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Full text of "The decimal system in numbers, coins, and accounts : especially with reference to the decimalisation of the currency and accountancy of the United Kingdom"

Digitized by the Internet Archive 

in 2007 with funding from 

-Microsoft Corporation 



http://www.archive.org/details/decimalsysteminnOObowruoft 





Tt 






^J 




SIR JOHN BOWR1NG, LL.D. 



THE 



DECIMAL SYSTEM 



IN NUMBEES, COINS, AND ACCOUNTS: 




SIR JOHN 



GOVERNOR OF HONG EONG, HER BRITANNIC MAJESTY'S PLENIPOTENTIARY AND SUPERINTENDENT OF TRADE 

IN CHINA. 



Illustrated foitlj <$ite |5wt&«& unb Staig (ghrgrabiugs of Coins, 
gwrieni H«b $$toterw. 




LONDON: NATHANIEL COOKE, MILFORD HOUSE, STRAND 

AND ALL BOOKSELLERS. 

1854. 



F rr i 

o 

t * „ 







PREFACE. 



In bringing this little work before the public, the Author has 
to request more than usual indulgence at the hands of his 
readers. The pressing calls upon his time, and the impossi- 
bility of delaying his departure for the scene of his duties in 
a distant land, have prevented his being able to give as much 
attention to the final revision of this work as he could have 
desired. Some errors, in such circumstances, and in a work 
of this character, are almost unavoidable ; but the Author 
hopes they will be found to be neither numerous, nor of 
much importance. 



ERRATA. 



Page 2, line 13, is omitted. 
„ 20, note, for Balthorn read Ballhom. 
„ 35, note *, for cap. i. read cap. x. 
„ 46, note f, line 4, for four re&djive. 
„ 48, line 28, for if read Or. 
,, 69, line 29, for 438 read -438. 
„ 106, note *, for Gerard read Girard. 
„ 106, note f- for Leirinde alle Reckeningen read 

leerende alle rekeninghen. 
„ 111, line 11, for testime read testerne.. 
„ 111, line 14, for well-wisher read well-wilier. 
„ 137, note %, for Spix and Martin read Spix and 

Martius. 
„ 143, note *, for p. 586 read p. 386. 
„ 153, line 1, for Pehleir read Pehlevi. 
„ 161, note, for 5-f-l read 54-1. 




THE DECIMAL SYSTEM, 

IN 

NUMBERS, COINS, AND ACCOUNTS. 



CHAPTER I. 

ANCIENT HISTORY OF ARITHMETICAL NUMERALS. 

Every human being 1 — man, woman, and child— has been provided 
with a set of decimal machines, in the shape of fingers and toes, 
which, even from early childhood, and among- the rudest nations, 
have been used for the purposes of account. Ovid speaks of the 
fingers with which we are accustomed to enumerate * — the word 
digits, in its Latin signification, meaning" equally fingers and arith- 
metical figures. So, in German, Zehen is used alike for tens and 
toes. John Quincy Adams says, " The division of numbers by 
decimal arithmetic is distinctly proved to have been established 
before the general deluge," — which proof may, indeed, be deduced 
from the fact that as ten fingers were given to man, they would 
naturally be employed for intellectual as well as physical purposes, 
to calculate with, and to perform the common handicraft functions 
of existence. Certain it is, that the years of the antediluvian patri- 
archs are spoken of, in the Book of Genesis, in hundreds, and tens, 
and units ; and that three tens, and five tens, and three hundreds of 
cubits are reported as the height, and the breadth, and the length 
of the ark. So four times ten days, and four times ten nights, 
are stated as the time during which the rain fell upon the earth, 
where it rested a hundred and half a hundred days. The first time 
that the word " thousand" occurs in the Bible is where Abimelech 
tells Sarah he has given her brother a thousand pieces of silver — 
(Gen. xx. 16). The word " thousands " first is found where 

* Seep. 48. 



2 THE DECIMAL SYSTEM, 

millions are also mentioned, and benedictions are brought to 
Kebekah (Gen. xxiv. 60) as the mother of future " thousands of 
millions ; " and it is somewhat remarkable that this is the only 
instance where the word u million " occurs from one end of the 
Bible to the other. The greatest numbers mentioned anterior to the 
flood are the years of Methuselah, which amounted to nine 
hundred (i. e. hundreds) and sixty (i. e. six tens) and nine years. 

It is curious to trace the various exhibitions of the decimal nota- 
tion through all the tongues and tribes of the world. In all early 
histories, the Bible not excepted, men are grouped together in tens, 
and hundreds, and thousands, and tens of thousands. The common 
title given to the Emperor of China, in the temples of that empire, 
Wan Sui, wan sui, wan wan sui — ten thousand, ten thousand, 
ten thousand times ten thousand years ; which, indeed, implies 
immortality. Viva usted mil ahos — " May you live a thousand 
years " — is the ordinary phrase in Spain for wishing longevity to a 
friend. So in Chinese, for a man of unchangeable purpose, they 
say, u One mind ten thousand years ; " and to teach prudence in 
conversation, they have a proverb, " A whispered word may be 
heard a thousand miles away." "We, to express a strong conviction, 
say "Ten to one," "A hundred to one," "A thousand to one." — 
One of the commonest forms of asseveration in Chinese is, 
Wan yih, which means, " Ten thousand to one it is so and so." 
Again, instead of saying, "Wine assists the settlement of dis- 
putes," the Chinese proverb runs, "One cup will arrange ten 
thousand affairs." 

The opposite Table, exhibiting the comparative number of 
times in which arithmetical figures occur in the Bible, has been 
calculated from the passages referred to in Cruden's concordance.* 

In the Book of I. Genesis (xviii. 24-32), Abraham implores the 
Lord to spare the city of Sodom if there he fifty righteous found 
within the city : he lowers the number by Jive to forty-five, and 
then to forty, and then to thirty, and then to twenty, and then to 
ten, and proceeds no farther in his intercessions. 

The groupings in scores {i.e., two tens) is a common mode of 
representing numbers, and the phrase " forty less one" is found an 
apter and more popular way of speaking than simply to use "thirty- 
nine." Threescore, threescore and ten, and fourscore, are commonly 
employed for sixty, seventy, and eighty. In various parts of the 

* London 4to edition, 1828. 



IN NUMBERS, COINS, AND ACCOUNTS. 



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4 THE DECIMAL SYSTEM, 

Bible decimal progression is employed. In the Book of Genesis, in 
Jethro's counsel to Moses, he is recommended to nominate " rulers 
of thousands, and rulers of hundreds, rulers of fifties, and rulers 
of tens " (Exodus xviii. 21) ; and in the assembly of the people 
spoken of in the Book of Judges (xx. 10), they decided to take 
" ten men of a hundred throughout all the tribes of Israel, and a 
hundred of a thousand, and a thousand of ten thousand, to fetch 
victuals for the people." So in Amos, Jehovah decrees, "The 
city that went out by a thousand shall have a hundred, and that 
which went forth by a hundred shall have ten." In Leviticus 
(xxvi. 6) it is foretold to the Hebrews that " Five shall chase a 
hundred, and a hundred put ten thousand to flight." " A thou- 
sand shall fall at thy side, and ten thousand at thy right hand." 
(Psalm xci. 7.) Again in the Apocrypha, " There is no inquisition in 
the years, whether thou have lived ten, or an hundred, or a thou- 
sand years." (Ecclesiasticus xli. 4.) "Judas ordained captains 
over the people, even captains over thousands, and over hundreds, 
and over fifties, and over tens." (1 Maccabees iii. 55.) 

Fix on what portion we may of ancient history, we shall find 
the decimal notation prevailing*. When Herodotus (Book II.) 
gives an account of the building of the pyramids, he says, they 
were the work of bodies of 100,000 men, who were occupied 10 
years in making the road over which the stones were dragged 
for erecting the pyramids, and that 20 years were employed in 
the construction ; that each stone was 30 feet in length ; that 
the cost of radishes, onions, and garlic, for the consumption of the 
workmen, was 160,000 silver talents ; and that the pyramids stood 
on a hill, which is 100 feet high. Herodotus reports that the 
Egyptians accurately number the years, and states that between 
Hercules and Amases 17,000 years elapsed, and between Pan and 
Abasis 15,000 years ; but, as he comes nearer to his own time, he 
uses the word " about," and says he lived about 800 years after 
the siege of Troy. (Book II.) 

The employment of numerals representing large amounts is an 
evidence of considerable intellectual development, and may be 
accepted as an undoubted proof that the civilisation of the earliest 
periods recorded in the Bible was greatly superior to that of the 
more barbarous tribes who now occupy large portions of the earth \s 
surface. The associations of vast numbers with the sands of the 
sea, or the stars of heaven, which are found in the earliest biblical 
records, would be alike discovered in the traditions and in the 



IN NUMBERS, COINS, AND ACCOUNTS. 5 

language of uncultivated tribes ; but we should nowhere find, as 
in the book of Job, among barbarous people, references to flocks of 
sheep in seven thousands — to herds of camels in three thousands 
— to yokes of oxen and multitudes of she-asses in five hundreds — 
representing at the same time approximation to what is definite in 
numbers associated with vastness in amounts. 

The system of numerals adopted by the Hebrews was natural 
enough. They took their alphabet and applied the first nine 
letters to the nine digits, the second nine to the tens, and the third 
nine to the hundreds. By this means they arrived at the amount 
of 900, the maximum sum represented by a single sign or letter ; 



but 1000 


was 


represented by two dots upon the character for 1. 




M 


a 


3 


-r n 


1 


l n 


a - 


3 


b 


Q 


3 D V 


3 


z 


1 


2 


3 


4 5 


6 


7 8 


9 10 


20 


30 


40 


50 60 70 


80 


90 


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100 


200 


300 


400 


500 


600 


700 


800 900 












k 


V 


s 


sh 















a n 
1000 2000 

Unlike the Arabs, whom we have imitated by placing the 
highest numbers on the left hand, the Hebrews placed their units 
on the left, thus s * » is 11, M ap 121 ; the number 15, however, 
is not written n- but *n. 

The Greeks generally employed the same method as the 
Hebrews, by using as their numerals the letters of their alphabet ; 
but inscriptions are found, showing that they also used, like the 
Eomans, the first letter of numeral words as signs to represent 
quantities.* They employed a single line for the unit ; the letter 
n, the initial of ttc vre, (Pente,) to represent 5 ; — a, the initial of 
AEica, (Deka,) for 10 ; and H ? the initial of Hkarov, (Hekaton,) 
for 100. Five of any number are represented by enclosing 
the number in n : thus, T^T is 5°j or five tens; |h~T is 500; and 
Yh] hu JaT aaa mill is 789. In the Greek alphabet the first nine let- 
ters, from a to 0, represent the nine digits ; the next eight, from t 
to 7r, the tens up to 80 ; for the numeral 90, a character resembling 
the Hebrew koph is employed, ? ; the following eight, from p to w, 

* Greek numerals :_ I II A HX M SH M 



6 THE DECIMAL SYSTEM, 

exhibit the hundreds up to 800, where again a character somewhat 
resembling the Hebrew Tsaddi if is used to denote 900. Thou- 
sands are represented by a dash following the letter, thus : 
a/, j3/— 1000, 2000. 

g (t rv (pX^Cu^AK a a ft 

Professor De Morgan remarks, that the English word air is a 
convenient key to the three stages of Greek numeration. 



a 


/3 


y 


d 


c 


*$ 


y 

s 


V 


9 


1 


2 


3 


4 


5 


6 


7 


8 


9 


i 


K 


X 


/* 


V 


C 





X 


n 


to 


20 


30 


40 


60 


60 


70 


80 


90 



r . .100 200 300 400 500 600 700 800 900 

«/ PI 7/ 5/ 1/ «/ J/ ,/ 0/ 

1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000 

Of the three letters { which do not form a part of the common 
Greek alphabet, it has been supposed that two, ? and }, representing 
90 and 900, were used at a time when the Greek alphabet consisted 
of 27 instead of 24 letters. The character v (stigma) is a well- 
known and frequently-used combination of g sigma, and r tau. 

There is a curious passage in Aristotle's " Problems" in which, 
recognising the universality of a decimal system equally among 
civilised and barbarous nations, he attributes its existence to some 
universal and all-pervading law, and denies that it could be the result 
of accident.* This law, or the habit of decenary grouping, is in- 
deed, as before observed, a necessary emanation from the fact, that 
every child is born with the instruments of quinary and decimal 
notation. 

Archimedes, in his tract entitled " Psammites/'t professes to find 
the means of representing the number of sands which would be 
required to fill the sphere of the universe ; and starting from the 
unit of a hundred millions, he proposes to proceed multiplying 

* Tb de aii icai k-xi -iravTOiv, ovk cnrb TVXVGt aXXa <pioiKOV. 
t VanniTTjg. 



IN NUMBERS, 

each number by itself and then by the product, so that the pro- 
gression would be eight times faster than in a multiplication by 
tens. He would carry on this system as far as eight periods, which 
would correspond to a number which we should express by sixty- 
five digits in Arabic numerals. But the introduction of the cipher 
to mark the rank of the digits, and thus determine their value, 
gives to our forms of notation an immense superiority over any 
of those of antiquity. 

The powers of the Greek notation, as exhibited by the letters of 
the alphabet, were limited to the amount of 9999 : but their word 
myriad (fivpiag), which they represented by M or Mv, augmented 
the means of notation ten thousandfold, and enabled them to record 
by symbols the sum of 99999999 thus, 9 $ h9M9J h9* But Archi- 
medes, whose grasp of mind and notions of numbers were not to 
be satisfied by instruments so limited as eight places of figures, 
insisted that the numbers of the sands of the sea were not infi- 
nite, but were within the powers of language. Starting from the 
point at which arithmetic had reached, he made a myriad myriads 
the new point of departure or unit for secondary numbers, and 
this secondary unit another point for numbers of a third and fourth, 
and so up to the eighth progression, each added step of pro- 
gress being represented by eight figures ; and he then shows that 
eight of these progressions, or 63 places of figures, would exceed 
the number of sands which would be contained in what was called 
the Cosmos, (Koodoo,) or the sphere of which the earth is the centre, 
and its radius the distance of the sun. f 

* Examples will be found in the Commentaries of Latinus, and 
the works of Diophantus and Pappus, quoted by Dr. Peacock. See 
Note, p. 12. 

f The following description of the mode of calculation adopted by 
Archimedes in his "Arenarius," has been condensed by Col. T. P. 
Thompson. 

He takes " a myriad of myriads," or 100,000,000, and uses it pre- 
cisely as Locke does " million." He calls 100,000,000 " the unit of the 
second class," 1 and then takes of these units 100,000,000. This he 
calls " the unit of the third class," 2 and so on (p. 42). 

He assumes the diameter of a poppy-seed to be the 40th part of 
an inch (p. 49), and then calculates that a sphere of an inch diameter 
must contain six myriads and four thousand (64,000) of these seeds 

1 Movag devrkpujv dpifyiwv. 2 Movag rpiTwv dpi9[iu>v. 



8 THE DECIMAL SYSTEM, 

But the word myriad, being the highest numeral employed by 
the Greeks, had a definite and indefinite meaning: the* definite 
implying 10,000, the indefinite any vast number. And it is often 
similarly employed in the English language. 

By Homer, and some of the earlier Greek writers, it is always 
used in the vague sense of multitude. 

The passage in Homer where Proteus numbers the seals by fives 
has often been quoted as one of the earliest examples of digital 
notation.* 

* First, of the seals there assembled he reckoned the numbers, 
Five after five did he count them and set them in order, 
Then, like a herd with his flock, did he lay down among them." 

Most of our translators have allowed the manner of counting, 
which is the most remarkable characteristic of the passage, wholly 
to escape notice, and, moreover, give very inaccurate renderings. 

Pope says, as if phocse (sea calves) were fishes : — 

" Stretch'd on the shelly shore, he first surveys 
^ The .flouncing herd ascending from the seas, 

Their numbers summ'd ; repos'd in sleep profound, 
The scaly charge their guardian God surround." 



(p. 51). He then assumes that a myriad grains of sand are equal in 
dimension to one poppy-seed ; and thence proceeds to calculate how 
many must be in his sphere of 3,000,000 of stadia in circumference. 
He finally makes the number to be a thousand myriads of a myriad 
of myriads to the 8th power, or, 1000,0000,0000,0000,0000,0000,0000, 
0000,0000,0000,0000,0000,0000,0000,0000,0000. 

In the treatise on the Measurement of the Circle, he ascertains 
that the proportion of the circumference to the diameter lies between 
ajg and 3j? to l. 1 A wonderful improvement on Solomon's knowledge, 
as expressed in 1 Kings, vii. 23 (p. 97.) 

* $>w»eac p.kv rot 7rpu>Tov apiOfirjeei kcli tiruoiv' 
Avrdp iirriv 7ra<xac ireniraooeTai, r)de idjjrai, 
Aefctrai kv fikoayai, vofievg wc 7rw£<xi fit]\u)v' 

OSvaa. s. 411-14. 

1 Taken from small 8vo edition of "Arenarius," and "Dimensio Circuli," by 
Wallis, Oxon., 1666. See also Archimedis Opera (Oxon, 1792), pp. 325-6, &c. 



IN NUMBERS, COINS, AND ACCOUNTS. 9 

Cow per is scarcely more literal, and sadly feeble : — 

" And now the numerous phocse, from the deep, 
Emerging, slept along the shore; and he 
At noon came also, and perceiving there 
His fatted monsters, through the flock his course 
Took regular, and summ'd them." 

Sotheby is better : — 

" He first his herd will count, 
And passing through them, tell their just amount, 
Tell five by five— " 

The best of the English, translations is Hobbes', though he has 
lost sight of the quinquinary * counting : — 

u The old sea-god his flock will number then, 
And, having done, i' the midst of them will lie, 
Just as a shepherd lies among his sheep." 

But how superior to all, in accuracy and point, is the German 

Voss : — 

" Erstlich zahlt er der Robben gelagerte Reihen umwandelnd 
Aber nachdem er alle bei Fiinfen gezahlt und gemustert, 
Legt er sich mitten hinein wie ein Hirt in die Heerde der Schafe." 

