SOS 
N U M B E R, 
performs this operation mull know, that feven eights and 
i'even ones make the fame number as fix tens and three 
ones ; and the knowledge of this, together with the life 
of the names in the Table, forms the whole of oft ary 
arithmetic. The learner will now divide the whole Table 
by 8 in the fame manner, and fet them down thus, learn¬ 
ing to l'peak them as under: 
77-77 ‘77. 77'77 ’77,77 
Seven min feven parvum, feven min feven minor, and 
feven min feven primo. Seven min feven parvum, feven 
min feven minor, and feven min feven. Seven min feven 
parvum fraction. 
“ He wdio will not take the pains to habituate himfelf 
to this denies himfelf the greatelt pleafure that reckoning 
man can enjoy; viz. that of doubling and halving with 
eafe and celerity to any extent, as well as the pleafure of 
abfolutely perfecting meafures and weights, and of Am¬ 
plifying the wdiole of the fciences, both of number and 
quantity, by which their acquifition will be rendered 
eafy ; by which every tyro, who vow vvaltes four years of 
his youth, at lead, in learning rules which will then be 
ufelefs, will be able to apply that precious period of his 
time to more valuable purpofes. There is not exifting 
at prefent a Angle table of any kind, nor fcarceiy any in- 
ftrument, that has not been produced for the better ac¬ 
commodation of the number ten, or of jive, the half of ten ; 
ail and each of which mud therefore fall into a gradual 
decline; and, after a long period of time, Anally Ank into 
oblivion, leaving the oftary arithmetic complete mader of 
the Aeld ! 1 have a drong conviction that this will take 
place, for this reafon : man will not long continue to work 
hard, when he can perform the fame bufinefs with eafe ; 
and it is eaAer in an immenfe ratio, becaufe the young 
dudent will have no tables to learn except his numeration 
and multiplication tables.” 
We have given thefe particulars at length from Mr. 
Richardfon’s curious and original letter. But the con- 
clufion of it, where the author mentions only “ J'ome of 
the alterations” which he propofes in fcience, is dill more 
curious, and will probably make the reader fmile : “The 
12 Agns of the zodiac are to be taken down from the 
Iky, and the 8 Agns of 45 degrees to take their place. 
The 12 months of the calendar to follow, and the 8 fec- 
tions of the year to take their place. The year in the 
new calendar to begin on the 2id of March, becaufe it 
does equal judice to both hemifpheres. The card of the 
mariner’s compafs to be made with 64. complete points ; 
the circle to be divided into 64 degrees, and the whole 
day into 64 hours; the degree and hour into 64 minutes 
both of time and fpace, and the minute of each into 64 
feconds of time by clock and watch ; the 64th of the fe^ 
cond is the third of fpace, and minor-ruler, the 64th 
Xif which is the fourth of fpace, or new inch, the 64th of 
which is the minimum of the planetarian ruler. 
“ The alteration in the weights is not the lead im¬ 
portant, as it will place them on an eternal and immutable 
bads, and the whole human race will joyfully adopt them 
as foon as they underdand planetarian menfuration. The 
weight of a cube of water, whole iide is the dandard of 
long-meafure, will be the dandard of weight, and is almod 
exaftly 1627 prefent half-grains; 512 cubic dandards All 
the planetarian bulhel, the folid content of which is 1627 
of the prefent inches, and weighs 59Ib. 20Z. 9dr. 49 half-gr. 
The bulhel is fet down in oftaries, thus, io'oo, which di¬ 
vides by 2 twenty-feven times fucceldvely without Aiadow 
of trouble. When the dandard is made of lead or copper, 
its name is the weight, not a weight; for I can allow the 
exidence of no other individual weight; the half of it 
being the half-weight, and two of them being an aggregate 
of weights. When the weight is made of derling Alver, 
it is the money; and no other piece of Alver can bear this 
name ; the piece will be divided by 2 Ax times fucceffively, 
and its fraftions bear the names of the half-money, the 
quarter-money, &c. 
