业 Remarks on the multiplication NUMBERS. "The sons of Judah were Shelah, Pharez, and Zerah. His grandsons by Pharez were Hezron and Hamul. Hezron had two sons. Suppose each of them had six children, which will make 12 for the first generation; to eight of whom allow eight children, and nine to each of the others, and there will be 100 for the second generation. To 92 of these then give 18 children, and 19 to the eight others; this will produce for the third generation 1,808. If we then suppose that 1,800 of these had each 18 children, and that each of the other eight had 19, the fourth generation will be 32,552, which, added to the product of the third, will make the descendants of Hezron amount to 34,360. "Hamul had two sons, who, multiplied by 10, produce the number of 20 for the second generation : these, multiplied by 20, will make 400 for the third, and these again by 25 will produce 10,000 for the fourth. And thus the two last generations will amount together to the number of 10,400. "If we allow five sons to Shelah, and six to Zerah, we shall have 11 for the first generation. To three of whom allow 10 children and 11 to the other eight, this will give us 118 for the second: To 113 of these give 14, and 15 to the other five, and 1657 will be produced for the third. Give 17 to 1643, and 18 to the 14 remaining, and for the fourth there will be 28,183. The third and fourth added together will produce the number of 29,840. "According to this calculation, all these generations will amount to the following numbers : Hezronites Hamulites Shelanites and Zarhites V.-ISSACHAR 54,400. of the Israelites. generation will be 51,378; the third and fourth generations, then, will produce a number of 54,400. VI.-ZEBULUN 57,400. "Zebulun had three sons. If we suppose that two of them had in all fourteen children, and the third, six, here will be 20 for the first generation. The second will produce 143, on multiplying, 17 by 7, and 3 by 8. If we multiply 135 by 16, and 8 by 17, the third will amount to 2,296. By multiplying the third by 24, the fourth will give us 55,104. The two last will produce, together, 57,400. Amount of generations III. and`IV. II. Ditto multiply 10 by 11 10 110 990 - 11,880 12,870 1 8 80 960 1,040 All these generations added together, amount to 41,500 34,360 10,400 29,840 IX.-JOSEPH. II. Ditto multiply 6 by 13, and 4 by 14 Amount of generations III, and IV. ISSACHAR had five sons. Suppose that three of sons, and each of the other four had 18, the fourth "I. Generation II. Ditto multiply by 10 Amount of generations III. and IV. 625,850" Amount of generations III. and IV. "I. Generation XI. DAN 62,700. II. Ditto multiply by 12 III. Ditto multiply by 19 IV. Ditto multiply by 24 Amount of generations III. and IV. XII. NAPHTALI 53,400. 35,400 The Levites (chap. iii. 39) amount to "He had 4 sons, the half of whom, multiplied 7, and the other half by 6, give us for the I. Generation II. Ditto multiply 16 by 11, and 10 by 12 III. Ditto multiply 288 by 12, and 8 by 13 IV. Ditto multiply by 14. Amount of generations III. and IV. 11 26 296 3,560 - 49,840 The whole number together, as above In the above calculations, Scheuchzer and Reyher 132 take for granted, 1. That from the going down to 2,508 Egypt to the exodus there were four generations. -60,192 2. That the first two generations had died in Egypt. 3. That the promise of God in multiplying them as the 62,700 stars of heaven, had taken place particularly in the two last generations. 4. That these two last generations alone form the aggregate sums given in the sacred by text. 5. That their method of accounting for this aggregate through the four generations, is not only perfectly natural and mathematical, but strictly accordant with the promises made by God to them, as the sum of each tribe sufficiently proves. 6. That the whole account shows the truth of the Divine promise, the great accuracy of the Jewish lawgiver, and a proof of the inspiration of the sacred writings. But even to these calculations and deductions there may be objections, e. g., "Scheuchzer gives to 2,508 families of Dan, 24 male children, each above the age of 20: we may fairly allow an equal number of females, and add 5 more under 20, as in the note under Exod. xii. 37, and we have 53 children on the average through all the families of a tribe; whilst to 4,425 families of Benjamin are allotted 7 males aged 20, and adding 7 females at 5 children, we have 19 children in each family; a tolerable number; but apparently more reasonable than the other."