There is great vagueness among classical authorities in many of 
the terms used to denote distance. Herodotus sometimes reckons 
a day's journey at 150 stadia, and at others at 200. The Roman 
lawyers allowed 20 miles, or 160 stadia, as the legal day's journey, t 
but in ordinary language the idea was as undefined as among the 
Greeks. A Sabbath day's journey among the Hebrews was much 
shorter than the journey of a working day, as it implied merely 
such a distance as might be walked for the purposes of recreation, 
and such as would not interrupt attendance upon the services of 
the Temple. 

Mr. Edwin Norris says, there can be no doubt that the 
Assyrians, and all the nations who used the cuniform character, 



* Other instances of Greek quinary notation occur in J2sch. 
Eum. 748; Apoll. Rod. ii. 975; iv. 350, ib. 
■j" Larcher on Herodotus, iv. xcix. 



30 THE DECIMAL SYSTEM, 

adopted the decimal system as their notation, though not in 
their weights and measures. All numbers, from 1 to 9, were 
made by perpendicular strokes. The Assyrians used / ;/ m ",' '// 
and so forth ; the Persians had l ? tf )) /// , or some modifications 
of these modes. All used < for 10, adding strokes for the digits, 
as < for 11 ; <* for 12 ; <P 14 ; up to 20, which was <& ; 
50 was written ^ ; when they reached 100, the character was 
<|- ; 1,000 was <3C1-. Of higher notation than thousands no 
evidence is found; but as they had astronomers among them, 
they may have used signs for millions. The year 1854 would 
have been thus written : — 

<BBS <h «£ f 

/» too SO * 

Of ancient Assyrian numerals Dr. Hincks writes : — 
"The Assyrians were partial to the sexagesimal system as 
opposed to the decimal, of which they were probably the inventors. 
They had a noun denoting ' a sixty,'* analogous to our score or 
dozen ; and, in expressing 360, would say three hundred and a 
sixty. Their talent (tikun), from the root 'to weigh,* contained 
CO manah (mana), from the root ' to count ;' and this again con- 
tained 60 of what we may call provisionally shekels, but of which 
the Assyrian name is unknown, the monogram only having been 
yet found. With reference to the measures of the Assyrians, I 
believe they invented the sexagesimal divisions still in use in this 
country ; but it would seem that their measurement of terrestrial 
lengths was decimal. The oldest palace recorded to have been 
built (on Michaux's stone) is said to have been in length three 
lengths, and in breadth one length and fifty — vvv . The palace 

was probably, then, as long as it was broad, which would give 100 
of the smaller measures, equal to that called ' a length.' I take 
the monument to be of the date 1200 B.C. In confirmation of 
this, we have in the Khorsabad balls the cubication, 6 lengths 
and 50 cubits. What I here suppose to be a cubit, must be nearly 
of that value ; but some colossal figures are said to have been 
nine of this measure in length. Now we know that the Assyrians 

* The ancient Bohemians had kopa, and the Danes to this day use 
skok, for sixty. 



IN NUMBERS, COINS, AND ACCOUNTS. 11 

had a cubit (in the inscription of Nebuchadnezzar, at the India 
House, 680 ammat are mentioned), and it is extremely unlikely 
that they had another measure so near this in magnitude, as that 
a statue should contain nine of it — a statue spoken of as l the 
pride of Khamana/ and evidently of colossal size. I regard it, 
then, as certain, that the smaller measures were cubits, and ' the 
length/ of course, 100 cubits. It is natural to suppose (and yet 
not certain) that the series was continued in decimal progression. 
In Egypt, however, though the square measures in the time 
of the Ptolemies were certainly the arura of 10,000 square cubits, 
the square measure of 100 square cubits, and the cubit itself; and 
though we may presume the existence of measures of length equal 
to the sides of the two latter, we know that the royal cubit 
contained 7 hands, or 28 digits ; and it is possible, I may say 
probable, that the Assyrians had a similar division of their cubit.' 7 * 
The Latins were even less provided with terms for high 
numbers than were the Greeks. Centum and mille, or 100 and 
1,000, were their highest denominations. The common use of 
definite terms for the higher ranges of numbers is due to the 
Arabic numerals, which brought into familiar use numbers far 
greater than could be expressed by Roman characters — of which 
the Italian word millione is one of the most striking examples. 
Millione is the augmentation of mille, meaning a great thousand, 
and was employed to represent a thousand multiplied by itself. 
The natural analogy of language led to the use of billions, 
trillions, &c, and to such combinations, once introduced and 
understood, there are no limits. 

The Roman numerals exhibit some of the simplest forms of 
record.f They have their foundation in decimal progression. The 
first nine numerals being represented by so many single strokes, 
thus, /, //, ///, and so forth, the next step would be a line in a 
different direction, upon the last of the nine; thus X, or two 

•. M. S. Letter from Dr. Hincks. 
f Forms of Roman numerals: — 

I VA X CT C M~C*fc7o CMO 
I V X L C M CIDCIIDD 

CCtf CClDO Id do ddClDDD 



12 THE DECIMAL SYSTEM, 

strokes, 'would represent ten ; the next series, up to a hundred, 
would be a repetition of X's — as XX twenty, XXX thirty, and so 
on ; and three strokes, E (the ancient form of C), would denote 
a hundred ; which carried on by E E, E E E, exhibit two 
hundred, three hundred, &c. The fourth stage, beginning- by a 
thousand, M, has four strokes l\/l to represent it ; and two or 
three M's recorded two or three thousand. In process of time a 
division of these marks furnished characters for intermediate 
numbers. Half of X (10) was V (5) ; half of E (100) was L (50) ; 
and as the form of M became rounded into G), the character D, 
being half of the (I), was employed for 500.* 

There may be some doubt whether the Eomans did not take 
the letters C and M as the capitals of centum and mille. As, 
however, the Latin words are obviously of Greek derivation, from 
kicarov (Hekaton, the consonant c was by the Latins pronounced 
hard, as Kentum), and %i\ia, Khilia, which have neither C nor M 
in their composition, the coincidence may have been accidental. 

The Roman numerals are not very creditable to the sagacity 
of that nation in the field of arithmetical notation. They are 
exceedingly cumbrous, and, in the higher regions of figures, utterly 
unmanageable. * 

By the table on the opposite page it will be seen, however, that no 
other figures are employed than those which represent decimal pro- 
gession, as : — 
I 

V which is the half of X, 
X or double V, 

L half of C, anciently written E, 
C or double L, 

D five hundred, or half of CD, or mille, 
M the initial of mille. 
All the intermediate numbers are represented by figures placed 
either to the right or the left of the decimal numbers — those to the 
right imply addition, those to the left subtraction. Thus : — 
IV is 4, 1 subtracted from V. 
VI „ 6, 1 added to V. 
LXXX „ 80, 30 added to L. 
XXC „ 80, 20 subtracted from C. 

* See Dr. Peacock's article on Arithmetic, Encyclopaedia Brit., 
p. 532,— an invaluable and almost exhaustive contribution to our 
knowledge of the history and application of numerals. 



IN NUMBERS, COINS, AND ACCOUNTS. 



13 







1 




















|- 


6 










o 










8 


o 








O 


o 
o 












» 








O 


O 










I 
o 
o 


o 
o 
o 
o 


l> 

O 
O 


o 

o 
o 
o 


o 
o 
o 


o 
o 

o 
u 


O 
U 

o 
o 










o 


o 





8 

© 


© 


© 


o 










§ 


8 


§ 


8 


§ 


8 










rH 


<N 


uf 


©" 

i-H 


S" 


© 

l-H 


cT 

8^ 


























o 






















o 




















o 


o 




















o 


o 


















o 


o 


o 


















u 


o 


















o 


o 


■■ 


d 












o 




o 


■ 


d 


o 










o 


o 


o 




d 


o 


u 








O 


O 


o 




o 


u 


o 


o 




CO 


u 


o 


U 


o 


Q 


a 


a 


a 


a 




H 






















3 


8 


© 


© 


o 


© 


© 


© 


© 


© 




I 






© 


© 


© 


© 


© 






l-H 






U5 


© 


t^ 


00 


© 




W 






















S 










































t3 






















fc 














u 

X 


o 
X 






fc 














X 


u 
o 






3 














1 


x 






£ 






X 








X 


X 






§ 




X 


X 






X 


X 


X 






X 


X 


X 




X 


X 


X 


X 






X 


X 


X 


-1 


_l 


_i 


_l 


-1 








© 


© 


© 


© 


8 


© 


© 


© 








CO 


CO 


* 


o 


t^ 


CO 


© 
























X 


X 










> 

X 


> 

X 

o 








X 


X 

8 












— 






■J 


— 


— 






_ 


~ 


g; 


— 


> 


> 


> 


> 


> 




X 


X 


X 


X 


X 


X 


X 


X 


X 


X 




o 


l-H 


<N 


CO 


«• 


W5 


© 


t^ 


00 


© 










> 








X 

i 


X 

i 






- 


= 


= 


£ 


> 


> 


> 


> 


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<N 


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K> 


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t^ 


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14 



THE DECIMAL SYSTEM, 



The mental arithmetic of the Romans was, no doubt, far 
advanced beyond their writing 1 symbols ; their language exhi- 
bited the decimal stages, at all events, as far as the hundreds and 
thousands are concerned. Our dictionaries give the word myrias 
as representing ten thousand ; I do not know that there is any 
classical authority for its use. 

The following examples of Roman numerals, with the autho- 
rities quoted, are taken from " Facciolati's Dictionary " : — 

B 500 Ursatus 

100 

50 Nicolaus 
1,000 [Nicolaus 

10,000 Vet. Glos. Anon. & 
100,000 Probus 



C 9 
O 

IVI 

c 

CCIOO 

CCIOO 00 

CCIOO CCIOO 

CCIOO CCIOO CCIOO 

CCIOO 100 IOC 

CCIOO IOOO • 

CCIOO CCIOO CCIOO IO LX 

CCIOO CCIOO CCIOO CCIOO 

CCIOO CCCIOOO 

CCIOO 00 00 CO CC 

CCIOO CCIOO CO 100 

CCIOO CCIOO CO GO CO DCC 

CCIOO CCIOO CO CO CO CDXXCIX 

CCIOO IOOO CO C GO XII 

CCIOO 100 DCCC LXVII 

CCIOO 100 GO ccc 

CCIOO GO IOC 

CCIOO 00 GO GO CC XX III 

CCIOO IOO DCCCC L 



10,000 Augustinus 

11,000 „ 

20,000 „ 

30,000 „ 

15,600 Ursatus 

40,000 Augustinus 

30,560 Rosinus 

40,000 Augustinus 

90,000 „ 

13,200 Rosinus 

24,000 „ 

23,700 

23,489 „ 

41,912 

15,867 

16,300 „ 

11,600 

13,223 

15,950 • 



* Other forms of ancient Roman numerals : 



IN NUMBERS, COINS, AND ACCOUNTS. 



10 



The notation of the ancient Egyptians is given by Sir Gardner 
Wilkinson, as in the annexed plate, and presents some remarkable 
evidences of the influence of the decimal points, since both in the 
hieroglyphic and hieratic — i. e., the mystical and commoner forms, 
a new series of characters is adopted at every decimal division. In 
the hieroglyphics the units are represented by one up to nine strokes 
( i ) ; ten by n, and tens by the repetition of the same sign ; the 

EGYPTIAN NUMERALS. 



*• 


HIERATIC 


ENCHORIAL 


N° 


NICROCIYPHIC 


HIERATIC 


N° 


WCROtLYtHIC 


HIERATIC 


e 


1 


1 


/ 


| 1 


T ' I I 


/«? 


Q <2 


-*' * 


2" 


& 


z 


z 


1 1 


k— Zi 


ZOO 


^ 


^-—> i J——H 


3 d 


a 


1S\ 


3 


Ml 


"\ i Zt| 


2,00 


W 


19^ .£» 


/," 


1 <, 


1,2 


A 


Mil 


"l /«a| 4 


LOO 


*W* 


^J»>jJ2>JJ£} 


5" 


0.2 


2± 


5 


m u^ 


1 / 1 


500 


^?W 


_^,_^>H» 


6 th 


14 


l\ 


6 


III III 


f ' i 


600 


WW? 




rjth. 


±1 


n 


7 


mini 


/t'^-lX S&\ 


too 


f^f 


-2£jJp» 


8 ik 


TIW 


iz 


8 


M ii 
1 1 it 


555Jl / mSkm 


300 


■w 




atli 


\ 


K 


9 


n in 
in i 


V 


900 


m 


^sLgyz-=^' 


Jv 


y 


10 


n 


iT> A A 


1000 


f 


-b 


N* 


y 


!/ 


a 


m 


»n / iX 


2000 


if 


>? , >* 


12* 


8/ 


a/' 


20 


nn 


nn ' «X 


3.000 




>*».>•* 


&* 


aA/ 


2/ 


nni 


«nrt')\ 


k-OQO 


mr 


J^.^t 


id 1 


^ 


/ 


SZ 


nnnn 


MllAA^X 


5.000 


nm 


>^"». 


*y» 


&/ 


tt 


nnn 
ni i i 


«i/\nnn>«H-^ 


6.000 


mm 


*s% ■*■>% 


2S it 


w 


*V 


64 


nnnn 

n i M 1 


4 >nnnn< y *y\ 


looo 


ffiiffi 


JJW^fcJJ*^ 


(/»/ 


&£! 


*z 


66 


nnnn 

noiini 


^mwnn' - ? m 


SOOQ 


11 


^, s£\ 


N" 

/ 
3 


HIE808WWC 


J-IIEJWIIIC 


7b 


nnnnn 
nninni 


^nnmwrv ' <£ ^ 


9.000 


mfi 


^■^^a 


III 


"1 


87 


nnnnnn 
nniinui 


^nnnnnnnfv^^UCi 


l,8oo 


i???? 


_yj, 


J / 
) * 


1 1 1 1 


^ 


98 


nnnrrnn 
nnmiini 


~*j,r i-*") '"j, 


U6o 


JrKruwi* 


ii3>>, 


/ 
6 


Mill 1 


T 








io,ooo 


1 


T f 


1 /" 


n. I 


i^ 


1oooo 


J„, 


i nnm 



hundreds by ^ ; the thousands by £ ; the ten thousands by 
1, the writing being from left to right. In the hieratic, the 
figures are written from right to left, and though less simple 
than the hieroglyphic forms, a new character is adopted at every 
decimal division— thus, I represents 1 ; r> (as in the hieroglyphic) 
or x, or b, 10; 1, 100; 5, 1,000; P , 10,000; but, instead of 
simple repetitions of the same signs, modifications or combina- 



16 



THE DECIMAL SYSTEM, 



tions are adopted for the numbers between the decimal divisions. 
Thus, 4 is written «» ; 20 *X 5 300 _s*> ; 4,000 -^. In the 
numeral employed for reckoning' the days of the months, some 
extraordinary resemblances to our modern figures appear — and 
some combinations not less remarkable : thus, the 5th day is thus 
represented : — 25—2 -f- 3 ; the 6th, 33—3 + 3 ; the 7th, yj — 
3 + 4 ; the 8th, *n — 4 + 4 ; while, for the 9th, we have the 
simple figure \ ; and at the 10th a new notation begins by 
j) ; the 11th being j. 

The numerals of Palmyra present new signs at 5, 10, and 20 — 
and new combinations at 100, 500, and 1,000. Like the Phoenician, 
they are to be read from right to left. Up to 19 they remarkably 
resemble the Roman numerals, both in the form and combinations, 
after which all resemblance ceases. 



/ y 

2 // 

3 /// 

4 ///r 

5 ///// 

6 ////// 

7 /////// 

8 //////// 
-P ///////// 

10 /) or - 

// /- 

1Z //- 

13 /// - 

/« //// — 

15 ///// - 

/S //////— 

17 ///////- 

J 8 /////y// — 

19 J //////// — 

20 jTar A- 

21 / rf 

22 // jy 

£1* /iJf JV 

25 g / / / • yV 



30 —Jf 

ko J/JY 

50 — JVJS 

60 Jrjv,* 

70 -SSA'JV 

80 Jf A'JSA' 

so — a" jv yy y 

ICO IS 

200 .5// 

300 /£/// 

400 161/ II 

500 />///// 

600 />////// 

700 />/////// 

SOO HI ////// / 

300 /J///////// 
$99 ///////// -jwtMYMI/Mlli 



/\ 17 J ///t 6/ 
////oilj/p^TL 

Pl/7/ PJ 



* Dr. Peacock's Arithmetic. 



IN NUMBERS, COINS, AND ACCOUNTS. 17 

The Phoenician numerals, which Dr. Swinton elucidated in the 
u Philosophical Transactions," from coins found at Sidon, have 
simple signs for ten and twenty, by which they proceeded up to 
99, and at 100 adopted a new form of notation, thus : — 



1 i 26 />0 

2 a W " >3 

3 /// 28 ///>0 
t, mi 29 //// >D 

5 . i* 30 2^D 

6 /s» £0 OO 

7 //> 50 ^OD 

8 ///>• 60 OOO 

9 ////> 70 ^DOO 

10 *^ 80 ODOO 

11 , t^ 90 -2^00 

12 ss2^ 100 *2^/ 

13 •••^ 200 ^// 



15 ^^ WO -2^//// 

16 •^i^ 500 i^^ 
1/ • •s*^. GOO 2s*. / > 

18 ,/s^*^ 700 ^//> 

19 ,,/s>2=^ 800 T^///> 

20 D 900 ^ / / / / 
2/ 



/O 920 D^//// 



22 HO 9/yO OD^//// ^ . 

23 IllO 960 ODD^////^ 
2i, /HID 980 OOOO^^ // / / >* 
25 >D 1000 ^^/ # 



Few languages proceed so far as the Sanskrit in pursuing a 
decimal system into numbers of immensity. 

Eka 1 

Das'a 10 

S'ata 100 

Sahasra 1,000 

Ayuta 10,000 

Laksha 100,000 

Prayuta, or Nujuta. . 1,000,000 



* Dr. Peacock's Arithmetic. 



