805 
NUMBER. 
fecms probable, that Pythagoras was acquainted with the 
quaternary fyftem, which he brought from Egypt and 
India. Hence perhaps the myftical veneration which the 
followers of that philofopher profeffed to entertain for the 
tetmBys, or quaternion, the root of the fcale, which con¬ 
tains befides, within itfelf, the number denoting tire ele¬ 
mentary mufical proportions. Near the end of the feven- 
teenth century, Weigelius ferioufly propofed, in Germany, 
the adoption of the tetraSlic or quaternary numeration, 
which he explained, with copious detail, in a learned 
work, entitled AretologiJ'tica, printed at Nuremberg in 
1687. This writer even goes fo far as to invent names 
for the feveral orders of his TetraBic Sijjtem. They will 
appear to have a fufficiently German air, though not 
hardier than the terms we now life: 
Second Order, or 4, - 
Third Order, or 16, 
Fourth Order, or 64, 
Fifth Order, or 256, 
Sixth Order, or 1024, 
Seventh Order, or 4096, 
Eighth Order, or 16384, 
* Er ff- „ 
Zwerjf. 
- Sec/ii. 
School;. 
- Erff' Sr/ioch. 
Secht Schock. 
Schoch maid fchok. 
Example. 
5)1820 
Quinary Scale. —The quinary fyftem, or that which 
reckons by pentads, or fives, has its foundation in nature, 
being evidently derived from the practice of counting 
over the fingers of one hand. It appears accordingly, at 
a certain ftage of fociety, to have been adopted among 
different nations. Thus, the Omaguas and the Zamucas 
of South America reckon generally by Jives, which they 
call hands The Toupinambos, a molt ferocious and war¬ 
like race that inhabit the wilds of Brazil, would l'eem, ac¬ 
cording to the relation of Lery, to ufe the fame kind of 
numeration. To denominate fix, feven, and eight, thofe 
tribes only join to the word hand the names for one, two, 
and three. The fame mode, as we learn from Mungo Park, 
is prafrifed by fome African nations; particularly thejalofs 
and Foulahs, who defignate ten by two hands, fifteen by 
three hands, and fo progreflively. The quinary 
numeration feems likew.fe, at a former period, 
to have obtained in Perfia; for the word 
pentcha, which denotes Jive, is obvioufly de¬ 
rived from the radical term pendj, fignifying 
a hand. Upon this fyftem, the date of the 
enfuing year 1820, will be expreffed, as in 
the Example, by 24240. 
Senary Scale. —The fenary arrangement, or that which 
reckons by Jextads, is fpoken very flightly of by Mr. Leflie; 
but the writer of the article Notation, in Dr. Rees’s 
Cyclopaedia, does it morejuftice; truly obferving, that 
« it certainly poffeffes fome important advantages. Firft, 
the operation with this-fyftem w'ould be carried on with 
facility ; the number of places of figures for exprefting a 
number would not be very great, befides that thofe quan¬ 
tities equivalent to our decimals would be more frequently 
finite than they are in our fyftem: for example, every 
fradiion, whole denominator is not fome power of one of 
the fadlors of 10, is indefinite, and thofe only are finite 
that contain the powers of thofe fadtors; and it is exadlly 
the fame in every other fcale of notation; viz. thofe frac¬ 
tions only are finite that have denominators compounded 
of the powers of the fadiors of the radix of that fyftem ; 
therefore, in the decimal fcale, only fradtions of the form 
are finite, and in the fenary fcale the finite fradtions 
364 
O 
7 2 
4 
1 + 
2. 
2 
4 - 
O 
2 
5 * 
are of the form _ 1 — ; and, as there are neceffarily more 
2 ” 3 " 
numbers of the form 2" 3”’ within any finite limit, than 
there are of the form 2” 5 m , it follows, that in a fyftem of 
fenary arithmetic we fhould have more finite expreffions 
for fradtions than we have in the denary; andconfequently, 
on this head, the preference mull be given to the fenary 
Vol. XVII. No. 1179. 
fyftem; and indeed the only poflible objedtion 
that can be made to it is, that the operations - 
would proceed a little flower than in the de¬ 
cimal fcale, becaufe in large numbers a greater 
number of figures nnift be employed to exprefs 
them.” The foregoing date will be noted in 
the fenary fcale thus, 12232. 