-ANON. 53,400 Moses commanded to teach the Israelites how they are to pitch their tents, and erect the ensigns of their fathers' houses, 1, 2. Judah, Issachar, and Zebulun, on the EAST, amounting to 186,400 men, 3-9. Reuben, Simeon, and Gad, on the soUTH, with 151,450 men, 10-16. The Levites to be in the midst of the camp, 17. Ephraim, Manasseh, and Benjamin, on the WEST, with 108,100 men, 18–24. Dan, Asher, and Naphtali, on the NORTH, with 157,600 men, 25-31. The sum total of the whole, 603,550 men, 32. But the Levites are not included, 33. The people do as the Lord commands them, 34. Ijar or Zif. saying, pitch by his own standard, with b far off about the tabernacle of 2 Every man of the children of Israel shall the congregation shall they pitch. A. M. 2514. An. Exod. Isr. 2. their camp in the wilderness. As God gave them the Verse 2. Every man—shall pitch by his own stand-plan, it was doubtless in every respect perfect; and ard] Commentators, critics, philosophers, and profes-fully answered the double purpose of convenience and sional men, have taken a great deal of pains to illustrate this chapter by showing the best method of encampment for such a vast number of men, and the manner in which they conceive the Israelites formed security. Scheuchzer has entered into this subject with his usual ability, and in very considerable detail. Following the plan of Reyher, as in the preceding chapter, he endeavours to ascertain the precise order 14 Then the tribe of Gad: and the captain of the sons of Gad shall be Eliasaph the son num-off Reuel. 4 And his host, and those that were bered of them, were threescore and fourteen thousand and six hundred. 5 And those that do pitch next unto him shall be the tribe of Issachar: and Nethaneel the son of Zuar shall be captain of the children of Issachar. 6 And his host, and those that were numbered thereof, were fifty and four thousand and four hundred. 7 Then the tribe of Zebulun: and Eliab the son of Helon shall be captain of the children of Zebulun. 8 And his host, and those that were numbered thereof, were fifty and seven thousand and four hundred. 15 And his host, and those that were numbered of them, were forty and five thousand and six hundred and fifty. 16 All that were numbered in the camp of Reuben were a hundred thousand and fifty and one thousand and four hundred and fifty, throughout their armies " And they shall set forth in the second rank.. h 1 17 Then the tabernacle of the congregation shall set forward with the camp of the Levites in the midst of the camp: as they encamp, so shall they set forward, every man in his place by their standards. 18. On the west side shall be the standard of the camp of Ephraim, according to their ar9 All that were numbered in the camp of mies: and the captains of the sons of Ephraim Judah were a hundred thousand and four-shall be Elishama the son of Ammihyd. score thousand and six thousand and four 19 And his host, and those that were numhundred, throughout their armies. These bered of them, were forty thousand and five shall first set forth. hundred. 10 On the south side shall be the standard of the camp of Reuben according to their armies and the captain of the children of Reuben shall be Elizur the son of Shedeur, 11 And his host, and those that were numbered thereof, were forty and six thousand and five hundred. 12 And those which pitch by him shall be the tribe of Simeon and the captain of the children of Simeon shall be Shelumiel the son of Zurishaddai, . 20 And by him shall be the tribe of Manasseh: and the captain of the children of Manasseh shall be Gamaliel the son of Pedahzur. - 21 And his host, and those that were numbered of them, were thirty and two thousand and two hundred. 22 Then the tribe of Benjamin and the captain of the sons of Benjamin shall be Abidan, the son of Gideoni. 