18 THE DECIMAL SYSTEM, 

Coti 10,000,000 

Arvuda 100,000,000 

Ab J aor I 1,000,000,000 

Padma ) 

C'harva 10,000,000,000 

Nicharva 100,000,000,000 

Mahadpadma 1,000,000,000,000 the large Padma, or 

Saucur 10,000,000,000,000 [billion 

Saludhior > 100,000,000,000,000 meaning the ocean 

Samudra ) 

Antya 1,000,000,000,000,000 

Madya 10,000,000,000,000,000 

Parard'ha 100,000,000,000,000,000 

Of all Orientals the Buddhists appear to have advanced farthest 
into the regions of interminable numbers. In order to obtain the 
sanctification and deification of a Buddha, it is declared by the 
great authorities of that extraordinary religion, which is professed 
by about one-third of the human race, that a mortal man may 
acquire omniscience and the attributes of divinity, if, for a million 
otasanlias of calpas, he persevere in holy aspirations after deification 
— that he then continues to give expression to such aspirations 
during the existence of 387,000 successive Buddhas, who has each 
undergone the same probation — and that, in the course of 400,000 
asankas of calpas he obtains admission to the presence of twenty- 
four Buddhas, and receives from each an assurance that at some 
future time he shall be exalted to the rank of a Buddha godhead. 
During the 400,000 asankas of calpas, the sacrifices he will have 
to make exceed all powers of numbers, and the aggregate will 
exceed the drops to be found in a thousand oceans added to the 
numbers of the stars. 

" To form a notion of the duration of a calpa, imagine a cube 
of solid rock, whose squares are 4 goros each, and that a person 
endued with Ird'hi, or the power of soaring in the air, should once 
in a thousand years pass over it, allowing the hem of his garment 
to trail on the rock — the rock might, in consequence of such 
slight attrition, become dwindled to the size of a mustard seed, but 
the years of a calpa will not yet have expired — thus, the number 
of individuals' lives in the course of a calpa is inconceivable."* 

I do not find the extent of a goro any where defined; the 

* " Kitelegama Dewamitta Unnasee," as translated in the Ceylon 
Almanac for 1832. 



IN NUMBERS, COINS, AND ACCOUNTS. 10 

inquiry as to its size might probably open another door into 
illimitable and incalculable quantity. 




This figure is copied from a fine specimen of carved ivory, 
representing the figure of Buddha, in the possession of Sir J. 
Emerson Tennant. 



C 2 



20 



THE DECIMAL SYSTEM, 



The Buddhist system of notation is thus recorded : — 
10 decads . are equal 

10 hundreds „ 

100 thousand, or laksha 

100 lakshas .... 



100 


» 


of koti . 


100 


» 


of kotiprekoti 


100 


}) 


of nahuta . 


100 


)) 


of ninnahuta 


100 


» 


of akshohini 


100 


}> 


of bindu , 


100 


» 


of arbuda . 


100 


» 


of ninarbuda . 


100 


)} 


of ahapa 


100 


}t 


of ababa . 


100 


» 


of atata 


100 


M 


of soghandika 


100 


» 


of uppala 


100 


}) 


of kurauda 


100 


ii 


of poondareka 


100 


>t 


of paduma 


100 


» 


of kat'haa . 



to 100 

„ 1,000 

„ 100,000 

„ 1 kela or koti 

„ 1 kotiprekoti 

„ 1 nahuta 

„ 1 ninnahuta 

„ 1 akshohini 

„ 1 bindu 

„ 1 arbuda 

„ 1 ninarbuda 

„ 1 ahapa 

„ 1 ababa 

„ 1 atata 

„ 1 sogbandika 

„ 1 uppala 

„ 1 kumuda 

„ 1 poondareka 

„ 1 paduma 

„ 1 kat'haa 

„ 1 mahakat'haa 

100 mahakat'haa (or great kat'haa) „ 1 asanka. 

Notwithstanding this most burdening aggregation of decimal 
force, it is more easy to rush into the region of infinity by supposing" 
that a billion represents a million millions; a trillion, a billion 
billions ; a quadrillion, a trillion trillions ; a quintillion, a quadrillion 
of quadrillions, and so forth, &c. Let the experiment be made of 
recording such vast amounts, and the patience will be thoroughly- 
exhausted. But such an experiment may help our imperfect 
notions of what is interminable, infinite, eternal. 

The ancient Runes do not go beyond 19 in their numerals. 
They are the letters of the alphabet, 
iutho rkhnia stblmyal mm tt 
12 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 

p n v a k r * |k * A * ■ * * r Y k jt nt ♦ 

For any number above 19 the amount was represented by repeating 
the letter, thus M (2 tens) =20 ; M V = 21, &c. ;* but there is 
nothing to show any knowledge of decimal division. 



Balthorn's Alphabets," p. 4. 



IN NUMBERS, C0I1SS, AND ACCOUNTS. 21 

No higher numbers than a hundred or a thousand are to be 
found till the 16th century in any of the languages of Gothic or 
Scandinavian origin. In the Sclavonic dialects the introduction 
was still later. The word million was unknown in the Russian 
language till the time of Peter the Great j and the Russian word 
for thousand is still ten hundred.* 

As among rude tribes the hands and fingers have been always 
employed for the commonest purposes of numeration ; so have they 
among more cultivated races been used in the higher regions of 
arithmetic, and multitudes of allusions to digital calculations will 
be found in classical authors.! The left hand and fingers were 
employed to denote the nine digits and the succession of numbers 
up to 100 ; while the hundreds and thousands were exhibited on the 
right hand up to the amount of 10,000, by the same inflections which 
exhibited the digits and the tens on the left. Bede extended this 
digital numeration to a million by adding ten variations, such as 
opening or closing the hands, raising the fingers upwards or pointing 
them downwards, placing them on different parts of the body. He 
suggests, too, a system of communication by the fingers in which 
the numbers should be taken to represent the natural order of the 
letters ; so that if a person wanted to convey the information to a 
fiiend that he was surrounded by sharpers, he might make signs 
representing 3, 1, 20, 19, 5, 1, 7, 5, which would convey the words 
Caute age, or take care ! J or in other numbers in English it would 
be 19, 1, 11, 5, 3, 1, 18, 5. 

Thus, from the remotest times traces of the quinary, decenary, 
and vicenary scale may be found in the languages that have come 
down to us. Their universality may be traced to the physiological 
construction of the human being ; and in the same way in which 
the finger (difjit) has been employed as the primary elemen of 
notation; so the palm, the span, the foot, the cubit (1^ foot), the 
arm (braccio), the yard (gyrd — Anglo-Saxon for girth) — all 
measures which every human being carries about with him, have 
been employed from all times and in all regions of the world. § 

* The ancient Russians, like the other Sclavonic tribes, had the word 
tisyashcha for 1,000. 

f Juvenal Sat., x. 248. Pliny's Epistol., 20, lib. ii. Seneca's 
Epist., 88, lib. i. 

X De Compoto vel de Loquela per Gestum Digitorum. 

§ V. Pott Zahlmet,hod> anhang liber Fingernamen. 



22 THE DECIMAL SYSTEM, 



CHAPTER II. 

ARITHMETICAL HISTORY POSTERIOR TO THE INTRODUCTION OF 
ARABIC NUMERALS. 

The introduction of what is called the Arabic system of numbers 
was the grandest step ever made towards the introduction of a 
universal language among the nations of the world. In the whole 
field of arithmetic and accountancy the same or nearly similar signs 
are now used, not only throughout the European continent and 
its adjacent islands, but in all the civilised parts of North and 
South America, through Northern Africa, and Western Asia, and 
in every locality where European adventurers or their descendants 
have fixed themselves. By whatever variety of name the numeral 
symbol is called, the symbol itself is everywhere nearly the 
same ; and though the languages employed are multitudinous, and 
few of the various peoples of the world could teach an arithmetical 
sum, or convey by language to any other people the idea associated 
with a particular numeral sign, yet the written sign itself would 
be intelligible to them all, from the tropics to the pole. In the 
domains of language translation often fails to convey correct ideas; 
for words supposed to be synonymous are frequently really different 
in their signification and association. House, for example, rendered 
into various idioms, would present images to the mind as varied as 
houses present in their infinite variety of construction in different 
regions. The notions of industry, virtue, valour, patriotism, and 
every abstract quality would take their coloring from an infinite 
variety of sources, modifying the original idea to the peculiar 
circumstance of the individual or the nation employing the term 
which represents the idea itself. But in the numeral signs every- 
thing is definite ; the ideas they present are the same to every 
mind; their exact value is recognised and understood by all who 
employ them. 

It has been shown by a variety of evidence that the Hindoos 
used the numerals, which we call Arabic, many centuries before 
the Arabians. Aryabhatta, wrote in Sanscrit on Algebra and 
Arithmetic as early as the fifth century. He is quoted as an 




THE DEAN OF ELY 



IN NUMBERS, COINS, AND ACCOUNTS. 23 

authority by Brahmegupta, who flourished in the early part ot 
the seventh century. Brahmegupta is again frequently referred 
to by Bhascara, whose works were published in the middle of the 
twelfth century, and exhibit those forms of decimal notation which 
are now universally adopted by civilised nations. 

" The first Arabian," says Dr. Peacock, * " who wrote upon 
Algebra and the Indian mode of computation is stated, with the 
common consent of Arabic authors, to have been Mohammed Ben 
Musa, the Khuwarezmite, who flourished about the end of the ninth 
century; an author who is celebrated as having made known to 
his countrymen other parts of Hindu science, to which he is said to 
have been very partial. Before the end of the tenth century 
those figures, which are called Hindasi from their origin, were in 
general use throughout Arabia; among others is mentioned the 
celebrated Alkindi, who was nearly contemporary with Ben 
Musa, and who, among his numerous other works, wrote one on 
the Indian mode of computation (Hisabu 'IHindi). The same 
testimony is repeated in almost every subsequent author on 
Arithmetic or Algebra, and is completely confirmed by their 
writing their figures from left to right after the manner of the 
Hindoos, but which is directly contrary to the order of their own 
writing.f 

ORIENTAL FORMS OF ARABIC NUMERALS. 

h'\&>% CT6 C IV^ bo 

i rrY<sivA<? u 



* lb. 413. 

f Though the method of writing the Arabic numerals from left to 
right has been deemed conclusive of their Sanscrit origin, independently 
of other evidence, might it not be maintained that the Arabic numerals 



24 THE DECIMAL SYSTEM, 

" The use of this notation became general among Arabic writers, 
not merely on Arithmetic and Algebra, but likewise on Astronomy, 
about the beginning of the tenth century. We find it in the works 
of the astronomer Ebn Younis, who died in the year 1008, and it 
is found likewise in all subsequent astronomical tables. It was, of 
course, communicated to all those countries where their language 
and science were known. In the eleventh century the Moors were 
not merely in possession of the southern provinces of Spain, but 
had established a flourishing kingdom, where the favourite sciences 
of their Eastern ancestors were cultivated with uncommon activity 
and success ; and from that quarter, and from the Moors in Africa, 
they chiefly appear to have been communicated to the Spaniards 
and other Europeans. * 

" The learned Abbe Andres considers that the earliest example 
of the use of these figures, which is to be found in Spain or in 
Europe, is in a translation of Ptolemy in the year 1136 ; fac-similes 
of the former of these figures are said to be given in the Paleografia 
Espanola of Terreros, who found them in all the mathematical 
MSS. subsequent to that period, but in no other books or docu- 
ments — not even in accounts which were kept in the Castilian, 
which differed little from the Roman numerals ; — the calendars 
which were chiefly constructed in Spain, both in that age, and 

were invented by a people accustomed to write like the Hebrews, 
Arabs, and many other Oriental nations, from rigbt to left, and not as 
we do, from left to right, on the very ground tbat the simplest of the 
arithmetical signs, the units or digits, are placed on the right side, and 
the larger and more complicated on the left. Arithmetical science, 
like every other, must have commenced with the simpler form, and have 
proceeded to the more elaborate. Had a people, writing as we are 
accustomed to write, from left to rigbt, introduced a new system of 
notation, would it not be natural that the highest amounts should be 
the farthest from, and not the nearest to, the starting points We 
should have probably written the units first, and then the tens, and 
then the hundreds, and then the thousands, and so on — just in the 
contrary way in which the record would be made by a Persian or an 
Arab. Language easily accommodates itself to the symbols which 
represent it, and the use of one and twenty is quite as familiar to our 
ears as twenty-one; three score, as sixty; or half a hundred as fifty. 

* It has been held by some writers that Leonardo's writings are to 
be referred to the beginning of the fifteenth century; but the great 
weight of evidence gives him two centuries earlier. 



IN NUMBERS, COINS, AND ACCOUNTS. 25 

until the end of the fourteenth century, and were sent from thence 
to other parts of Europe, continued to be written in the old 
notation." 



ANCIENT EUROPEAN FORMS OF ARABIC NUMERALS. 

iiZjM <?A8 <3 to 
\Z 3 4 '\6 <V8 9X0 

; 2.3 4- 5 * 7 3 ?*£ 

SUNDRY FORMS OF ARABIC NUMERALS. 

7ytA2VVVA 
8.-S- ft * 
9-t^ 



26 TBE DECIMAL SYSTEM, 

The Arabs indeed do not claim the honour of having invented, 
the decimal system of numeration, but attribute it to the Hindoos, 
whose name in Arabic * it bears ; but its progress is not very 
clearly traceable in Europe. It is certain that in the beginning 
of the sixteenth century Roman figures were used by merchants 
and accountants. They lingered longer in England than in any 
other part of the European world, having found an asylum in the 
dark and dull regions of the Exchequer. 

According to the Hindus, numeration is of divine origin ; the 
invention of nine figures (anca), with the device of places to 
make them suffice for all numbers, being ascribed to the beneficent 
Creator of the universe, in Bhascara's " Vasana," and its glossary, 
and in Crishna's " Commentary on the Vija-ganita." Here nine 
figures are specified; the place where none belongs to it being 
shown by a blank, Sunja, which, to obviate mistake, is denoted 
by a dot, or small circle. 

From the right, where the first and lowest number is placed, 
towards the left hand, increasing regularly in decuple proportion : 
namely, unit, ten, hundred, thousand, myriad, hundred thousands, 
million, ten millions, hundred millions, thousand milllions, ten 
thousand millions, hundred thousand millions, billion, ten billions, 
hundred billions, thousand billions, ten thousand billions, hundred 
thousand billions. 

A passage of the "Veda," which is cited by Surya-dasa, exhi- 
bits the decimal notation thus : — " Be these milch-kine before me, 
one, ten, a hundred, a thousand, ten thousand, a hundred thou- 
sand, a million Be these milch-kine my guides in this 

world."f Ganesa observes, that numeration has been carried to 
a greater number of places by Srid'hara and others ; but adds, 
that the names are omitted on account of the numerous contra- 
dictions, and the little utility of those designations. The text of 
the Ganita-Sara, or abridgement of Srid'hara, does not correspond 
with this reference, for it exhibits the same eighteen places, and 
no more-! 

The subject of numbers is approached with reverence by the 
great Hindoo writers. The Brahmagapta is introduced by this 
invocation : — " Salutation to Ganesa, resplendent as a blue and 
spotless lotus, and delighting in the tremulous motion of the dark 

* Hindi. f u Colebrooke's Hindoo Algebra," p. 4. 

t Gan-sar., §§ 2, 3. 



IN NUMBERS, COINS, AND ACCOUNTS. 27 

serpent, which is perpetually twining within his throat." And the 
volume is ushered in by this flowery announcement: — "Having 
bowed to the deity, whose head is like an elephant's,* whose feet 
are adored by gods ; who, when called to mind, relieves his 
votaries from embarrassment, and bestows happiness on his wor- 
shippers ; I propound this easy process of computation^ delightful 
by its elegance,t perspicuous, with words concise, soft, and correct, 
and pleasing to the learned." § 

While on the subject of Hindoo numerals, it may be amusing 
to see a specimen or two of the delicate and winning forms in 
which arithmetical questions are propounded to the student for 
solution : — " Beautiful and dear Lilavati, whose eyes are like a 
fawn's ! tell me what are the numbers resulting from one hundred 
and thirty-five, taken into twelve ? If thou be skilled in multi- 
plication, by whole, or by parts, whether by subdivision of form, 
or separation of digits, tell me, auspicious woman, what is the 
quotient of the product divided by the same multiplier ? " Cole- 
brooke, p. 6. 

Again, — " Pretty girl, with tremulous eyes, if thou knowest the 
correct method of inversion, tell me what is the number, which 
multiplied by three, and added to the three-quarters of the pro- 
duct, and divided by seven, and reduced by subtraction of a 
third part of the quotient, and then multiplied into itself, and 
having fifty-two subtracted from the product, and the square root 
of the remainder extracted, and eight added, and the sum divided 
by ten, yields two ? " 

To a question so complicated, it is hardly fair to keep back 
the solution. Statement : — Multiplier, 3 ; additive, f ; divisor, 7 ; 
decrease, ^ ; square — ; subtractive, 52 ; square root — ; additive, 8 ; 
divisor 10 ; given number, two. 

Answer : — Proceeding as directed,, the result is 28, the number 
sought. Colebrooke, pp. 21-2. 

All the operations are inverted. The known number 2, multi- 
plied by the divisor 10, converted into a multiplicator, makes 20 ; 
from which the additive 8 being subtracted, leaves 12; the square 
whereof (extraction of the root being directed) is 144; and adding 

* Ganesa, represented with an elephant's head and human body, 
f Arithmetic. Pati ganita ; Pati, Paripati, or Vyaeta ganita. 
J Lilavati — delightful, — an allusion to the title of the book. 
§ Colebrooke's Translation of "Brahmagapta and Bhascara," 4to, 
1817. p.l. 



28 THE DECIMAL SYSTEM, 

the subtractive 52, becomes 196; the root of this (squaring was 
directed) is 14; added to its half, 7, it amounts to 21 ; and multi- 
plied by 7, is 147. This again divided by 7, and multiplied by 3, 
makes 63; which, subtracted from 147, leaves 84; and this 
divided by 3, gives'28. — pp. 21-2. 

