If 2 pipes of wine cost £315, what is that per gill? 13. A farmer bought a yoke of oxen, and paid £40 in ready money, which was of the cost: what did they cost?

14. Bought a house, and paid £630 in goods, which was of the price of it: what was the cost of the house?

15. A young man lost £256 by gambling, which was is of all he was worth: how much was he worth?

16. A man having £1,500, paid of it for 112 acres of land: how much did his land cost per acre?

17. If a stack of hay will keep 350 sheep 90 days, how long will it keep 525 sheep?

18. If 440 barrels, of flour will last 15 men 55 months, how long will the same quantity last 28 men?

19. If 136 men can build a warehouse in 120 days, how long will it take 15 men to build it?

20. If of a pound of tea cost 1s. 8d., what will † of a pound cost?

21. If of a yard of broadcloth cost 8s. 6d., how much will of a yard cost?

22. Bought of a ton of hay for £3 5s.: how much will of a ton cost?

23. Bought of a hogshead of molasses for £38: how much will of a hogshead cost?

24. If of an acre of land cost £108, how much will of an acre cost?

25. If of a barrel of flour cost £2 10s., how much will of a barrel cost?

26. Paid £4,200 for of a vessel: how much can I afford to sell of the vessel for?

27. Sold 18 baskets of peaches for 34 crowns: how much would 651 baskets come to?

28. If I pay £12 10s. for building 20 rods of wall, how much must I pay for 215 rods?

29. A man can hoe a field of corn in 6 days, and a boy can hoe it in 9 days: how long will it take them both together to hoe it?

Analysis. Since the man can hoe the field in 6 days, in 1 day he can hoe of it; and since the boy can hoe it in 9 days, in 1 day he can hoe of it; consequently, in 1 day they can both hoe + of the field. Now, if of the field requires them both 1 day, of it will require them of a day, and will require them 18 times as long, or of a day, which is equal to 3 days. Ans.

30. If A can chop a quantity of wood in 4 hours, and B in 6 hours, how long will it take them both to chop the same quantity?

31. A can dig a trench in 6 days, B in 9 days, and C in 12 days: how long will it take all of them together to dig it? 32. A man bought 25 pounds of tea at 6s. a pound, and paid for it in corn at 4s. a bushel: how many bushels did it take?

Analysis.-If 1 lb. of tea costs 6s., 25 lbs. will cost 25 times as much, which is 150s. Again, if 48. will buy 1 bushel of corn, 150s. will buy as many bushels as 4s. is contained times in 150s.; and 1508.4-37. Ans. 37 bushels.

The last and similar examples are frequently arranged under the rule of Barter.

Barter signifies an exchange of articles of commerce at prices agreed upon by the parties.

Such examples are so easily solved by Analysis that a specific rule for them is unnecessary.

33. A cheesemonger bought 110 lbs. of sugar at 4d. a pound, and paid for it in lard at 8d. a pound: how much lard did it take?

34. How much butter, at 12 d. a pound, must be given for 250 lbs. of tea, at 3s. a pound?

35. How many pounds of tea, at 2s. 6d. per pound, must be given for 56 yds. of cloth, at 4s. 3d. per yard?

36. How many pairs of boots, at 15s. a pair, must be given for 50 tons of coal at £1 10s. per ton?

37. A, B, and C, united in business; A put in £250 · B

When two or more individuals associate themselves together for the purpose of carrying on a joint business, the union is called a partnership or copartnership.

The process by which examples like the last one are solved, is often called Fellowship.

38. A and B join in a speculation: A advances £1,500 and B £2,500; they gain £1,200: what was each one's share of the gain?

39. A, B, and C, entered into partnership; A furnished £3,000, B £4,000, and C £5,000; they lost £1,800: what was each one's share of the loss?

40. A's stock is £4,200; B's £3,600; and C's £5,400; the whole gain is £2,400: what is the gain of each ?

41. A's stock is £7,560; B's £8,240; C's £9,300; and D's £6,200; the whole gain is £625: what is the share of each ? 42. A bankrupt owes one of his creditors £400; another £500; and a third £600; his property amounts to £1,000: how much can he pay in the pound; and how much will each of his creditors receive?

The solution of this example is the same in principle as that of Ex. 37.

Examples like the preceding are commonly arranged under the rule of Bankruptcy.

A bankrupt is a person who is insolvent, or unable to pay his just debts.

