N U M 
again counted 9 perfons in each row, entertained no'fuf- 
picion of what had taken place. But 4 more men were 
introduced; and the abbefs, again counting 9 perfons in 
each row, retired in the full perfuafion that no one had 
either gone out or come in. How was all this poffible ? 
This problem may be eafily lolved by infpefting the 
four following figures ; the firft of which reprefents the 
original difpofition of the counters in the cells of the 
fquare ; the fecond, that of the fame counters when 4 
are taken .away; the third, the manner in which they 
mud be difpofed when thefe 4 are brought back with 4 
others ; and the fourth, that of the fame counters with 
the addition of 4 more. It is here evident that there are 
always 9 in each external row ; and yet, in the firft cafe, 
the whole number is 24, while in the fecond it is 20, in 
the third 28, and in the fourth 32. 
It would feem that Ozanam had not obferved that thefe 
variations might have been carried ftill farther; that 4 
men more might have been introduced into the convent, 
without the abbefs perceiving it; and, that all the men 
might have afterwards gone out with fix nuns, fo as to 
leave only 18, inftead of the 24 who were in the cells at 
firft. The poflibility of this will appear, by infpefting the 
two following figures: 
It is almoft needlefs to explain in what manner the il- 
lufion of the good abbefs arofe. It is becaufe the num¬ 
bers in the angular cells of the fquare were counted twice; 
thefe cells being common to two rows. The more, there¬ 
fore, the angular cells are filled, by emptying thofe in the 
middle of each row, thefe double enumerations become 
o-reater; on which account the number, though dimi- 
niflied, appears always to be the fame ; and the contrary 
is the cafe, in proportion as the middle cells are filled, 
by emptying the angular ones. 
The works confulted in the compilation of this article 
are —Phil. Tranf. abr. vol. viii. p. 32-41/ Leflie’s Philo- 
fophy of Arithmetic, 1817, the fubftance of which is in 
the Ency. Supp. art. Arithmetic. Gent. Mag. 1768. 
Franklin’s Works. Ozanam’s Math. Recreations, Mon- 
tucla’s edit, tranftated by Dr. Hutton. Tranf. of the Soc. 
of Arts, vol. xxx. Archseologia, vol. x. Remains of 
Japhet. Patrick’s Chart of Numerals, in 200 Tongues, 
1812. Barlow’s Inveftigation of the Theory of Numbers, 
1811. Legendre’s Effai fur la Theorie des Nombres, 4to. 
Paris edit, of 1815. Edinburgh Review, N° 35. Richard- 
fon’s 06 tary Arithmetic, and private communication. 
Snart’s Power of Numbers, and private communications. 
Chronological Tracts, 1819. 
NUM'BER,/ Many, more than one.—Much of that 
we are to fpeak may feem to a number perhaps tedious, 
perhaps obfcure, dark, and intricate. Hooker. —Water- 
lily hath a root in the ground ; and fo have a number of 
other herbs that grow in ponds. Bacon. —Ladies are al¬ 
ways of great ufe to the party they efpoufe, and never 
fail to win over numbers. Addifon. —Multitude that may 
be counted.—Of him came nations and tribes out of num¬ 
ber. 2 EJd. iii. 7.—Loud as from numbers without num¬ 
ber. Milton. —Comparative multitude.— Number itfelf im- 
porteth not much in armies, where the people are of 
weak courage: for, as Virgil fays, it never troubles a 
wolf how many the Iheep be. Bacon .—Aggregated mul- 
Vol. XVII. No. xi 80. 
N U M 329 
titude.—If you will, fome few of you (hall fee the place; 
and then you may fend for your lick, and the reft of 
your number which ye will bring on land. Bacon's New 
Atlantis. —Sir George Summers, fent thither with nine 
fhips and five hundred men, loft a great part of their 
numbers in the ifle of Bennudaz. Heylin. —Harmony; pro¬ 
portions calculated by number : 
They, as they move 
Their (tarry dance, in numbers that compute 
Days, months, and years, tow’rds his all-cheering lamp 
Turn fwift. Milton's P. L. 
Verfes ; poetry: 
Then feed on thoughts that voluntary move 
Harmonious numbers, as the wakeful bird 
Sings darkling. Milton's P. L. 
Yet (hould the mufes bid my numbers roll 
Strong as their charms, and gentle as their foul. Pope. 
In grammar. The variation or change of termination to 
fignify more than one.'—How many numbers is in nouns ? 
Shakefpeare's M. IV. of Wind/or. 
GOLDEN NUMBER. See the article Chronology, 
vol. iv. p. 537. 
NUM'BERER, J". He who numbers. 
NUM'BERFUL, adj. Many in number. Not in ufe .— 
About the year 700, great was the company of learned 
men of the Englilh race ; yea, fo numberfull, that they 
upon the point excelled all nations in learning, piety, and 
zeal. Waterhoiije's Apol. for Learning, 1653. 
NUM'BERLESS, adj. Innumerable; more than can be 
reckoned.—The foul converfes with numberlej's beings of 
her own creation. AddiJ’on. 
About his chariot numberlefs were pour’d 
Cherub and feraph. Milton's P. L. 
Travels he then a hundred leagues, 
And fuffers numberlej’s fatigues. Swift's MiJ'cellanies. 
NUM'BERS, a canonical book of the Old Teftament, 
one of the five books called the Pentateuch, and afcribed 
juftly, as we conceive, to Mofes.—This book is called by 
the name of Numbers in our language, becaufe it begins 
with an account of the numbering of the people in the 
beginning of the fecond year after they came out of 
Egypt: though it contains a great many things befides 
that; particularly another numbering of them (ch. 26.) 
towards the conclufion of their travels in the wildernefs. 
Bp. Patrick on Numbers. 
The Book of Numbers contains the hiftory of the 
journeys of the Hebrews in the defert, including about 
thirty-nine years. It relates the hiftory of the numbers, 
ftation, and marching-order, of the various tribes, and 
of the offerings of their princes at the dedication of the 
tabernacle; the confecration of the levites; the obfer- 
vance of the fecond paffover; the inftitution of the el¬ 
ders ; the deftru&ion of the people by a fiery plague, and 
by the quails they lulled for; Miriam’s leprofy; the 
fearch and contempt of Canaan, and the begun punifh- 
ment thereof; the punifhment of Korah and his compa¬ 
nions, and the plague among the people for quarrelling 
thereat; the budding of Aaron’s rod; Mofes and 
Aaron’s mifbehaviour, when the people murmured at 
Kadefh ; the death of Miriam and Aaron; the plague 
and cure of the bites of fiery ferpents ; the conqueftand 
divifion of the kingdom of Sihon and Og; the oft-de¬ 
feated attempts of Balak and Balaam to curie Ilrael; the 
Hebrews enticement to whoredom and idolatry by 
the Midianitifh women, and the revenge thereof in the 
death of 24,000 Hebrews, and the almoft total ruin of the 
Midianitifh nation ; a delineation of the borders of Ca¬ 
naan, and an appointment of twelve perfons to divide 
it. With thefe narratives are mixed a variety of laws 
concerning fufpicion of adultery, nazaritefhip, blefting 
of the people, chap. v. vi. concerning the lighting of the 
lamps, obfervance of the paffover in the fecond month, 
4 P blowing 