One more example of what is called reduction of differences : * — 
" Out of a swarm of bees, one fifth-part settled on a blossom of 
Cadamba,\ and one-third on a flower of SidincThri ; % three times 
the difference of those numbers flew to the bloom of a Cutaja. 
One bee, which remained, hovered and flew about in the air, 
allured at the same moment by the pleasing fragrance of a jasmin 
and pandanus. Tell me, charming woman, the number of bees ?" 

This reverent and graceful way of dealing with arithmetic and 
its powers among Orientals, stands in strange contrast to the 
vituperations of an English writer, one Thomas Lawson, who, 
addressing specially those he calls " Heptatechnists," thus pours 
out his scorn upon those who patronise human learning, and the 
knowledge of figures as one of its branches : — " Herein (i.e., in 
arithmetical study), any member of Italian Babylon, with mass- 
book, mass for the dead, fabulous legend ; and Mahometan, with 
his dreggy Alcoran; any flint-hearted Jew, with his Talmud, a 
mingle-mangle of Jewish, divine, and humane matters ; any dead, 
dry, unfruitful formalist may grow profound, exquisite, nimble ; 
yea, and though involved in the intricate windings of degeneration, 
out of the royal state of regeneration and heavenly transformation, 
may apprehend the feats, terms, and parts of this natural art, as 
digits, articles, mixed numbers, ciphers, terniries, golden rule direct, 
golden rule reverse, a cube, Pythagoras's table, algorism, &c, 
yet be strangers to the Divine exercise which leads to Christ, the 
Lion of the Tribe of Judah, who alone opens the Seals of the 
Book." Attention is then directed to the number of the 
Beast.|| 

Whatever may be the opinions as to the exact dates in which 
the Arabic numerals were introduced, it may be safely laid down 
that their progress was from India to Arabia, from Arabia through 
the Moors to Spain, from Spain to Italy, and from Italy to the 

* Visleshajdti,— assimilation of difference; reduction of fractional 
differences. 

f Cadamba, — Nauclea Orientalis, or N. Cadamba. 

J Sulind'hri, — a plant resembling the Cachora. 

|| A.D. 1680. Vide De Morgan's Arith. Books, p. 49. 



IN NUMBERS, COINS, AND ACCOUNTS. 29 

rest of Europe. Claims on behalf of Pope Sylvester the Second 
have been put forward. It is certain he visited Spain in the 
latter part of the tenth century, and our English historian, 
William of Malmesbury, who wrote in the middle of the twelfth 
century, says that Sylvester (whose name was Gerbert) brought 
the abacus from the Saracens.* But the evidence of his 
having introduced the Arabic digits is founded on no other data 
than the general reputation he enjoyed of having mastered all 
the learning of his time. In an inquiry such as this, it is scarcely 
likely that any investigation should lead to the discovery of the 
very earliest period in which the " new figures " were employed. 
MSS. of the fourteenth century show how imperfectly the system 
was then understood, for not only are Roman and Arabic numerals 
mixed together, but the value of the zero was unknown — thus we 
have X, Xl, X2, X3, to represent 10, 11, 12, 13; we find in 
sequence XXX, XXXI, 302, 303, for 30, 31, 32, and 33; 
XXXX, 401, for 40 and 41. 

From the middle of the fourteenth century down to the 
fifteenth, when the Arabic system began to be generally adopted 
in calendars (long before its application to common accounts in 
bookkeeping), explanations clearly pointing out the power of 
place, which gives to the digit its decimal value, are frequently 
attached. Of one of them the translation is : — 

" Every number or figure of algorism in the first place repre- 
sents itself; in the second place it is multiplied by ten ; in the 
third by a hundred ; in the fourth by a thousand ; in the fifth by 
ten thousand; in the sixth by a hundred thousand; in the 
seventh by a thousand thousand ; in the eighth by ten thousand 
thousand ; in the ninth by a hundred thousand thousand ; and 
so multiplying by tens, hundreds, and thousands into infinity." f 
The first calendar in the English language in which the Arabic 
numerals are employed, bears the date of 1431. 

A period much anterior to this has been frequently claimed 
for the introduction of the Arabic numerals into this country, and 
some old inscriptions in Arabic ciphers have been referred to the 
very beginning of the twelfth century ; but there is no positive 
evidence of their employment before the fourteenth century ; and 

* Abacum certe primus Saracenis rapiens, regulas dedit quae a sudan- 
tibus abacistis vix intelliguntur. The claims of Gerbert are discussed 
at length by Dr. Peacock, pp. 415, et seq. 

t Corpus Christi College MSS. Peacock, 418. 



30 THE DECIMAL SYSTEM, 

all the dates which exist, and which are supposed to be anterior 
to that period owe their fancied antiquity to the rudeness and 
imperfection of the character employed, which has allowed some 
play to the imaginative faculty. There was a brick building at 
Stratford, in Buckinghamshire, which was at one time supposed 
to bear the date of 1182, but it was afterwards found to be 
certainly not older than 1382, and most probably 1582, as in the 
reign of Elizabeth the figures 3 and 5 were often so written as 
to lead to considerable confusion between them. A vehement 
and learned controversy raged at the end of the last century as 
to the age of a mantel-piece in the Rectory of Helmden, in 
Northamptonshire. First the date was read Anno Domini 133. 
Then it was held that the letter M had been erased, and a thousand 
years were summarily taken away from the antiquity of the in- 
scription. Then the 1 was suspected to be a 5.* The mixture 
of Roman with Arabic numerals was common for a considerable 
time after the introduction of the latter. MD58 is found in Nor- 
thamptonshire, on the monument of Mr. John Carr.f 

The following combinations of Roman and Arabic numerals 
are also found.in ancient MSS.: — 

C\X\ Tci ?ta *3 X4 W- f<^ 3 CZ 3°3 3H Ccf x 

It has been remarked that on no sepulchral monument, down 
to the latter end of the eleventh century, are Arabic numerals 
employed ; and the earliest date known on a tombstone is of Elen 
Cook, in the church at Ware, 1454, written according to the 
ancient manner of dividing 8 to make 4 — thus 1 Q 5«. In seals 
only one example has been found anterior to the sixteenth 
century, which bears the date l e 8 a (1484). § There is an urn of 
Edward the Sixth's, in which the Roman and Arabic numerals are 
blended, MDX47, for 1547. The first English book which bears 

* Mr. Hasted contends that the date of A.D. 1102 is engraved 
on a stone window frame of a barn at Preston Hall, in Kent (vol ii. 
175). See a valuable paper in the Archseologia, vol. xiii., p. 107 (1168), 
by the Rev. Samuel Denne, in which Mr. Hasted's opinion is shown to 
be without foundation. A representation of the real date was shrewdly 
suspected to be 1533. 

t See ante p. 29. 

X Brodie's History of Northamptonshire, vol. i. 5S2. 

§ Archaeologia, xiii. 127. ; ib. 130. 



IN NUMBERS, COINS, AND ACCOUNTS. 31 

its date in Arabic numerals was printed at St. Alban's, the Rhe- 
torica Nova Gulielmi de Saona 14a8 (1478). There is a letter of 
the time of Henry VI. which has in Arabic numerals the date 
1459, but there is reason to suspect the date was inserted subse- 
quently to the writing the letter. A calendar, however, exists on 
vellum, bearing the date of 1qa2 — 1472.* 

Chaucer, who was born in 1328, and died in 1400, has been 
frequently quoted f as referring to the introduction of the newe or 
Arabic numerals in a passage of his Dreme, where he describes 

THE WODDE. 

Shortly it was so ful of bestes, 

That though Argus, the noble countour, 

Ysate to rekin in his countour, 

And rekin with his figures ten ; 

For by the figures newe al ken, 

If they be crafty, rekin and nomber, 

And tel of every thing the nomber ; 

Yet should he fail to rekin even 

The wonders we met in my sweven.J 

There is in " Record's Arithmetic," the first edition of which 
was published in 1540, and dedicated toEdward the Sixth, a curious 
example of the employment of Roman as well as Arabic numerals 
to exemplify decimal numeration. 

P. 17. "A general rule. — Scholar. If I make this number 
91359684, at all adventures there are eight places. In the first 
place is 4, and betokeneth but four ; in the second place is 8, and 
betokeneth ten times 8, that is 80 ; in the third place is 6, and 
betokeneth six hundred ; in the fourth place 9 is nine thousand ; 
and 5 in the fifth place is XM times five, that is fifty M. So 3 
in the sixth place is CM times 3, that is CCCM. Then 1 in the 
seventh place is one MM ; and 9 in the eighth ten thousand 
thousand times 9, that is XCMM, i.e. XC thousand thousand 
CCCLIX thousand, 684, that is VICLXXXiiij." It is obvious 
the word million had no popular currency at this period. 

Arabic numerals are found in various MSS. written in Italy, 
bearing the dates of 1212, 1220, and 1228. Among early instances of 
their use, is a curious record in the handwriting of Petrarch, stating 
upon a MS. of St. Augustjn that it was given him by Boccaccio : — 



Archaeologin, p. 155. f lb. 123. 

J Id. est, dream (Danish, " s^tw"). 



32 THE DECIMAL SYSTEM, 

\f hoc Tmetrftl of> &>-n-a.u.vt -nv -inf cci'Cqi o1-\j 
Johes 3?«cca.c$Lj S>e ^ertaVj? vcclt^ yirv ipztS CJ d 

The figure of 3 resembles that which has come down to our 
hands ; that of 5 has undergone many changes, but was main- 
tained in the above form for several centuries. 

The introduction of the Hindoo system of numerals into 
Arabia and Persia was not accompanied by the invention of new 
words to represent the higher decimal numbers. A million was 
called a thousand thousands; a thousand millions, a thousand 
thousand thousands. The repetition of the smaller decimal sums 
to represent the greater, has prevailed in languages and countries 
the most remote from one another. Taihun-laihwid, ten ten, to 
mean a hundred, is found in Bishop Ulphilas's Moeso-Gothic 
Translation of the Evangelists.f So natural is this combination, 
that exactly the same form of decimal notation is found among a 
hunting tribe on the northern shores of Lake Superior, who 
express 100 by mitana mitenah, ten ten, and 1000 by mitana mitenah 
mitanah. And the Sapibocones of South America express 10, 
100, and 1000 by tunca, tunca tunca, and tunca tunca hinca. In 
examining the numerals of different nations, similar examples will 
be found in abundance. 

The invention of the cipher was a great step in arithmetical 
discovery. Why the Greeks, having adopted their letters for 
numerals, should not have discovered that if a represented 1, /3 2, 
and y 3, that the three united might represent 123, may be ex- 
plained by the embarrassment which they must have felt when they 
had to write 100 and no more, or any number in which a blank 
occurred ; thus they felt the necessity of employing distinct sym- 
bols for tens, hundreds, and thousands. The use of marks above 
or below the letters was used to augment their arithmetical value ; 
but the device was imperfect. The cipher solved every difficulty, 
and made the nine digits competent to any amount of figures. 
The word cipher is from an Arabic word, meaning vacancy or 
nothingness. 

The Arabs employ a dot instead of the cipher ; thus 1020 
would be written \ % (*. The Spaniards frequently adopt a very 

* See Colebrooke's Dissertation, p. 409. Peacock, p. 413. 

f Codex Argenteus, preserved at Upsala, in Sweden. 

X Humboldt " Vue des Cordilleres," &c, p. 251. Peacock, 379. 



IN NUMBERS, COINS, AND ACCOUNTS. 33 

small circle instead of a cipher, and in numbering their streets, 
particularly in the southern provinces of the Peninsula, a dwarfish 
cipher often replaces the Arabic dot; thus No. 2°1 is found instead 
of 201. 

There is no end to the fancies which have traced in the Arabic 
numerals self-expressing symbols. 

What is worthy of notice is, that the most ancient forms of the 
two and three, whether in Egyptian or Sanscrit writing,' as well as 
in ancient Persian, in Thibetan, Mahratta, and other languages, 
resemble the Arabic numerals, which is not the case as respects 
any other of the digits. 

The Arabic numerals were thus written by the Arabs. 

I f r r • 1 v a <* • 

1234 56 78 90 

But the letters of the alphabet were among the Arabs, as among 
the Hebrews and other nations, employed to represent numerals, 
not in their alphabetical order, but as follows : — 

a b t th g h kh d j r z s sh ss dd tt 

J -r-» CL» l±j £ £ t * o J j IT (^U 5 ^^ 

1 2 400 500 3 8 600 4 700 200 7 60 300 90 800 9 
tz kh kkh f kll k 1 m n h w y 

900 70 1000 80 100 20 30 40 50 5 6 10 

The Arabic alphabet was probably originally arranged ac- 
cording to the value of the numerals ; or rather the numerals 
followed the order of the letters, as in the Hebrew and the Greek ; 
which would, in fact, restore the Arabic letters to the position they 
hold in the Hebrew and Greek alphabets. 

The use of counters remained long after the Arabic numerals 
were introduced. Head or mental arithmetic had not made much 
progress among the people two hundred years ago — so says a 
master of arithmetic. " The feat with the counters would not 
only serve those who cannot write and read, but also for them 
that can do both, but have not at some time their pen or tables 
ready with them."* So Shakspeare's clown — "Let me see— 
every shorn wether tods — every tod yields — pounds and odd 

* Record's Arithmetic, 1658, p. 179. 



34 THE DECIMAL SYSTEM, 

shillings — fifteen hundred shorn, what comes the wool to ? I 
cannot do it without counters." * 

The works of Cocker have passed into oblivion, but his name 
and fame are become " household words." The first edition of 
his " Arithmetick — the Incomparable Art " — as the title-page calls 
it, was printed 1677. In 1720 (such was its popularity), the work 
had reached the thirty-seventh edition. Cocker himself appears 
to have formed a high estimate of his mission, and says com- 
placently : "By the sacred influence of Divine Providence I have 
been instrumental to the benefit of many ;" but Professor De 
Morgan seems disposed to launch a theory, that Cocker is, after 
all, the Mrs. Harris of arithmetic — that as far as the book is con- 
cerned, he was but " the shadow of a name," and that " John 
Hawkins, writing master, near St. George's Church, in South- 
wark," who professed to publish "Cocker's Arithmetic by the 
author's correct copy," may have himself been the author of 
the much renowned volume.f 

The great and useful change which the Arabic or decimal 
system introduced, was, to give to the same symbol a different 
value by altering its position — the figure on the right hand 
representing the least value — the figure on the left hand the 
highest, and every figure acquires a ten-fold value by every 
remove from the digit on the right hand. By this simple and 
beautiful arrangement, only nine figures were required for the 
representation of any amount, however great ; while, on the less 
perfect system, great or complicated numbers could only be repre- 
sented by numerous and complicated figures. With the Arabic signs, 
the value of any number can be altered and defined, by merely 
shifting its place. If the simplicity and condensation of the 
system of Arabic numerals be compared with the complexity and 
elaborateness of either the Greek or the Roman method, the 
benefits conferred by their introduction will be most obvious. 

In the Greek and Roman schemes, whatever might be the 
position of the letter representing a numeral, its value would be 
the same ; while, in the Arabic system, its value would be deter- 
mined by the place in which it stands. Thus while 5 stood alone, 
it would mean five units — another five added to it would add 5 
tens 55, a third 5 hundreds 555, and so forth, the increased value 
being always ten-fold. 



* Winter's Tale, Act iv. Scene 3. f De Morgan's Aritb. Books. 



IN NUMBERS, COINS, AND ACCOUNTS. 35 



CHAPTER III. 



DECIMAL SYSTEM EXPLAINED. 



To read all the books that have been written on any one topic, 
and its ramifications, would be a labour far beyond human patience 
or human industry; and nowhere more than in the field of figures 
do the embarrassments of superfluity accompany inquiry. 

Professor De Morgan estimates, that since the year 1500, no 
less than 3,000 works on arithmetic have been published in Latin, 
French, German, Dutch, Italian, and English,* which would give 
to each of these languages an average of one production a year. 
In this portion alone of the expanse of human inquiry, how much 
of ingenuity has been employed — how much of anxious thought 
and elaborate calculation has been wasted — how little has been 
saved to the present and the future out of the wrecks and ruins of 
the past ! And yet, instead of indulging in melancholy thoughts 
over so much of toil and trouble that has passed into oblivion, 
ought we not rather to rejoice that so little has been lost of that 
which was really worth preserving ? 

The decimal system, though found in some shape or other, 
more or less perfect, in almost every region of the globe, had really 
no adequate or even convenient mode of sound till the Arabic 
scheme of notation,. with its beautiful simplicity of expression, and 
its wonderful powers of expansion, supplied wants which must 
have been constantly felt in every department of arithmetical 
inquiry. 

The popular use of decimal fractions must be attributed to 
Stevinus,t whose works, originally written in Flemish, were trans- 

* No doubt the first English print on arithmetic is cap. 1 of " The 
Mirrour of the World, or Thymage of the same," headed> " And after 
of Arsmetrike, and whereof it proeeedeth." Printed by Caxton in 
1480. — De Morgan, Arith. Books, p. 101. 

f Stevins thus describes the decimal power. " Disme is a species 
of arithmetic invented by the progression of tens, consisting in 
characters of ciphers, oy which any number is described, and by 

D2 



36 . THE DECIMAL SYSTEM, 

lated into indifferent French by Simon of Bruges, and who adopted 
the word disme as the device or representative of the new system 
of arithmetic. The English translation of Stevins' work is by 
Eichard Norton (1608), and bears a title which is self-explanatory : 
— " Disme, the art of tenths, or decimal arithmetic, teaching- how to 
perform all computations whatsoever, by whole numbers without 
fractions, by the four principles of common arithmetic ; namely, 
addition, subtraction, multiplication, and division; invented by 
the excellent mathematician Simon Stevin." Dr. Peacock con- 
siders Oughtrede, the author of the Clavis Mathematica (1631), to 
have contributed more than any other to the propagation of 
decimal arithmetic, and that from this date the system may be 
deemed fully established. 