43. A bankrupt owes £5,000, and his property is worth £3,500: how much can he pay in the pound?

44. A man died owing £1,640, and his effects were sold for £410: how much per cent. did his estate pay?

45. If a man owes A £624, B £876, and C £900, and has but £1,150, how much will each creditor receive?

46. If I owe £4,800, and have property to the amount of £3,200, how much per cent. can I pay?

47. How much. per cent. can a man pay, whose liabilities are £12,000, and whose assets are £4,500?

48. How much per cent. can a man pay, whose liabilities are £150,000, and whose assets are £15,000?

It often happens in storms and other casualties at sea, that masters of vessels are obliged to throw portions of their cargo overboard, or sacrifice the ship and their crew. In such cases, the law requires that the loss shall be divided among the owners of the vessel and cargo, in proportion to the amount of each one's property at stake.

The process of finding each man's loss, in such instances, is called General Average.

The operation is the same as that in solving questions in bankruptcy and partnership.

49. A, B, and C, freight a ship from Liverpool to New York; A had on board 100 tons of iron, B 200 tons, and C 300 tons; in a storm 240 tons were thrown overboard: what was the loss of each?

50. A packet worth £36,000 was loaded with a cargo valued at £65,000. In a tempest the master threw overboard £25,250 worth of goods: how much per cent. was the general average? 51. A steam ship being in distress, the master threw of the cargo overboard; finding she still laboured, he afterwards threw overboard of what remained. The steamer was worth £12,000, and the cargo £24,000: how much per cent, was the

The mixture=60 bu.

60s., 60s., 66

66

corn; 66 oats.

and 270s., value of whole mixtr.

Now, if 60 bu. mixture are worth 270s., 1 bu. mixture is worth of 270s., and 270s.-60-418. Ans.

PROOF.-60 bu. at 4s. 270s., the value of the whole mixture.

The process of finding the value of a compound or mixture of articles of different values, or of forming a compound which shall have a given value, is called Alligation. Alligation is usually divided into two kinds, Medial and Alternate.

When the prices of the several articles and the number or quantity of each are given, the process of finding the value of the mixture, as in the last example, is called Alligation Medial.

When the price of the mixture is given, together with the price of each article, the process of finding how much of the several articles must be taken to form the required mixture, is called Alligation Alternate. Alligation Alternate embraces three varieties of examples, which will be pointed out in the following notes.

53. If you mix 40 gallons of sperm oil worth 8s. per gallon, with 60 gallons of whale oil worth 3s. per gallon, what will the mixture be worth per gallon?

54. At what price per pound can a grocer afford to sell a mixture of 30 lbs. of tea worth 4s. a pound, and 40 lbs. worth 7s. a pound?

55. If 120 lbs. of butter at 10d. a pound are mixed with 24 lbs. at 8d. and 24 lbs. at 5d. a pound, what is the mixture worth?

56. A tobacconist has three kinds of tobacco, worth 3s. 9d.,. 4s. 6d., and 6s. 3d. a pound: what is the mixture of 100 lbs. of each worth per pound?

57. A liquor dealer mixed 200 gallons of gin worth £1 a gallon, with 100 gallons of brandy worth £1 5s. a gallon:: what was the value of the mixture per gallon?

58. A grocer sells the finest souchong tea at 10s. a pound;, and hyson at 48.: what part of each must be taken to form a mixture which he can afford to sell at 68. a pound?

Note.-1. It will be observed in this example that the priceof the mixture and also the price of the several articles or ingredients are given, to find what part of each the mixture must contain.

Analysis. Since the souchong is worth 10s. and the required mixture 68., it is plain he would lose 48. on every pound of souchong which he puts in. And since the hyson is worth 48. a pound and the mixture 68., he would gain 28. on every pound of hyson he puts in. The question, then, is this: How much hyson must he put in to make up for the loss on 1 lb. of souchong? If 2s. profit require 1 lb. of hyson, 48. profit will require twice as much, or 2 lbs. He must, therefore, put in 2 lbs. of hyson to 1 lb. of souchong.

PROOF.-2 lbs. of hyson, at 48. a pound, are worth 8s., and 1 lb. of souchong is worth 10s. Now 8s.+108.-188. And if 3 lbs. mixture are worth 188., 1 lb. is worth of 18s., which is 6s., the price of the mixture required.

59. A farmer has oats which are worth 208. a quarter, rye 55s., and barley 60s., of which he wishes to make a mixture worth 50s. per quarter: what part of each must the mixture contain?

Analysis. The prices of the rye and barley must each be compared with the price of the oats. If 1 quarter of oats gains 30s. in the mixture, it will take as many quarters of rye to balance it, as 5s. (the loss per quarter) are contained times in 30s., viz. 6 quarters. Again, since 1 quarter of oats gains 30s., it will take as many quarters of barley to balance it, as 10s. (the loss per quarter) are contained times in 30s., viz. 3 quarters. Hence, the mixture must contain 2 parts of oats, 6 parts rye, and 3 parts barley.

60. If a man have four kinds of currants worth & 9 11 and