“ I had forgot to mention, that the quadrant of the 
circle is no longer unity, the whole circle being a 
better unit : 64 X 64 X 64 X 64 X 64X 64 X 64- X 64 = 
281,474,976,710,656 =: One bino.” 
Nonary Scale.—I f a reprefentation of a number on 
the ternary fcale be broken at every alternate place, and 
the values of thofe periods adopted, 1 being adopted for 
01, 3 for 10, 4 for 11, &c. the whole will be converted 
into the nonary fcale. 
Example.—The expredion for 1819 on the 
ternary fcale, as we have feen at p. 304, is 
2111101, which mark od' thus, 2,11,11,01; 
and, by the rule, that number on the nonary 
fcale will be expreded by 2441, as it appears 
alfo in the margin. 
2)1819 
202 
22 
Denary Scale. —We are thus condufted by fuccedive 
advances to that fydetn of numeration which has pre¬ 
vailed among all civilized nations, and become incor¬ 
porated with the very drufture of language. Thisalrnod 
univerfal confent, clearly befpeaks the induence of fome 
common principle. Nor is it difficult to perceive that 
the arrangement of numbers by tens would naturally dow 
from the praftice fo familiar in the earlier periods of fo- 
ciety, that of counting by the dngers on both hands. 
Aridotle, in his Queries, points at this origin, hut with a 
lefs decided tone than might have been expefted from him. 
The philofopher even hints at other concurring caufes, 
fome of which appear to be very fanciful. Such, for in- 
dance, is his conjecture, that the root of the denary fcale 
might be derived from the fummation of the numbers 
one, two, three, and four, included in the Pythagorean 
tctraStys. If the original import and compofition of the 
Greek terms inzrov, yt.'Kia,, and [avqicc, for ten, a 
hundred, a thoufand, and tea thoufand, could be fafeiy 
traced, we might difcern the induence of the denary 
fyftem in the formation of thofe words. The Roman terms 
for numerals proceed not farther than mille, a thoufand ; 
but they are evidently of the fame family, with fome of 
the {lighter modidcations. 
But the origin of the names impofed on the radical 
numbers appears mod confpicuoufly difplayed in the 
nakednefs of the Aivage dialefts-. The Muyfca Indians, 
who formerly occupied the high p!ain_of Bogota in the 
province of Grenada, were accudomed to reckon Ard as 
far as ten, which they called quihicha, or a foot, meaning 
no doubt the number of toes on both feet, with which 
they commonly went bare and expofed ; and, beyond this 
number, they ufed terms equivalent to foot one, foot two. 
See. correfponding to eleven, twelve, &c. Another tribe, 
who likewife inhabit South America, the Sabiconos, call 
ten, the root of the fcale, tunca, and repeat only the fame 
word to Agnify an hundred and a thoufand ; the former 
being termed ttinea-1itnca, and the latter tunca-tunca- 
tunca. 
Etymology, guided by the fpiritof philofophy, furniAies 
a fure indrumeut for difcloAng the monuments of early 
conception, preferved, though difguifed, in the drufture 
of language. Our own dialed, as immediately derived 
from its Gothic dem, betrays a compofition not iefs rude 
orexpreffive than the Ample articulation of the Sabiconos. 
According to the authorities collected by a celebrated- 
German philologid, the late very laborious and accurate 
Adelung, the word eleven was mod anciently written 
ciniif or einlivin, being compounded of ein, or one, and 
the verb liban, “ to leave,” and therefore AgniAed merely 
one, leave; that is, “ retain one, and fet afide (no doubt) 
ten,” the root of the fcale. Twelve has the fame etymon. 
The names twenty, thirty, forty, See. have the termi¬ 
nating fyliable ty, which correfponds to zig in German, 
and zug or znch, among the olded writers of that parent 
tongue. This termination is derived from the verb 
ziehen, to draw, and hence twenty means Amply “ two 
drawings,” thirty “ three drawings,” Sec. intimating evi¬ 
dently, that fo many tens are feparated from the heap. 
The 