The object of arithmetic is to give definite and correct results 
from calculations of numbers, and the rules of arithmetic are in- 
tended to facilitate these calculations. As regards the simpler 
processes of addition and subtraction, much may be accomplished 
by what is sometimes called " head work," the exercise of the 
mind, unassisted by figures, or what is appropriately denominated 
mental arithmetic ; but for the more complicated operations of mul- 
tiplication and division, which are but addition and substraction 
on a larger scale, it is not easy to conceive how they can ever have 
been satisfactorily carried on without the use of decimal divisions ; 
and, even with their aid, what child has not repeated the ancient 
rhyme with strong sense of its truthfulness ? 

• Multiplication is my vexation, 
Division is twice as bad ; 
The Rule of Three puzzles me, 
And Practice makes me mad."* 

In the first efforts of mind, distinct perceptions of numbers do 
not reach very far ; and it is impossible that the ideas can acquire 

which we despatch all calculations of human affairs by whole numbers 
without fractions." Consult a curious paper of Professor De Morgan's, 
in the " Companion to the Almanack," for 1851. 

* These verses are thus given from a MS. of about the date of 
1570, by Mr. Davies. — Key to Hutlon's Course, p. 17. 

" Multiplication is mie vexation, 
And Division is quite as bad ; 
The Golden Rule is my stumbling-stool, 
And Practice drives me mad." 



IN NUMBERS, COINS, AND ACCOUNTS. 37 

distinctness unless by a gradual process — moving step by step 
from the lower to the higher regions of numerals. The steps of 
progression afforded by the decimal system are singularly easy. 
The child who, for the first time, is taught the difference between 
ten and a hundred, even when told that a hundred is ten times ten, 
would assuredly get only a vague and loose conception of the 
greater number until his mind had gone over the ground by 
adding one ten to another until the process was completed. But 
if the child had been so far instructed as to get a correct notion of 
twenty, and were then told that a hundred represented twenty 
five times repeated, he would probably reach a correct notion of the 
value of a hundred by a swifter process ; and again, if the num- 
bers to fifty were accurately appreciated, and he were taught that 
two fifties make the hundred, the process of accurate appreciation 
would be still more rapid. In the same way, a correct idea of the 
value of a hundred would lead to a true conception of the value of 
a thousand,* being ten hundreds, — that of a thousand, of a million ; 
but the distinctness of impression would be weakened with every 
augmentation of the numbers. 

It will be seen in the languages of all civilised nations, 
that a far greater number of words mark the various steps of 
decimal notation than are found to represent any other arithmetical 
progression. 

In the English language, associated with the idea of ten,we have — 

Of Saxon roots — ten, tenths, tenfold, tithes, tithing, tithing- 
man, teinds. 

Of Norman roots — decimal, decimate, decimation, decime, 
dime, or disme. 

Of Latin roots — December (tenth month or moon), Decemvir 
decennial. 

Of Greek roots-^decade, decagon, decalogue. 

Of Hundreds. In Saxon — hundred, hundreds (geographical), 
hundreder. 

In Norman, Latin, and Greek — cent, centime, century, cen- 
tenary, centuple, centurion, centigrade, centesimal, centumviral 
centipede, centuple. 

Of Thousands. In Saxon — thousand, thousandth-. 

In Norman, Latin, and Greek— mil, mile (1,000 steps), milfoil 

* Egli e maggior fatica a guadagnare il primo migliaio che poi col 
primo il decimo e il vigesimo. — Cam. Letter e, 69. 



38 .THE DECIMAL SYSTEM - , 

(a thousand leaves), millennium (a thousand years), millesimal, 
millennarian, millenest, milleped, millennary, millet (seed of a 
thousand grains), chiliad. 

Ten thousand — myriad. 

Million — millionaire. 

The decimal progressions are, in most languages, made the 
resting-place from which start new groupings of words and their 
associated ideas. The first ten units generally stand separate and 
alone, and furnish the rests or foundations upon which the whole 
arithmetical structure is built. From eleven to ninety-nine, every 
amount is represented by some combination of the units, generally 
by a euphonious abbreviation, such as thirteen, fourteen, fifteen, 
instead of three ten, four ten, five ten, — or sixty, seventy, eighty, 
to represent six tens, seven tens, eight tens, &c. Next, up to nine 
hundred ninety and nine, hundreds and units are the elements of 
account, but, the use of higher numbers being less frequent than 
that of lower, abbreviations are seldom employed. The same rule 
applies to thousands, myriads, millions, billions, &c, when abbre- 
viations or separate words are only used to represent decimal ideas. 
It would be obviously most inconvenient to say, ten tens for a 
hundred, or ten times ten tens, or a hundred tens, for a thousand, 
and so on. But there are few or no comprehensive or abbreviated 
terms in any other than decimal multiples ; and if there be such, 
they are of narrow and local signification. Locke says, " In the 
way we take now to name numbers by millions of millions of 
millions, it is hard to go beyond eighteen, or, at most, four-and- 
twenty decimal progressions without confusion." Happily, such 
enormous quantities are little required in the ordinary concerns of 
life, but calculations to the twentieth decimal power are needful to 
determine real astronomical distance. 

Dr. Lardner expresses a very natural surprise, that what is 
called the "device of place," by which all necessity for distin- 
guishing the value of the units by distinct and separate symbols, 
should have remained so long undiscovered. But the most simple 
and striking results are frequently the produce of elaborate thought, 
and one of the highest and noblest exercises of the human intellect 
is to trace through the entanglements and perplexities of imperfect 
knowledge some great and pervading element or principle, which 
brings all disorder into harmony. An easy and intelligible form 
of decimal expression soon changed the whole system of figures. 
The process by which the system now universally adopted among 



IN NUMBERS, COINS, AND ACCOUNTS. 39 

civilised nations probably made its way originally, is very intelli- 
gibly laid down in the following- extract : — * 

"Let us imagine a person possessing a clear notion of the decimal 
method of classifying numbers, being desirous to count a numerous 
collection of objects by the help of common counters. He will, 
probably, at first pursue the method practised by the savage tribes 
of Madagascar. f The objects to be counted being passed before 
him one by one, he places a counter in a box A for each object that 
passes ; but presently the counters in A become so numerous, and 
form so confused a heap, that he finds it as difficult to form an idea 
of their number as he would of the objects themselves which he 
wishes to count. Being able, however, to form a distinct and clear 
notion of ten counters, he pauses when he has placed the tenth 
counter in the box A, and withdraws all the counters from it, 
placing a single counter in the box B, to denote that ten objects 
have passed. He then recommences his tale ; and, as the objects 
continue to pass before him, places counters in the box A, and 
continues to do so until ten more objects have passed, and ten 
counters are again collected in A : . he withdraws this second col- 
lection of ten counters from A, and places a second counter in B ; 
signifying thereby that two sets of ten objects have passed. 
Eecommencing a third time, he proceeds in the same way, and, 
when ten have passed, withdraws the counters from A, and places 
a third counter in B. He continues in this manner, placing a 
counter in B, for every ten which he withdraws from A. If the 
objects to be counted be numerous, he finds, after some time, that 
the counters would collect in B so as to form a number of which 
he would still find it impossible to obtain a clear notion. For the 
same reason, therefore, that he allows no more than ten counters to 
accumulate in A, he adopts the same expedient with respect to the 

* Lardner's Arithmetic, pp. 31-34; 

f When the people of that island wish to count a great multitude 
of objects, such, for example, as the number of men in a large army, 
they cause the objects to pass in succession through a narrow passage 
before those whose business it is to count them. For each object that 
passes they lay down a stone in a certain place; when all the objects 
to be counted have passed, they then dispose the stones in heaps of 
ten : they next dispose these heaps in groups, having ten heaps, so as 
to form hundreds; and in the same way would dispose the groups of 
hundreds so as to form thousands, until the number of stones has been 
exhausted. 



40 THE DECIMAL SYSTEM, 

box B. When ten sets of objects have been counted, he finds that 
ten counters have collected in B : he withdraws them, and places a 
single counter in the box C, that counter being the representative 
of the ten withdrawn from B, each of which is itself the repre- 
sentative of ten withdrawn from A. The sing-le counter in C will 
thus express the number of objects in ten sets of ten ; and such a 
number, as already explained, is called a hundred. When one 
hundred objects have passed, there will therefore be only a sing-le 
counter expressing it placed in the box C. The objects to be 
counted continuing to pass, the computer proceeds as before, placing 
counters in the box A, withdrawing them by tens, and signifying 
the collections withdrawn by placing single counters in B, until 
ten counters again collect in B ; these are withdrawn, and a second 
counter placed in C. Let us now conceive the three boxes 
inscribed with the names of the units signified by the counters 
which they respectively contain. It will be obvious, that by the 
aid of twenty-seven counters, all numbers under a thousand may 
be expressed. Thus, nine hundred and ninety-nine would be 
expressed by placing nine counters in each box ; the nine counters 
in the box C would stand for nine hundreds ; those in the box B 
for nine tens, and those in A for nine original units. 

" It will be sufficiently evident that the same method may be 
continued to any extent. A fourth box, D, inscribed thousands, 
may be provided, in which a single counter will be placed for every 
ten counters withdrawn from C ; and a fifth, E, inscribed ten 
thousands, in which a single counter will be placed for every ten 
withdrawn from D, and so on. Under such circumstances more 
than nine counters could never collect in any box. 

" We have here supposed the counters to be all similar to each 
other, and not bearing on them any character or mark ; but as we 
have inscribed the several boxes with the names of the order of 
units which the counters they contain express, there is no reason 
why the counters themselves may not be inscribed with a character 
by which a single counter may be made to express any number of 
units from one to nine. Let us, then, suppose the computer 
furnished with an assortment of counters, inscribed with the figures 
1, 2, 3, 4, 5, 6, 7, 8, 9 ; when he would express the number of units 
in each box, instead of placing in it several individual counters, the 
number of which might not be easily perceived, he places in the 
box a single counter, inscribed with a character which expresses 
the number of single counters which would otherwise be placed in 



IN NUMBEBS, COINS, AND ACCOUNT8. 41 

the box. Thus, instead of leaving' six individual counters in a box, 
he would place in it a single counter, marked with the character 6 ; 
by such an arrangement the number to be expressed would be 
always evident on inspection, as here exhibited : 



F 


E 


D 




C 




B 


Lil 


3 


m 




7 




3 


Hundreds T 
of Th 
Thousands 


ens 
ousa 


of Thousands 
nds 


Hundreds Tens 



m 

Units 



Four hundred and thirty-five thousand seven hundred and thirty- 
one. 

"Having adopted such a method of reckoning*, he would naturally, 
for convenience, always arrange the several boxes in the same 
manner, and very speedily the place in which the box stood would 
indicate to him the order of the units which it contains ; thus he 
would be at no loss to remember that the second and third boxes 
from the right would always contain tens and hundreds, and the 
like of the others. The formal inscription, units, tens, &c, would, 
therefore, become unnecessary ; and since, by the method of in- 
scribing" the counters with figures, no more than one counter need 
be placed in any box, the boxes themselves would be dispensed 
with, and it would be sufficient to place the counters one beside the 
other, the place of each counter indicating the rank of units which 
it signifies. A slight difficulty would, however, occasionally present 
itself. Suppose that it should so happen that, when the last object 
to be counted passed, the tenth counter was placed in the box C, 
according to the system explained, all the counters would be with- 
drawn from C, and a single counter placed in D, or a counter con- 
taining a figure higher by one than that which was placed in it 
before. When the complete number is expressed, the box C would, 
in this case, contain no counter. When the boxes are superseded, 
and th.e counters alone used, the place of the third counter from the 
right would be unoccupied, and the number would be expressed by 
the counters thus : — 

© © © O ® 

" The space between the counters inscribed 5 and 3 here shows 
the absence of the counter which would express hundreds; but in 



42 THE DECIMAL SYSTEM, 

placing 1 the counters, through negligence or otherwise, it might 
happen that the two counters which should thus be separated by a 
space might be brought so close together, that in reading the 
number the space might be overlooked, in which case the counter 
inscribed 5 would erroneously be supplied to express 5 hundreds. 
To provide against such an error, let us suppose blank counters to 
be supplied, and one of these placed in the position which would be 
occupied by an empty box ; the above number would then appear 
thus: 

© © © © © 

and no mistake could possibly ensue. 

" The next step in the improvement of this method would be to 
abandon counters altogether, and immediately to write down the 
figures which would be inscribed on them if they were used ; these 
figures being written in the same order in which the counters were 
supposed to be placed. In this case a character would become 
necessary to signify the place of a blank counter, wherever such a 
one might occur. The character which would be naturally adopted 
for this purpose would be 0, and the above number would then be 
435031. 

" Such is the system of numerical notation, which has obtained 
in every part of the world an acceptance, the universality of which 
can only be attributed to its admirable simplicity and efficiency." 

The decimal power may be said to lose itself in infinity of ad- 
dition and multiplication, subtraction and division, by regular grada- 
tions of which tens multiplied or divided by tens are the instrument. 
It starts from a point, and by regular successions of decimal increase 
rapidly exhausts not only the powers of recording numbers, but even 
the conception of their immensity. If the attempt be made at a mul- 
tiplication of progressive decimal quantities, such as by 10 — ten by 
tens, hundreds by hundreds, thousands by thousands, millions by 
millions, billions by billions, trillions by trillions, and so forth, 
it. will soon be found that the manual and intellectual labour of 
merely placing the units on paper will exceed all the powers of 
patient application. But take any other numbers than ten, and 
continue to multiply the product by itself, such as 9 by 9, 81 by 81, 
6561 by 6561, and so forth, and the immense superiority of the 
decimal over every other scale will be strikingly elucidated. Far 
more than the telescope has done in exploring what is vast and 



IN NUMBERS, COINS, AND ACCOUNTS. 43 

distant in the regions of space — far more than the microscope has 
accomplished for exhibiting 1 the adjacent and the minute in the 
world invisible to mortal eye — the decimal system has effected for 
arithmetical and astronomical science. 

That the powers of figures are limited, whether decimal or not, 
may indeed be easily demonstrated. Mr. Babbage's calculating 
machine must be arrested somewhere ; and in division, as well as 
multiplication, we are stopped by those laws of necessity which 
prevent finite comprehensions from stretching into infinity. For 
example, no figures will show the square root of 5. And the proof 
is irresistible, insomuch as that no figure multiplied by itself will 
make 5. Take the nearest approaches to the square root, and go 
through the whole nine digits. Suppose you have 2*231 — will that, 
multiplied by itself, make 5*000? Assuredly not ; but it will make 
4*977,361. Take 2*232— that will not give 5*000; neither will 
2*233— nor 2*234— nor any one of the digits up to 2*239, which, 
multiplied by itself, gives 5*013,121. The square root of 5 is 
therefore something between 2*236 and 2237, but it is inaccessible 
and indefinable by decimal or any other figures ; nor am I aware 
of any system by which the square root of prime numbers could 
be represented. This indeed is but to say that we lose ourselves in 
the vast extent of the field of investigation, comprehending all 
space and all time. However far we are able to pursue inquiry, 
it must ultimately lead towards the unapproachable. It may be 
said of all knowledge, that its boundaries are lost in infinity. From 
infinite wisdom all true science emanates ; towards infinite wisdom 
all true science progresses ; and in infinite wisdom all science loses 
itself. 



44 THE DECIMAL SYSTEM, 



CHAPTER IY. 

ON NUMBERS, WITH ELUCIDATIONS OF DECIMAL DIVISIONS. 

Is pursuing* inquiries into the history of arithmetical science 
— though the decimal grouping 1 is undoubtedly the most salient 
point of observation — it is scarcely possible to pass by unnoticed 
the superstitions which have, in all periods of the world, been con- 
nected with particular numbers.* Keeping out of view the 
decimal distinctions, we find in the Bible remarkable evidence of 
partiality to particular units. While the number 6 only occurs 
123 times ; and the number 8 only 56 times ; the number 7 is 
found 413 times. So the number 11 appears 36 times; the number 
13 only 17 times j while the number 12 is found in 138 different 
places. 

Independently of its decimal character, the number 10 had a 
peculiar sanctity in the minds of the Hebrews, especially as 
associated with the Decalogue ; so had the number 40, as repre- 
senting the period of days passed by Moses with Jehovah on the 
mount ; and that during which the waters of the deluge were poured 
upon the earth. Seven is one of the most frequently occurring 
numbers, from having a somewhat indefinite meaning. Seven 
was employed vaguely to represent an uncertain but not a large 
number of persons or things. In the very earliest of the Biblical 
records we find, " If Cain shall be avenged seven fold, truly 
Lamech seventy and seven'' (Genesis iv. 24). And in the book of 
Job, "In seven troubles (i.e. many troubles) no evil shall touch 
thee" (Job. v. 19). Again, out of many examples in the Apocry- 
pha, " A man's mind is sometimes wont to tell him more than 
seven watchmen that sit above in a high tower." " How often 
shall my brother sin against me, and I forgive him until seven 
times ? " (meaning, should I often do so ?) ; and the answer is, u I 

* Scaliger will have the word number to be derived from the 
Greek ve/xuv (to distribute), and insists that vo/iog (law) means that 
each shall be protected in the property he possesses, or that is 
distributed to him. 



IN NUMBERS, COINS, AND ACCOUNTS. 45 

say unto thee, not until seven times, but until seventy times 
seven" (Matt, xviii. 21), meaning", times innumerable; or, rather, 
that to forgiveness there should be no bounds. 

Independently of its frequent use as an undefined number, 
seven had a holy and mysterious meaning", associated as it was in 
the minds of the Hebrews with the day on which Jehovah rested 
from the work of Creation; the seventh month was deemed more 
sacred than the other months; the seventh year was one of 
Sabbatical rest ; and seven times seven years introduced the year 
of jubilee (Levit. xxv. 9, 10). 

The Book of Revelation presents remarkable evidence of the 
attachment of the Jews to particular numbers, among" which 4, 7, 
12, 24, and 144, are the most prominent : — 

Four he&sts, four angels, four wings, four corners, four winds.* 

Seven churches, seven golden candlesticks, seven stars, seven 
spirits of God, seven lamps, seven horns, seven eyes, seven angels, 
seven seals, seven trumpets, seven thunders, seven heads, seven vials, 
seven mountains, seven kings, seven thousand slain, seven plagues. 

Forty and two months = 6x7; 1*260 days = 30 X 6 X 7 ; 
xi. 3, xii. 6. 