23 And his host, and those that were num d Chap. x. 14; Ruth iv. 20; 1 Chron. ii, 10; Matt. i. 4; Luke Deuel; chapter i. 14; vii. 42, 47; x. 20.iii. 32, 33. - Chap. x, 14. in which the several tribes were disposed; and as his work is both scarce and dear, the reader will not be displeased to meet here with a translation of all that refers to the subject. Chap. x. 17, 21. Chap. x. 18. which we inhabit, where every thing is formed in order, number, weight, and measure; and in all bodies, great and small. It is certain that Noah's ark is a perfect model of naval architecture. The temple of Solomon, and that of Ezekiel were likewise masterpieces in their kind. But at present we are to consider the Divine arrangement of the Israelitish camp, and the manner in which it was formed. "The Israelitish army was divided into three principal divisions. The first, which was the least in extent, but the strongest and the most powerful, occupied the centre of the army: this was the throne of God, i. e., the TABERNACLE. The second, which was composed of the priests and Levites, surrounded the 26 And his host, and those that were num-fathers: all those that were numbered of the camps throughout their hosts were six hundred thousand and three thousand and five hundred and fifty. 33 But the Levites were not numbered among the children of Israel; as the LORD 27 And those that encamp by him shall be 29 Then the tribe of Naphtali: and the 34 And the children of Israel did according to all that the LORD commanded Moses: " so they pitched by their standards, and so they set forward, every one after their families, according to the house of their fathers. ם. Gen. xlix. 14; to ZEBULUN a ship, Gen. xlix. 13; to REUBEN a river, Gén. xlix. 4, (others give Reuben the figure of a man ;) to SIMEON a sword, Gen. xlix. 5; to GAD a lion, Deut. xxxiii. 20; to Ephraim a unicorn, Deut. xxxiii. 17; an or to MANASSEH, Deut. xxxiii. 17; a wolf to BENJAMIN, Gen. xlix. 27; and a serpent to DAN, Gen. xlix. 17, though others give him an eagle. In short, they pretend that the ensign of ASHER was a handful of corn, Gen. xlix. 20, and that of NAPHTALI a stag, Gen. xlix. 21. Chap. x. 22.- Chap. x. 25.- Exod. xxxviii. 26; chap. i. 46; xi. 21.- Chap. i. 47.- - Chap. xxiv. 2, 5, 6. first. The third, and the farthest from the centre, colours, and the figures or arms, of the very ensigns. took in all the other tribes of Israel, who were at They pretend that on that of JUDAH a lion was painted, least about a mile from the tabernacle. t For it ap- with this inscription: Rise, Lord, let thine enemies pears from Josephus, iii. 4, that the nearest approach be dispersed, and let those that hate thee flee before they dared make to the ark, except during the time thee;' and they found this description of Judah's enof worship, was a distance of 2,000 cubits. The re-sign in Gen. xlix..9. They give to Issachar an ass, verence due to the Divine Majesty, the numerous army of the Israelites, composed of 600,000 soldiers, with their families, which made about 3,000,000 souls, naturally demanded a considerable extent of ground. We are not to imagine that all these families pitched their tents pellmell, without order, like beasts, or as the troops of Tartary, and the eastern armies; on the contrary, their camp was divided according to the most exact rules. And we cannot even doubt that their camp was laid out, and the place of every division and tribe exactly assigned by some engineers, or geometricians, before the army stopped to encamp, in order that every person might at once find his own quarter, and the road he ought to take to reach the other tents. "Four divisions, which faced the four quarters of the heavens, each with his own ensign, formed the centre of the army. JUDAH was placed on the east, and under him he had Issachar and Zebulun; on the south was REUBEN, and under him Simeon and Gad: on the west was EPHRAIM, and under him Manasseh and Benjamin; finally, DAN was on the north, and he had under him Asher and Naphtali. It has been pretended by some that these four principal divisions were not alone distinguished by their ensigns, but that each particular tribe had likewise its standard or ensign. On this subject we might refer to the Talmudists, who have gone so far as to define the "To prove that the sums here are correctly added, we have but to join together the detached numbers, and see if they agree with the total. The text will furnish us with an example of this: there was in the quarter of Judah 186,400 ver. 9. Reuben 151,450 ver. 16. Ephraim 108,100 ver. 24. 157,600 ver. 31. Among other things we must remark that rule of military tactics which requires that the advanced and rear guards should be stronger than the centre. "In a well-regulated camp, cleanliness is considered indispensably necessary; this is particularly remarkable in the Israelitish army, where the most exact order was maintained. Hence every person who had Remarks on the NUMBERS. castrametation of the Israelites. any kind of disease, and those who were reputed un- | trance of the Israelitish camps. See the note on clean, were forbidden to enter it; Num. v. 2, 3; Exod. xxxii. 