The fenary arrangement feems at one period to have 
been adopted in China, at the mandate of the emperor 
Che-hoang-ti. This capricious tyrant, who murdered the 
literati and burnt their books, having conceived an aftro- 
logical fancy for the number Jix, commanded this to be 
uled in all concerns of bufinefs or learning throughout 
his vail empire. He diredded a fort of arithmetic to be 
compofed, with fix for its bafts ; and he enjoined, that all 
weights and meafures fhould be arranged on the fame 
fcale. He divided China into fix times (ix, or thirty-fix, 
provinces; and was fo much enamoured of this favourite 
number, as to order his chariot to be juft fix feet long, 
and to be drawn by fix horfes, with only fix attendants. 
Septary Scale. — If we fuppofe a feptary 
or feptenary fcale, from which we think no 
advantage could be derived, we fhould find 
the number 7777, when divided into Jeptads, 
equal to 31450. 
7)7777 
1111 
158 
22 
3 
o 
1000 
125 
0 
*5 
5 
1 
7 
0 
1 
Octary Scale. —If the binary expreffion for 1000, 
which we havefeen is mi 10x000, be divided into triplets, 
thus, 1,111,101,000, and each of thefe afterwards com- 
prefled into a fingle figure, by fubftituting the value of 
each period, or triplet, as 1 for 001, 2 for 010, 
4 for 100, 7 for in, &c. it will be converted 
into the o 61 ary fcale, and the refult will be 
1750, of which the Example in the margin, 
calculated in the uftual way, may ferve as a 
proof. 
M r. Barlow and Mr. Leflie ha ve fcarcely noticed theodlary 
fcale of numbers; but this fyftem has lately been revived 
or rather newly-modelled, by a Mr Richardfon, of Churchill 
in Somerfetfhire; an ingenious gentleman, who, we are lorry 
to fay, has been for many years totally blind. The title 
of his pamphlet, which lies before us, is “ OClary Arith¬ 
metic, or the Art of Doubling and Halving by the Cypher; 
containing a perfect Syftem of Meafure and Weight, with 
Specimens of the New Logarithms;” Loud. 181V. The 
work does not l'eem to have been much noticed by the 
public: it has been communicated to us, with fome letters 
of explanation from the author himfelf, by Mr. Snarr 
optician, of Tooley-ftreet, to whole kindnefs we have 
been indebted in fome former articles (particularly Me¬ 
chanics), and fome of whofe ingenious and laborious 
calculations we fhall introduce at the clofe of the prefent. 
Mr. Richardfon’s idea is original and bold; hut his 
ftyle is obfeure, and the new names and phrafes he in¬ 
troduces are not very harmonious. Moreover, the com¬ 
plete revolution which the introdudlion of this fyftem 
(or indeed of any other) would make in all books, rules, 
weights, meafures, and fyftems of education, makes us 
lefs fanguine than the author as to its ultimate fuccefs. 
Of this, however, we fhall leave our readers to judge, 
after they have perilled the following extradls and ex¬ 
planations. 
“ The failure of all former attempts to attain a perfedt 
fyftem of meafure and weight, has arifen from two caufes. 
ift. Our prefent mode of dividing the circle by fix chord¬ 
lines, and twelve fine-lines, which form the bafis of our 
fpace and time tables. 2d. Our common arithmetic, the 
author of which, by mifplacing his repeater, the cipher, 
has abfolutely fpoiled the art of reckoning. 
“ The number, to which we affix the unit and cipher, 
mull afford us its cube-root, or it cannot be ultimately 
fubfciffable, or femifciffable; the fquare of that number 
muft alfo afford its cube-root. But neither 6 nor the 
4 ^ fquare 