Ten days of tribulation, ten hours, ten crowns. 

Twelve tribes, twelve gates, twelve stars, twelve foundations, 
twelve apostles, twelve pearls, twelve fruits. 

Twenty-four seats, twenty-four elders. 2x12. 

Twelve times twelve, 144 cubit3 ; 144,000 of all the tribes, vii. 
4, of the redeemed, xiv. 1, 3. 

A thousand years. 

Twelve thousand of each of the twelve tribes. 

Two hundred thousand thousand horsemen. 

Ten thousand times ten thousand and thousands of thousands 
of angels. 

A superstitious reverence has been attached among many 
nations to the number seven, even down to our own time. A 
seventh son, when there has been no interruption of daughters, 

* Some of the Fathers give strange reasons for favouring certain 
numbers : " There must be four Gospels and no more, from the four 
winds and the four corners of the earth," says St. Irenaeus ; and St. 
Augustin's reasons for the choice of the twelve Apostles is, that the 
Gospel was to be preached in the four corners of the world in the 
name of the Trinity,—" and three times four," says he, " make twelve." 
—See Brand's Pop. Ant, vol. iii. p. 268. Ed. 1849. 



46 THE DECIMAL SYSTEM, 

has been supposed to possess supernatural powers to heal certain 
diseases ; and the seventh son of the seventh son, powers still more 
transcendent.* 

It was a curious fancy of the ancients, that 

*' God loves uneven numbers ;" f 

and the same still exists in the popular mind. Good women, says 
Grove, held it indispensable that a hen should sit upon an odd 
number of eggs. All salutes are given in an odd number ; and in 
many ancient medical prescriptions, in the taking pills, purgations, 
or bleedings, even numbers are ordered to be avoided. From this 
favourable opinion the number 13 is excluded ; which is attributed 
by some writers to the presence of 13 persons at the Paschal 
supper, when the treachery of Judas was proclaimed. 

The number 12, however, must be excepted from the general 
dislike to even numbers. It has been an object of partiality among 
many nations. A dozen is a favorite quantity in barter ; and a 
gross, or 12 X 12, is of frequent use among the inhabitants of the 
South. The Scandinavians employed the word tolpoed to make 
12 of 10 and 120 of 100. C C vietra tolpced, is 240 years; and in 
our own language the long hundred implies six score. 

In examining the affinities between the numerals of the great 
Indo-European family of languages, it will be seen that in the 
number one there is less of resemblance than in any other of the 
nine digits. Bopp very naturally supposes that the first numeral 
was in many cases only a representative of some noun or pro- 
noun and thence was probably scarcely regarded as a numeral 
at all. Reckoning would in fact begin with 2, the second digit, 
and in that the resemblance runs throughout the whole group 
of idioms ; and the same resemblance may be generally followed 
in all the units up to ten, and from ten up to a hundred, for which 
number many of the languages adopted independent words, not 
traceable to a Sanskrit, or, indeed, any other source. 

* For many curious elucidations of these superstitions, see Brand's 
" Popular Antiquities," Vol. iii. p. 265-8. Ed. 1849. 

f " Numero Deus impare gaudet." Virgil, viii. Eclogue. — My 
readers may amuse themselves, while we are on the subject of uneven 
numbers, by unravelling the puzzle which William Leybourn gives in 
his "Pleasure with Profit," a.d. 1694. "What are the four odd 
numbers which added together make twenty?"— Quoted by De Morgan 
in Arithmetical Books, p. 64. 



IN NUMBERS, COINS, AND ACCOUNTS. 47 

The first ten figures are called units, from the Latin unus or 
one ; or digits, from digitus or digiti, the fingers ; and in most 
languages these ten figures form the first group, and have separate 
and distinct names. The multiplication by tens or by combinations 
of tens is the ordinary mode of progression up to the highest 
groups of figures, — from hundreds, which are tens of tens, to thou- 
sands, which are tens of hundreds, and to millions, which are 
thousands of thousands. 

In the first groups of ten, from eleven to twenty, an irregularity 
is frequently found, especially in the European languages. We do not 
say one ten, two ten, for eleven and twelve, as we say thirteen (three 
ten), fourteen (four ten). But even with this exception, the English 
numerals proceed with great regularity up to one hundred ; and, as 
regards the seemingly irregular eleven and twelve, both words are 
associated with this symbol of ten, and mean leave one, and leave 
two : i. e., one and two to be added to the preceding ten. The 
process of the etymology may be easily traced through the Anglo- 
Saxone?idleqfan (one leave), through einlif, to the German eilf, and 
the English eleven : so in twelve — two leave, zwolif—zwolf in 
German — to twelve English. Twenty is a favourite resting-place. 
The word score, which implies a stoppage when the amount was 
scored or recorded, has a strong hold of the popular mind, and is 
of frequent occurrence in English talk. 

" Score me up for the lyingest knave in Christendom." 

Taming of Shrew, 2. 
And besides many other examples— 

" And thou shalt have more 
Than two tens to a score." 

Lear, 1. iv. 

Two score, three score, three score and ten, four score, four score 
and ten, are quite as familiarly used as forty, sixty, seventy, 
eighty, and ninety. 

So in the French language, though septante, octante, and 
nonante, are undoubtedly excellent French words, and to be found 
in classical authorities, the words soixante dice (sixty and ten) 
for seventy, quatre vingt (four twenties) for eighty, and quatre 
vingt dix (four twenties and ten) for ninety, are almost invariably 
employed to represent these numbers. 

Many other languages present peculiarities in the transition 
from ten to thirteen. In the old Sclavonic, the form is yedinyi na 



48 



THE DECIMAL SYSTEM, 



desyaty, for eleven (literally the first over ten) ; vtoryi na desyaty, 
for twelve (being the second over ten) ; in both cases the ordinal 
form is employed ; but from thirteen upwards the cardinal form 
is used, as chetyri na desyaty (fourteen), being four over ten. 

In the French, the irregularity is referable to a simple abbrevi- 
ation of the Latin form, undecim, onze ; duodccim, douze, where the 
termination ze may be deemed a mere shortening of decern for the 
sake of euphony. 

The Sanskrit preserves perfect symmetry from eleven to eigh- 
teen, and the Thibetan from eleven to nineteen. In Sanskrit, the 
word dasa, ten, follows, in Thibetan it precedes, the unit. 





Sanscrit. 




Thibetan. 




11 


Eka das 'a 


one ten 


Chu cheic 


ten one 


12 


Dva das'a 


two ten 


Chu gnea 


ten two 


13 


Triyo das'a 


three ten 


Chu soom 


ten three 


14 


Chatur das'a 


four ten 


Chu zea 


ten four 


15 


Pancha das'a 


five ten 


Chu gna 


ten five 


16 


Sho das'a 


six ten 


Chu tru 


ten six 


17 


Sapta das'a 


seven ten 


Chu toon 


ten seven 


18 


Ashta das'a 


eight ten 


Chu ghe 


ten eight 


19 


Unavinsati 


one (from) twenty 


Chu goo 


ten nine 


20 


Vinsati 


twenty 


Gnea chu turaba 


two ten 



Ovid gives a variety of reasons for holding the number ten in 
especial honour, the most obvious of which is, that everybody is 
accustomed to count with his ten fingers.* 

It is a favourite number with poets, and is crowded into one of 
Shakspeare's Sonnets thus : — 

* If ten times happier, be it ten for one ; 
Ten times thyself were happier than thou art, 
If ten of thine ten times refigured thee." 

Shakspeare's Sonnets, vi. 



* " Annus erat decimum cum Luna repleverat orbem 

Hie nurnerus magno tunc in honore fuit j 

Seu quia tot digiti, per quos numerare solemus 

Seu quia bis quino foemina mense parit, 
Seu quod ab usque decern numero crescente venitur 
Principium spatiis sumitur inde novis." 

Ovid, Fasti, lib. iii. 124. 



NUMBERS, COINS, AND ACCOUNTS. 40 

The tenth wave* was held in ancient times to be the most violent 
and perilous. Ovid says : — 

" The wave, of all most dangerous near the shore, 
Behind the ninth it rolls, the eleventh before." f 

While few of the numeral nouns serve as roots to verbs, to 
tithe, to teind, to decuple, to decimate, have found their way into 
dictionaries, and into the language of the people. 

Decimation is used in a variety of senses, from the earliest 
times. Herodotus speaks (vii. 132) of the assembled Greeks 
who compelled their opponents to pay the tenth part of their 
property (AtKctTtvaai), i.e., they decimated them — which some 
commentators have supposed to mean that they put every tenth 
man to death. 

Humboldt J remarks, that in the Toltec languages, spoken by 
the inhabitants of Central America, the year consisted of 18 months 
of 20 days each (with five supplementary days), many of which 
have monosyllabic names, unlike the dialects which prevail in 
America, and he points out a remarkable resemblance between 
the word Votan, for the third day, Odin's or Wodan's, or 
Wedn's-day — the twenty names being those of ancient chiefs. 
Vodan, according to the traditions of Central America, was a 
chief who, having escaped in a canoe from a great deluge, was 
the renewer of the human race. It has even been thought that 
the Odin of the West is identical with one of the Buddhas of the 
East, whose name in India is given to the third day of the week.§ 
These affinities open the door to curious speculations and inquiries. 

Grouping by sixties is an ancient mode of division among the 
Hindus. Their savan (or natural day), which is the time between 
two consecutive sun-risings, is subdivided into 60 Dhatas, of 
60 vinadihas, of 60 vipalas. . ' 

Their Taura (or solar day), the time during which the sun 
describes one degree of the ecliptic, and which, therefore, varies 
in length, is divided into 60 dandas, or halas, of 60 vikalas. 
The nakshatra, or true sidereal day — equal throughout the year — 

* Fluctus decumanus. 

f " Qui venit hie fluctus, fluotus supereminet omnes 
Posterior nono est, undecimoque prior." 
t Letter to Dr. Ahrendt, dated Potsdam, July 22, 1853. 
§ See Stephens's Thesaurus, i. p. 937. : 

B 



50 . THE DECIMAL SYSTEM, 

is again divided into 60 gharas, each being 60 pals or vighadias. 
The pal is again divided into 6 franas, or respirations ; but the 
"Surya Siddh'anta" and, all astronomical works carry on the 
sexagesimal division, thus : — 



60 kshanas = 


1 lava 


60 lavas =. 


1 nimesha 


60 nimeshas = 


1 kastha 


60 kasthas = 


1 atipala 


60 atipalas = 


1 vipala = 0'4 seconds 


60 vipalas = 


1 pala = 24 seconds 


60 palas = 


1 danda = 24 minutes 


60 dan das = 


1 dena = 1 day and night. 



60 denas = 1 vata or season. 

The year is divided into six seasons of two sidereal months, the 
succession of which is always the same, but the vicissitudes of 
climate in these seasons will depend on geographical position.* 

Our division of the minute into sixty seconds has thus an 
Oriental derivation. 

The unit of the Hindu system of currency was gold, and the 
old specimens found might either be 60 or 120 grains in weight, 
showing an evident connection with the Grecian drachma and 
didrachma of gold {x9 va °Q and Sixpvaog), and confirming the testi- 
mony afforded by the device and symbols of old Hindu coins of 
a direct descent from their Bactrian prototype.f 

Helvegius, as quoted by Junius, has a strange fancy respecting 
the origin of the word hundred, which he says is derived from 
kv rpiutv, en trion, or one in its third place (decimally considered), 
1 — 10 — 100. The old Gothic term for a hundred was taihun 
taihund, or ten tens. It was superseded by the briefer and more 
convenient hund, which was sufficiently intelligible after the re- 
moval of the three syllables that preceded it. Abbreviation of the 
word merely for the purpose of counting i3 natural, to save time 
and trouble. Most of the ten digits are monosyllables in the com- 
mercial languages of Europe, and when they are not so in writing, 
they become so by rapid pronunciation. 

The hundredth day after a particular event was deemed oy the 
ancients the most propitious for application to the gods for aid and 
guidance. 

* " Prinsep's Useful Tables." Calcutta, 1836. Part II , pp. 18, 19." 
f lb. : Part I., p. 15. . 



IN NUMBERS, COINS, AND ACCOUNTS. 



51 



When, as related by Herodotus, Croesus, the king of the 
Lydians, sent his messengers, to consult the oracles, he specially 
directed that their inquiries should be made exactly on the 
hundredth day after their departure from Sardis.* 

A curious example of the. disposition to run into decimal 
notation may be found in the enumeration of the Persian fleet. 
Herodotus says it consisted of 1,207 vessels,! of which he gives 
these details :— 



Phoenicians- 
Egyptians 
Cyprians .. 
Cilicians . 
Pamphylians 
Lycians . 
Dorians 
Carians . 
Ionians 
Islanders . 
iEolians 
Hellespontians 



300 

200 

150 

100 

30 

50 

30 

70 

100 

17 

60 

100 



1,207 



It is remarkable that the whole are given in round numbers, 
except the 17 vessels belonging to the islanders, which Diodorus 
rounds to 50. Diodorus adds, that there were 320 Greek vessels, 
but enumerates only 310. He makes the whole fleet to have 
consisted of 1,200 ships : — 



* The answer of the Delphic oracle, as given in hexameter verse, 
is amusing enough : — 

" The sands and their numbers I know, and the measure I know of 

the ocean, 
The dumb understand I — the silent I hear — and the savour 
Of tortoise — hard-shelled, boiled with lamb, in a vessel of brass — to 

my senses 
Is sweet — brass above, brass below must be laid there." 

Croesus sought to conciliate the Delphic god by sacrifices of 3,000 
head of cattle of every kind, and enormous offerings of gold and silver. 
f 'E7rra icat dirjKoaiai icai x^iat. vii. 184. 

E 2 



52 THE DECIMAL SYSTEM, 

Dorians 40' 

Cohans 40 

Ionians 100 \ 310 

Hellespontians ..... 80 
Islanders ...... 50 . 

Egyptians 200 

Phoenicians ...... 300 

Cilicians 80 

Carians 80 

Pamphylians , . 40 

Lycians . • 40 

Cyprians . 150 

1,200 

These discrepancies show the little confidence that is to be 
placed on numbers as given by historians. Some allowance must 
be made for errors of copyists or transcribers. 

Theocritus reproaches the Greeks for their decatombs and 
chiliombs ; their sacrifices of 100 and 1,000 oxen, upon which 
Larcher remarks, that the Greek sacrifices were trifling compared 
to those of the Jews — Solomon's peace-offering, at the dedication of 
the temple, consisted of 22,000 oxen and 120,000 sheep.* 

Aristophanes had an amusing company of thirty thousand 
Athenians in his comedy of " The Popular Assembly" : — 

" What citizen, dear master mine, 
Has half such happiness as thine ? 
Midst thirty thousand, thou alone 
Hast had no dinner. Happy one! " f 

As we approach the higher numbers of figures, all irregularity 
disappears, and the reason is obvious. The vulgar language, 
representing the daily and habitual wants of life, is little subjected 
to scientific rules; but in the more elevated regions, knowledge 
and science would create the symbols which they alone require. 
Beyond the lower numbers, little precision is required, and little 
exactness used in ordinary parlance. Children and uninstructed 

* 1 Kings, viii. 63. 

•f Tic y«P ytvo'iT av fiaWov oXfitiorepog 
"Ogti£, 7ro\ir(jjv irXtiov i) rp«r/tuptW 
*Ovtu)V to 7r\i]6og y ov SsSuirvtjKag fiovog. 

Arixt. Concio. v. 1131. 



IN NUMBERS, COINS, AND ACCOUNTS. 53 

persons frequently talk vaguely of hundreds and thousands and 
millions, giving way to fanciful expressions, and employing the 
first word of large figures which occurs. "I will give you a 
million of kisses," may be heard from the lips of a parent to a 
child. "A thousand thanks," is a common mode of expressing 
gratitude even for a trivial favour. " I have done it a hundred 
times," is often used merely to express the frequency of an action. 
Had any large numbers been habitually needed in the common 
intercourse of life, no doubt we should have had some single word 
to express ten thousand, as the Chinese have the word wan, or, a 
hundred thousand, for which the Hindoos use Ink. Million 
would seem to be the augmentation of mil, and to have conveyed 
the meaning of a larger thousand. On is in many languages the 
sign of aggrandisement : — hombre — hombron (Spanish), a man — a 
big man; ladro— ladrone (Italian), a thief— a great thief ; garcon 
for garce (French), a boy. 

The words billion, trillion, quadrillion, and so forth, are only 
expansions of the roots two, three, and four, as carried by decimal 
multiplication into the higher regions of figures. In the Sanskrit^ 
padma means thousands of millions ; mahadpadma, a great padma, 
is billions, or millions of millions. 

Herodotus speaks of the army of Xerxes as comprised of 
1,700,000 men,* — an incredible amount. Homer almost always 
avoids specific and defined numbers, generally employing myriad 
in its indefinite sense.t 

There is no end to examples of the use of the higher numbers 
to convey exaggerated notions of multitude. Berni says, in his 
Orlando Inamorato, ii. 21, 41 — 

" Of services which wait for doing, one 
Is worth a hundred thousand millions done." $ 

Hedi, in his Letters, desires his correspondent to give, in his 
name, to Father Carrara a million of millions of salutations.^ 
So Shakspeare in the " Winter's Tale" — 

* 'EfiSofirjicovTa kcu ttzarov [xvpiadeg, vii. 60. 

•J" Mvpiog, Infinitus, immensus, numerus (Lexicon). Example, Iliad, 
0. 320. 

I " Ch'un servigio val piu che s'abbia a fare, 
Che cento mile milion difatti." 
§ u Al padre Carrara renda in mio nome un milione di milioni di 
saluti,"— Lett, 149. 



54 



THE DECIMAL SYSTEM, 



" Autolicus. The loathsomeness of them offends me more than the 
stripes I have received, which are mighty ones and millions. 

" Clown. Alas, poor man! a million of beatings may come to a great 
matter." Act IV. sc. 2. 

And in Julius Csesar — 

u Oct. And some that smile have in their hearts, I fear, millions of 
mischief." Act IV. sc. 2. 