27. Deut. xxiii. 10. "Those who have the health of men, and of a whole army confided to them, are not ignorant that diseases may be easily produced by putrid exhalations from excrementitious matter; and that such matter will produce in camps pestilential fevers and dysenteries. For this reason, care should be always taken that offices, at a distance from the camp, be provided for the soldiers, and also that those who are sick should be separated from the others, and sent to hospitals to be properly treated. "In military tactics we find two distinct wings spoken of; the right and the left. The Israelitish army not only had them on one side, as is customary, but on all their four sides. On the eastern side, the tribe of Issachar formed the right, that of Zebulun the left, and that of Judah the centre. On the south, Simeon formed the right wing, Gad the left, and Reuben the centre, Towards the west, Manasseh composed the right, Benjamin the left, and Ephraim the centre. And on the north, Asher was on the right wing, Naphtali on the left wing, and Dan in the centre. Notwithstanding this, however, the army was not in danger of being easily broken; for evéry tribe being numerous, they were supported by several ranks, in such a manner that the first being broken, the second was capable of making resistance; and if the second gave way, or shared the same fate as the first, it found itself supported by the third, and so on with the rest. The square form in which the Jewish army was ordinarily placed, was the very best for security and defence. The use and importance of the hollow square in military tactics is well known. "For so large a multitude of people, and for so numerous an army, it was needful that all the necessary artícles of life should be prepared beforehand, or be found ready to purchase. In these respects nothing was wanting to the Israelites. Their bread came down to them from heaven, and they had besides an abundance of every thing that could contribute to magnificence. If we may credit Josephus, they had amongst them public markets, and a variety of shops. Ant., 1. iii. c. 12, sec. 5. The tabernacle being erected, it was placed in the midst of the camp, each of the three tribes stretching themselves on the wings, and leaving between them a sufficient space to pass. "It was, says Josephus, like a well appointed market where every thing was ready for sale in due order, and all sorts of artificers kept their shops; so that this camp might be considered a movable city. "In Exod. xxxii. 27 we likewise find that mention is made of the gates of the camp: Put every man his sword by his side, and go in and out from gate to gate throughout the camp.' From whence we may certainly conclude that if the camp had gates, the Israelites had also sentinels to guard them. If this be true, we may also believe that they were surrounded with entrenchments, or that at least their gates were defended by some fortifications. Sagittarius (de Jan. Vet., c. 18. § 10) pretends that the tabernacle was not only guarded by the Levites, but that there were likewise sentinels at the gates, and at the en "If we examine and compare the camp of Israel with that of our most numerous armies, which in these days are composed of 100,000 or of 150,000 men. we cannot but consider it of vast extent. The Jews say it was twelve miles in circumference; this is not at all improbable, and consequently the front of each wing must be three miles in extent. But taking in the tents, the soldiers and their numerous families, the beasts of burden, the cattle, and the goods, it certainly must have formed a very considerable inclosure, much more than twelve miles. See the notes on Exod. xii. 37, and xiii. 18. Reyher (Math. Mos., p. 568) assigns to the 74,600 Which makes square cubits. "We must observe that we are here merely speaking of the ground which the soldiers of this tribe occupied whilst remaining close to each other in their ranks, and that in this computation there is but one cubit square allowed for each man; wherefore, if we take in the arrangement of the soldiers, the tents, the necessary spaces, the families, the beasts of burden, and the movables, a much larger extent of ground is requisite. All those circumstances do not come into Reyher's calculation. He continues thus:— For the tribe of ISSACHAR, cubits in breadth in length |