Again, in the " Two Gentlemen of Verona" — 

" Vol. Madam and mistress, a thousand good morrows. 
Speed. I give you good even, here 's a million of manners, 

Sir Valentine, and servant to you two thousand." 
* Within thine eyes sat twenty thousand deaths; 

In thy hands clutched, as many millions j— in 

Thy lying tongue both numbers." 

Again, in his 115th Sonnet— 

" Time whose million'd accidents 
Creep in 'twixt vows, and change decrees of kings." 

The million is sometimes used as the Greek, bi ttoWoi (oi polloi), 
the many, the mob, the multitude. So in Hamlet — 

" The play, I remember, praised not the million." 

Dante has, I believe, no higher number than congregated 
thousands — 

* Thousands on thousands pass into the moat." * 
"More than a thousand leagues its splendours show." f 

Spencer has — 

" So fair, and thousand thousand times more fair 
She seem'd, when she presented was to sight." 

The Latins, having no word of number conveying the idea of 
multitude, invariably employed some superlative noun. 

Tacitus speaks of a populous city as " numerosissima civitas." 
The Italians, and several other nations, have a class of numerals, 
such as diecena, centenaia, migliaio, &c, which must be deemed 
rather approximative than precise. They accommodate them- 
selves well to poetical phraseology. 

* " Dintorno al fosso vanno a mille a mille." — Inferno, xii. 73. 
j- " Che refulgeva piu di mille milia." — Para., 26. 



IN NUMBERS, COINS, AND ACCOUNTS. 55 

Dante has— 

u And over thousands of enkindled lamps, 
I saw a sun which far outshone them all." * 

And Berni — 

" And Agricano to the combat then, 
Led two-and-twenty hundred thousand men." f 

A similar form of numeration existed among the Greeks. It is 
reported of Thyas, the king of the Paphlagonians, that he had a 
hundred varieties served at his repasts ; and so, where we have 
Herodotus translated by "he made rich presents," the words 
literally mean, " he presented him with ten things of each 
kind."t 

" And is nobody here but we two ? Yes, said the monk, there are 
thousands ! " § 

" Which conditions were not by tens but by hundreds." || 

No higher term than that of million has ever obtained currency 
in England. A thousand millions, a million millions, are used in 
preference to billions or trillions — words whose real meanings have 
often been inaccurately laid down. The French have introduced the 
word milliard, meaning a thousand millions. The yearly expen- 
diture of France is habitually spoken of as a milliard and a half; 
that is to say, 1,500,000,000 francs, or about sixty million pounds 
sterling. The French represent myriad and billion to be 
sjmonymous ; but English writers generally consider billion to 
represent a million millions, a trillion a million billions, and a 
quadrillion a million trillions, and so on ; each denomination repre- 
senting a million times the denomination preceding. Thus 
2,567,894,237,168,456,306,123,720 

* " Vedi io sopra migliaia di lucerne, 

Un sol che tutte quante l'aecendia." — Paradiso, 23. 
•j" " Venti due centenaia di migliaia 

Di combattante avessero Agricano." — Orl. In. i. 10, 30. 
I "Emrov itavra 7rapari9e<r9ai, which Larcher says ought to be 
translated omnia centena, — or, une centaine de tout. 'Edwprjaaro itaoi 
dkica. Her. iv. 88. 

§ " Non v' e egli phi persone che noi due? Disse il monaco : 

Si, a migliaia." Boccacio, Nov. xxviii. 21. 

|| " I quali patti erano a centenaia e non a diecine. " 

Lett, di Benv. Cellini, 47. 



56 THE DECIMAL SYSTEM, 

would represent 2 quadrillions, 567,894 trillions, 237,168 billions, 
456,306 millions, 123 thousands 720. But the words have little or 
no practical value ; for though such groups of figures may be em- 
ployed for the purposes of astronomical or arithmetical calculation, 
they never can be associated with the ordinary and every day 
business of life, which alone can give currency to new forms of 
speech. 

Independently of decimal divisions, most languages have 
non-decimal quantities or words, denoting either specific or 
approximative quantities. Dozen, in English, is the Norman 
form for twelve — duodecim or douzaine; and a gross may probably, 
in its original meaning, have represented a large dozen — grosse 
douzaine. The Scotch have threave, which, though generally 
meaning two dozen, or 24, sometimes denotes a multitude, as in 
Ramsay : — 

" In came visitants a threave, 
To entertain them she maun leave 
The looking-glass." II. 463. 

Upon the mysteries of numbers volumes without end have 
been written. Few are ignorant of the manner in which, by earnest 
Protestants, the number of the beast (666) has been made to apply to 
Rome, to the" errors of the papacy, and to a variety of individual 
popes ; to different forms of heresies, and to the heresiarch Luther 
especially, by equally zealous Catholics. Erudition and imagination 
have revealed wonders concealed under the mysterious three,* and 
the scarcely less distinguished seven.-f One eloquent author, J on 
the title-page of his work on " The Secrets of Numbers," calls them 
" pleasing to read, profitable to understand, opening themselves to 
the capacities of both learned and unlearned — being no other than 
a key to lead men to any doctrinal knowledge whatsoever." 

One of the most familiar illustrations of the power of progressive 
numbers is found in the answer which the inventor of the game 
of chess is said to have given to the prince who asked what 
reward would satisfy him for his great discovery — " One grain of 
wheat," said he, " for the first square on the board, two for the 
second, and so to proceed doubling to 64, the whole number of 
squares." Lucas de Burgo had the patience to solve the question, 
and gives as the number of grains 

* See Lucas de Burgo, as quoted by Dr. Peacock, p. 424-5. 
f See Heptalogium Virgilii Salzburgensis. 
$• William Ingpen, Gent., London, 1624. 



IN NUMBERS, COINS, AND ACCOUNTS. 57 

18,446,744,073,709,551,616. * 

He carries on the estimate by the Perugian measure, and, 
calculating that 100 boat-loads would fill a warehouse, 100 ware- 
houses a castle, he computes that somewhat more than 209,022 
castles would be necessary to hold the wheat which the ingenious 
chess inventor suggested as his becoming recompense. Now, 
supposing, instead of a dual, there had been a decimal progression, 
what numbers could have recorded the result, and what time would 
have been occupied in the record? 

It would be rather amusing to trace through the regions of 
fancy the various methods by which the ideas of infinity are 
associated with the functions of numbers. The graces and glories 
of the Virgin are given by Gaspar Scott, in his "Magia Uni- 
versalis Naturae et Artis," as exactly exhibited by the 256th power 
of 2, viz. : — 

115,792,089,237,316,195,423,570,985,008,687,907,853,269,984,665,640, 
564,039,457,584,007,913,129,639,936.f 

Others solved the same problem by writing down, in every 
possible way, the hexameter verses which might be made by the 
transposition of the letters in the following line : — 

" Tot tibi sunt dotes, Virgini, quot sidera coelo." 
" Thy graces, O Virgin, are told when the stars of the heaven are 
numbered." 

* This is the correct 64th power of 2, but the true answer is the 
63rd power of 2; viz., 9,223,372,036,854,775,808, 
t De Morgan's " Arithmetical Books," p. 45. 



S8 THE DECIMAL SYSTEM, 



CHAPTER Y. 

ADVANTAGES OF A DECIMAL SYSTEM AS COMPABED WITH THE 
EXISTING USAGES. 

VI 

To the value of the decimal system in coins and accountancy in 
the United States of America, Mr. Jefferson has left this emphatic 
testimony : — , 

" The experiment made by Congress in 1786, by declaring that 
there should be one currency of accounts and payment through the 
United States, and that its parts and multiples should be in a 
decimal ratio, has obtained such general approbation both at home 
and abroad, that nothing seems wanting but the actual coinage to 
banish the discordant pounds, shillings, pence, and farthings of the 
different states, and to establish in their stead the new denomi- 
nations."* 

The decimal system is, in fact, a method of easy and regular 
progression, by which correct ideas of small numbers enable us to 
attain accurate notions of large ones. Unless we proceed from 
stage to stage, from group to group of numerals, our associations 
become very vague and shadowy. If we take any other than the 
decimal form of enumeration, we shall soon find great difficulty in 
reaching the higher amounts, and the additions and multiplications 
become intricate and perplexing, A child that should be called upon 
to proceed by the lowest form of multiplication, say by two, would 
soon find its progress arrested : 2 X 2=4, 2 x 4=8, 2 x 8=16, and so 
forth ; and still sooner arrested if the progression were the multipli- 
cation of numerals into themselves, as 2 X 2=4, 4 X 4=16, 16 X 16 
=256 : but with the aid of decimals,! and in proceeding from tens 

* Report on Money, Weights, and Measures, by Jefferson, Secre- 
tary of State, 1790. 

f The decimal power is thus spoken of in a complimentary recom- 
mendation of Noah Bridge's " Vulgar Arithmetic " (1653). 

*' Melitides, who ne'er could thrive 
In computation beyond five, 
May now in 's noddle millions hive." 



IN NUMBERS, COINS, AND ACCOUNTS. 59 

to hundreds, and hundreds to thousands, the greatest facilities will 
be found both for the exact estimate and the intelligible expression 
of large amounts. 

The simplest form of exhibiting the decimal system of coins and 
accounts to the mind is probably to represent it as getting rid of 
all the complications of compound addition, subtraction, multiplica- 
tion, and division, and reducing all calculations to those simple 
rules, which are the first lessons learnt of the arithmetical art. 
When nothing but a decimal process is used, the greatest possible 
amount of simplicity will be attained. Any boy who has now to 
add up a sum in pounds, shillings, pence, and farthings, learns that 
when he has reached the column of pounds his principal difficulties 
are got over. The farthings perplex him because they are divided 
by 4 ; but that is a less difficult operation than the division of the 
pence by 12 ; the division of the shillings by 20 is perhaps the 
easiest task of the three, inasmuch as 20 has something of a decimal 
element, being comprised of two tens ; but the sum goes on glibly 
when on adding up the pounds there is no division at all, but 
merely the carrying on the number of tens from column to column, 
with the very distinct impression, that every column to the right 
is one-tenth, and every column to the left ten times the value 
of the adjacent column. 

The contrasted mode of working a decimal and non-decimal 
system is exhibited in a very simple form, as follows :— 

£ s. d. 

1,234 5 6i 

89 10 3| 

467 12 9£ 



The operation performed by the existing system is thus 
effected : — 

Farthings added make 6, which, divided by four, leaves 
2, and 1 to be carried forward to the pence column j 
4)6 

1—2 2 farthings 

Pence added, make 19, which, divided by 12, leaves 7, 
and 1 to be carried forward to the shilling column j 
12)19 

1 — 7 7 pence 



60 THE DECIMAL SYSTEM, 

Shillings make 28, which, divided by 20, leaves 8, and 1 
to be carried forward to the pounds column, 
20)28 

1—8 8 shillings 

Pounds 1791, no division, but the superior unit carried 

on to the next column £1791 8 1\ 

Decimally. 



£1,234 • 277 

89 • 515 

467 * 638 



•0863 
•0250 
•5416 



£1,791 • 430 .6529 
But if the farthing were decimalised, and made -j^, instead 
of g^th of a pound sterling, the account would stand thus : — 
£1,234 • 277 
89 ' 515 
467 • 637 



£1,791 • 429 
The whole operation being one of simple addition. 

Of the inconvenience of the existing system, as regards the 
bullion transactions of the Bank of England, no stronger evidence 
can be desired than that given to the Parliamentary Committee by 
Mr. Thomson Hankey, the late Governor. Mr. Hankey says: — 

" During the time I held the office of Governor of the Bank of 
England my attention was particularly called to the subject, in con- 
sequence of what appeared to me to be the extremely complicated 
system of keeping accounts with respect to all transactions in the 
purchase or sale of bullion at the Bank of England. I found, on 
examining into the system or mode of keeping such accounts, or of 
making such calculations, that there were three elements which 
entered into the consideration ; the first was the weight, which was 
calculated in troy pounds and ounces, of which there were twelve to 
the pound, pennyweights, of which there are twenty to the ounce, and 
grains, of which there are twenty-four to the pennyweight. The second 
element was the quality of the gold, which was subdivided by carats, 
a carat meaning the 24th part of any quality of gold ; the carat was 
again subdivided into eight. The third element was pounds, shillings, 
pence, and farthings. A more complicated system, and one more 
fraught with incidents to error, can hardly be conceived ; it requires, 
in fact, an extremely expert calculator to make even any ordinary 
calculations of the kind - } so much so, that I do not believe that any 




THOMSON 1IANKEY, ESQ., M.P. 



IN NUMBERS, COINS, AND ACCOUNTS. 61 

merchants or ordinary dealers ever make the calculations themselves ; 
they employ brokers who transact the business for them, and these 
brokers use a voluminous series of tables by which they arrive at the 
results of the calculations. This appeared to me to be so extremely 
inconvenient a system, and so extremely difficult for myself to learn,, 
that I was anxious to see whether I could not, for my own private 
purposes, make calculations by a system of decimal tables, and I found 
that by using the decimal ounce, and discarding altogether the pound 
troy, a very much more simple mode of calculation could be arrived 
at ; and it was after much consideration on the subject that the Bank 
of England determined to take advantage of the anomalous state 
of the law respecting the pound troy, and respecting troy weights 
generally, to discard altogether the use, from all other calculations, 
of the pound troy. They discarded it out of the Bank altogether ; 
they made use of the ounce troy, multiplying larger quantities by the 
multiples of the ounce, and a smaller quantity by a decimal subdivi- 
sion of the ounce ; and on that principle a set of tables was framed, 
which have been in use since that time. Though I believe in the first 
instance some little prejudices existed on the subject, yet those who 
were interested in such calculations found that they were much more 
simple than any they had hitherto used, and within almost a few 
months they came into such general use that I believe all dealers in 
bullion in London have adopted that system. I should mention that 
dealers in bullion are a peculiar class, confined to a small number 
of merchants in London and their clerks, and are of a very intelligent 
character ; and therefore the difficulty of persuading them to adopt 
a system which seemed so evidently calculated to save trouble, and is 
an improvement on the former system, was not very great. I think 
it has now been adopted generally, and that nobody would think of 
proposing any return to the former system. 

" Having removed, therefore, one of those conflicting elements out 
of the way, the calculations now really only have reference to the 
fineness of quality, and to the pounds,, shillings, and pence. If we 
could simplify that calculation by adopting decimal coinage with 
regard to pounds, shillings, and pence, I have no doubt that all calcu- 
lations in bullion, which called my particular attention to the subject, 
would be again extremely simplified. It was with that view that I 
first paid attention to the subject, and I have arrived at the conclusion 
that all calculations regarding bullion transactions would be extremely 
simplified by an adoption of a decimal system of coinage. A decimal 
system undoubtedly saves labour, and it attains greater accuracy. I 
should say that there is in all the calculations a great saving of figures, 
and there is also a saving in the mere recording of the weight of 
bullion. In recording one hundred bars of gold, there would be a 



62 THE DECIMAL SYSTEM, 

saving of more than forty figures ; and the weight would be recorded 
to the minuteness of something less than half a grain, whilst, by the 
old mode, it could only be recorded by the grain." 

Mr. Wm. Miller, of the Bank of England, one of the witnesses 
before the Parliamentary Committee, has kindly furnished the 
following striking exemplification, contrasting the simplicity of 
decimal calculations with the elaborate operations of a non-decimal 
system, which will illustrate Mr. T. Hankey's evidence. 

" The assayer imagines all gold to consist of 24 parts, or carats, as 
he calls them ; each carat he subdivides into 4 parts, which he calls 
grains (which, however, have no relation to the grain of weight), and 
each grain into 8 parts. Thus he defines the quantity of gold by 
degrees, each of which is the 768th part of the whole. 

" The report of the quality is made, not in relation to fine gold, but 
to standard gold, as so many carats, or grains, or eighths of grains, 
better or worse than standard. 

" Standard gold consists of 22 parts, or carats, of fine gold, and 2 
carats of alloy. 

* When the quality of a bar of gold has been ascertained, the next 
question is, what its weight would be, supposing it were converted 
into standard by the addition, or elimination of alloy. 

" For example: — We will suppose the assay report to be " 2 carats 
better," which would be equal to fine gold. To bring the mass to 
standard, it is clear that to every 22 elements of its weight, there 
must be 2 elements of alloy added. 

" The statement, therefore, of the question as to the amount of 
standard gold in a mass of gold better, would be — 

As 22 : 22 + *£*£?} ! : actual weight : standard. 
In the case of gold worse, the converse would hold — 

As 22 : 22 — **",£*•} : : actual weight : standard. 

" The question is simple enough, but the working is very tedious, on 
account of the incongruity of the terms. First we have the weight, 
in pounds, ounces, pennyweights, and grains; we have next the 
quality, in carats, grains, and eighths of grains. And, lastly, we have 
the money value, in pounds, shillings, and pence. None of these 
terms will work together arithmetically; they have, consequently, to 
be reduced into their lowest elements, and, when the calculation has 
been made, to be reproduced. 

"The following examples show the working under the old system, 
supposing the whole operation to be set down; the same under the 



IN NUMBERS, COINS, AND ACCOUNTS. C>3 

present system, in which the weight is expressed decimally ; and the 
same supposing a decimal currency existed, and that the quantity of 
standard gold were altered from ll-12ths to 9-10ths fine ; that is to 
say, that it were the same as the standard gold of France, Holland, 
the United States, and several other countries* 

"Example I. 
" What is the value of a bar of gold weighing 79 lbs. 7 oz. 17 dwts. 
12grs., reported by the assayer to be 5 carats 3 grains and 7-8ths 
worse, and what is the weight in standard? 

Carats. Carats. Cts. Grs. lbs. oz. dwts. grs. 

As 22 : 22 — 5 3£ : : 79 7 17 12 
4 5 31 12 



88 


16 ty 


955 


8 


4 


20 


'04 


64 


19117 




8 


24 




513 


76480 
38234 




458820 






513 




1376460 






458820 






2294100 




704)235374660(334339 






2112 






"2417 






2112 






3054 






2816 






2386 






2112 






2746 






2112 






6340 






6336 



64 



THE DECIMAL SYSTEM, 



" The above operation gives the standard weight in grains, which 
have to be reduced to pounds, ounces, pennyweights, and grains. 

Grains. 
334339 
24 " 



(8) 



2,0) 
12) 



111446:1 
1393,0:19 



:10:19 



Ib58:0:10:19 
Answer as to weight in standard gold. 

" Then comes the question of value at the Mint price of £3 17s. 10^d. 
per ounce. 



Oz. 


Grains. 


£ 8. d. 


As 1 : 


334339 


: : 3 17 10£ 


20 




20 


20 




77 


24 




12 


80 . 




934 


40 




4 


480 




3738 
334339 




33642 






11214 






11214 






14952 






11214 




480 


11214 




) 1249759182 ( 2603664 






960 






2897 






2880 


Farthings. 







4)2603664 




1759 
1440 


12) 650916 




3191 


2,0) 5424,3 




2880 



£2712 3s. 0d.— Answer as to value. 



3118 

2S80 

2382 
1920 

46 



IN NUMBERS, COINS, AND ACCOUNTS. 65 

"Example II. 

" The following shows the working of the same question under the 
present system, in which the weight is expressed decimally. 

• What is the standard weight of a bar of gold weighing 955-875 
ounces, at 5 carats 3| grains worse, and what is its yalue ? 

Carats. Carats. Cts. Grs. Ounces. 

31 : : 955-875 
513 



As 22 : 


; 22 - 


4 


5 3} 


88 


16 0J 


8 


4 


704 


64 




8 



513 



2867625 
955875 
4779375 

704 ) 490363875 ( 696539^.— Answer 
4224 [in Ounce Standard. 

6796 
6336 

4603 
4224 

3798 
3520 

2787 
2112 

6755 
6336 

419 



Value at £3 17s. 10£d. per ounce :— 
696-540 
3 


15 = \ 

2 6 -J 

3 -A 

1J-1 


2089-620 

522-405 

87-067 

8-706 

4-353 


Lswer as to value.- 


-£2712-151 
20 



8-020 



(>(> THE DECIMAL SYSTEM, 

* In this operation it will be seen that the two reductions are 
avoided, and the value is ascertained by the rule of practice, as in 
this case the whole working can be set down by that rule. 

"Example III. 

" The following is the operation, supposing all the elements of the 
calculation were in decimals, and that standard gold consisted of 
f s ths fine gold, which would make the Mint price £3 16s. 5£d., or 
thereabouts, or expressed as it would be in decimals, £3-823 (three 
pounds and eight hundred and twenty-three mils). The question 
would, therefore, have to be asked in somewhat different terms. 

" What would a bar of gold weighing 955-875 oz., reported by the 
assayer as 667*96 oz. fine, yield in ounces standard, and what would 
be its value ? 

[In working such questions as these, the abbreviated form of 
multiplication, as taught in all the school books, would be 
used, which consists in reversing the multiplier, and begin- 
ning to multiply with each figure of the multiplier that 
figure in the multiplicand which stands directly above it; 
by this means all useless figures are got rid of.] 

According to the previous formula — 

As 900 ; 667*96 : : 955875 

69766 — rate reversed. 



5735250 

573525 

66910 

8602 

573 



900 ) 6384860 

Answer — 709430 ounces standard. 
3283 — price reversed. 



2128290 

567544 

14188 

2128 

Answer— £2712-150— value. 

Nothing could be more simple than such a working ; and were the 
supposed changes really made, it could be shortened yet more, because 
the quality would never be reported to five figures." 



IN NUMBERS, COINS, AND ACCOUNTS. 67 

General Pasley gives us an example of the diminished labour 
of calculating the following ironmonger's account: — Value of 
215 tons 17 cwt. 3 qrs. 9 lbs. of cast-iron, at 91. lis. 6 x d. per ton ; 
reckoned by the common mode, it takes 208 figures ; reckoned 
decimally, 66 figures — a saving of more than two-thirds.* 

In illustration of the advantage of a decimal mode of accountancy, 
take an example given by Professor De Morgan. "If 161. 10s. 2\d. 
yield 23/. Is. ll\d., what will 146/. 35. 2f d. yield ? The ordinary 
mode of doing it by those who are not expert at the rule of practice, 
the way which is taught in schools, has not a figure less than the 
following: :— 



£ s. 

16 10 

20 

330 
12 

3962 
4 


d. 
ares, 


£ s. 

23 1 

20 

461 
12 

5543 
4 


d. £ s. 
11| 146 3 
20 

2923 
12 

35078 
4 


d. 

n 


15850 


22173 

158 

as in Gene 


140315 
22173 






420945 
982205 
140315 

280630 
280630 






50 ) 3111204495 ( 196290 

15850 49072 — 2 




4089 — 4 
152620 204 _ 9 

142650 

■ .,- AD""' " — fO(\± 0<s ALA 




99704 
95100 


and I a farthing. 




46044 
31700 






143449 
142650 




"208figi 


7995 
;ral Pasley 's statement. 



* Evidence, pp. 26, 27. 

p 2 



68 THE DECIMAL SYSTEM, 

* In order to compare this with the result of the proposed decimal 
improvement coinage, we are to remember that our present system, 
which turns the student away from ordinary decimal integer arith- 
metic before he is master of it, prevents him from practising use- 
ful abbreviations. The system, which would soon be taught, 
would give the following mode of working, in which the trouble 
is increased, by taking the tenths and hundredths of farthings. If 
we had begun with the new system, instead of representing the 
old, these fractions of farthings would be avoided. 

16-51041 23.09687 146-16145 

7869032 



292322900 

43848435 

1315453 

87697 

11693 

1023 



1651041 ) 337587201 ( 204-469 
737900 

77484 £204 9s. 4$d. 
11442 
1536 
« 118 figures. 50 

" But let the pound be divided, as is proposed, into 1,000 units, 
and the operation will be thus exhibited : — 

If 16-511 yield 23-097, what will 146-162 yield? 
16511 — 23097 146162 

79032 



2923240 

438486 

13154 

1023 



16511 ) 3375903 ( 204-464 
73703 

1 ... 208 figures. 7659 

2 ... 118 do. 1055 

3... 76 do. 64 76 figures."* 

• u Companion to Almanac for 1848," pp. 11, 12. 




PROFESSOR DE MORGAN. 



IN NUMBERS, COINS, AND ACCOUNTS. 69 

As contrasted with the ordinary mode of calculation, here is a 
saving" of 132 figures, or nearly two-thirds of the whole, as con- 
trasted with a decimal system applied to the existing currency, 
and the saving would be, as above exhibited, of 42 figures. It is 
true that the latter calculations are much assisted by abbreviated 
forms ; but the use of such abbreviations is decidedly connected 
with, and will immediately follow, the introduction of a decimal 
system ; for, as Professor De Morgan says : — 

" The only reason why those abridgments, which save about 
half the trouble of multiplication and division, are not now in 
common use, is simply that the paramount necessity of practising 
our present money system prevents young calculators from having 
time to learn them, or opportunity to use them. The want of them 
is a consequence of our present system ; the introduction of them 
would follow the new one." 

Another example from Professor De Morgan : — How much in 
the pound is 43/. 17s. 4|d. per cent, t The common operation is — 

£. £. s. d. £. 

As 100 : 43 17 4f : : 1 
20 

877 
12 

10528 
4 

4 ) 42115 



12 ) 105-1 

8-9 Answer 8s. 9^d. 

Here are 42 figures; but, written in decimals, the question is 
answered by the figures themselves. The amount is 43'869Z., the 
percentage obviously 438=8s. 9£d.* 

And a further instance is given by Professor Airy to the Par- 
liamentary Committee, who, in answer to the question whether 
the decimal system of coinage would not give great facilities in the 
way of calculating interest and discount, replies — " Every calcula- 
tion of that sort would be made very much easier. But I may 
mention, that even calculations of the smallest kind would be very 

* Ibid. p. 13. 



70 THE DECIMAL SYSTEM, 

much easier ; for instance, a few days ago I was looking" at a gas 
stove, and I inquired how much it burned ; I was told seven cubic 
feet in an hour. My gas cost me 4s. per 1,000 feet — how am I to 
calculate the hourly cost ? I found the easiest way was to turn it 
into decimals, and to do it by mils ; 4s. gives 200 mils, I multiply 
that by seven feet, and the result is 1 T % mil per hour. I am not 
a very bad calculator, and yet it would take me several times as 
long to do it by pence and farthings." 

And being asked for instances that have occurred in which the 
change to the decimal system has been fruitful of great advantages; 
in astronomy for instance, the Professor states, that the great 
centesimal change proposed by the French savans at the end of 
the last century he has had occasion to use very extensively, and 
its value is very great indeed ; and he adds, that it would be the 
means of a very great saving of labour to contractors and builders, 
and others.* 

Professor De Morgan is entitled to be heard with attention, as 
he speaks with authority on the advantages and assistance which 
the introduction of a decimal monetary system will bring to the 
education of the .people. 

" Has any one of our readers (he asks) ever taken the pains to 
form an idea how much of the time actually spent in education in 
Great Britain and Ireland, is spent in overcoming the disadvantage 
of our present system of coinage ? We say coinage, because by far 
the greater part of practice in commercial arithmetic is devoted to 
pounds, shillings, and pence. We believe that five per cent, is 
under the mark, taking in all classes ; we believe that in purely 
commercial schools it is a great deal more ; but that in all together, 
from Oxford and Cambridge down to the lowest village school, 
more than five per cent., more than one-twentieth of the whole time 
passed in every kind of learning and practising, is lost by the 
having two systems of arithmetic to learn — the common decimal 
and the monetary. We put down arithmetic — looking at the mass 
of places in which only reading, writing, and ciphering are 
taught — as more than 20 per cent, (we cannot say how much 
more) of the whole ; and we estimate the dead loss of time 
which arises out of our monetary system, as one quarter at least 
of that 20 per cent. We speak of time only : were we to com- 
pare what is done — as to efficiency, as to sound result produced — 

* Evidence, p. 36. 



IN NUMBERS, COINS, AND ACCOUNTS. 71 

we should say much more. But suppose it five per cent. — and we 
think we could maintain this statistically — or go lower, suppose it 
three per cent., and what is the result ? Three hours out of every 
hundred spent in education are employed in mere consequence of a 
system which is in itself, and without reference to the trouble of 
learning- it, a positive disadvantage. It would be well to abolish 
this system, even though it saved nothing in teaching ; and, besides 
this, we turn every 97 hours of useful school work into 100. Add 
to this the relief given by the abolition of the worst part of the 
drudgery of learning computation, which lies in this, that there is 
a lower deep beneath the lowest. As soon as the unfortunate 
schoolboy has mastered the four rules, there is a weary recom- 
mencement of his toil. 

" In all the earlier rules of arithmetic, there is nothing which 
appears to apply. The most ordinary questions of everyday life 
seem to be beyond the power of addition, subtraction, multiplica- 
tion, and division of ordinary numbers. And so they are ; because 
the money, weights, and measures, are all numbered on other 
systems. If the change were made in the money only, an im- 
mense power of application would be immediately given. The 
addition and subtraction of common units would give that of 
money ; by common multiplication and division the total price 
of integers, or the price of one from the total price, would be 
found."* 

Such is the liability to error under a non-decimal system, that Mr. 
Miller stated to the Committee, how on one occasion, when he sent 
for five superior clerks to work out arithmetically the value of an 
ingot of gold in the Bullion-office of the Bank of England, Jive 
different results were produced. Mr. Miller is of opinion, that 
the use of decimal arithmetic, independently of the greater security 
for accuracy, would enable the Bank of England to dispense with 
one clerk in twelve.f 

Professor Airy says, that the existing system brings with it 
" very great liability to error, and it costs a great deal of labour. I 
might say, that the labour is doubled in all cases ; by which I 
mean, that in multiplying there are two mental operations to be 
performed where one would suffice. For instance, suppose I mul- 
tiply 9 pence by 7 ; 7 times 9 makes 63, that is one operation in the 
mind : but then there is another operation, to convert that 63 into 

* Ibid. pp. 15, 16. f Minutes of Evidence, p. 120. 



72 THE DECTMAL SYSTEM, 

os. 3d. ; and although in that case the numbers are related in a 
simple way, yet in many they are related in such a complicated 
way that they present no similar features at all. For instance, if I 
had to multiply 7 pence by 5, it would be 35 — that is one opera- 
tion ; but then the mind has another operation to perform, to 
convert the 35 into 2s. lid. without any common figure in the 
calculation. 

" The difficulty of dividing under the existing scale is greater 
than the difficulty of multiplying. Supposing you have to divide 
31. 15s. 6d. by four ; in the first place, although the 31. is divisible 
in itself by 4, you do not treat it in that way, for you have to 
convert the 31. into 60s., and add that to the 15s., making 75 ; and 
then, again, you have to multiply the remainder from the 75, and 
convert that into pence, before you proceed to the next division."* 

To the immense advantages growing out of the introduction 
of a decimal system, Sir John Herschel gives this valuable 
testimony : — " I should say that, the decimal system being 
once introduced, the rules of 'Compound Arithmetic,' ' Reduc- 
tion/ and 'Practice/ would no longer require to be taught in 
schools. The relief thus afforded, both to the teacher and scholar, 
would be immense. The four essential rules of arithmetic would 
be better acquired, and the drudgery spared, and the time saved 
for the acquisition of real knowledge would tell upon the education 
of every individual in every class of society. Even the ' Ready 
Reckoner* would be dispensed with, or its place supplied by a general 
multiplication table of comparatively small extent, and possibly 
a table of logarithms might occasionally be seen where now such a 
thing is never dreamt of. All statistical, revenue, and general 
commercial computations would be facilitated, and the acquisition 
of clear views of the mutual relations of prices, imports and exports, 
duties, taxes, &c, very greatly so, by disencumbering the elements 
of computation of the infinite complexity of denominations under 
which they are now presented. The introduction of the decimal 
system would get rid also of the whole of that complexity which 
consists in what we call Rule of Three, sums of complicated 
denominations. In these calculations an immensity of labour 
would be saved, and a great deal of clerkship in the adding up of 
columns ; and the quantities of mistakes that arise with those 
who are not from their youth up accustomed to that work, is very 
great."f 

* Minutes of Evidence, p. 58. t Ibid, pp. 55, 56. 




SIR JOHN HERSCHEL. 



IN NUMBERS, COINS, AND ACCOUNTS. 73 

Professor De Morgan has long been, one of the most zealous and 
efficient labourers in the decimal field. His valuable contributions 
on the subject in the Companion to the Almanac,* are well worthy 
of attention. In the first he lays particular stress on the value of 
logarithmal tables, applied not alone to mathematical computations, 
but to the purposes of commerce and the ordinary business of life ; 
and he points out that a decimal coinage, useful as it must be in 
every other respect, would be of inestimable value if it caused the 
attention of people in general to be directed to the subject of 
decimal fractions. He recommends that system of decimal 
coinage and account which has been since sanctioned by the 
unanimous approval of the Committee of the House of Commons, 
viz., the division of the pound sterling into a thousand parts. This 
scheme indeed, admirable for its simplicity, — for its little inter- 
ference with the existing currency, — and for the amount of 
approval which it has elicited alike from men of science, teachers, 
merchants, and tradesmen, has also had the sanction of the Commis- 
sion of Weights and Measures, who, though speaking somewhat 
timidly and hesitatively about the introduction of a universal 
decimal system, have no doubts as to its desirableness as regards 
the currency. They say : — 

" The first point which has called for our especial notice, is the 
general question of the decimal scale. In introducing this subject 
we beg to invite the attention of the Government to the advantage 
and the facility of establishing in this country a decimal system of 
coinage. In our opinion, no single change which it is in the 
power of a government to effect in our monetary system would be 
felt by all classes as equally beneficial with this, when the 
temporary inconvenience attending the change had passed away. 
The facility consists in the ease of interposing between the 
sovereign or pound, and the shillings, a new coin equivalent to 
two shillings, to be called by a distinct name ; of considering the 
farthing, which now passes as the 960th part of a pound, as the 
1000th* part of that unit; of establishing a coin of value equal to 
the 100th part of a pound ; and of circulating, besides these 
principal members of a decimal coinage, other coins of value 
having a simple relation to them, including coins of the same value 
as the present shilling and sixpence. We do not feel ourselves at 
liberty to enter farther into this subject; but we have felt it 

* For 1841, 1848, and 1853. 



74 THE DECIMAL SYSTEM, 

imperative on ns to advert to it, because no circumstance whatever 
would contribute so much to a decimal scale in weights and measures 
in those respects in which it is really useful, as the establishment 
of a decimal coinage." 

Whatever may be the inconvenience suffered by the present 
generation, — trained as it has been to meet and in some respects to 
overcome the difficulties and complications connected with the 
existing system, — there can be no doubt that the coming and all 
future generations will be greatly benefited by the changes 
proposed ; they will be trained, with an immense saving of time 
and trouble, to the use of a simple and uniform, instead of a 
perplexing and varied system of accountancy. And, understood 
and adopted, it will be a matter of wonder that old habits and 
usages should have retained their hold so long ; our hesitations 
and delays will seem inexplicable to our better instructed des- 
cendants. As written accounts superseded the cutting of tally- 
sticks, — as the Arabic replaced the Roman numerals, — so will the 
decimal scale supplant the various and singular modes which have 
been adopted in commercial and monetary transactions, and 
which represent not the knowledge, but the ignorance, — not the 
improvements, but the caprices, — not the philosophical results, but 
the accidental usages of departed experience.* 

Professor De Morgan sums up some of the advantages of the 
change as follows : — 

"1. All computations would be performed by the same rules as 
in the arithmetic of whole numbers. 

"2. An extended multiplication table would be abetter interest 
table than any which has yet been constructed. 

" 3. The application of logarithms would be materially facili- 
tated, and would become universal, as also that of the sliding rule. 

" 4. The number of good commercial computers would soon be 
many times greater than at present. 

" 5. All decimal tables, as those of compound interest, &c, would 
be popular tables, instead of being mathematical mysteries. 

" 6. The old coinage would be reduced to the new by the simple 

* All the witnesses examined by the Parliamentary Committee 
concur in opinion as to the inconvenience of the present system, and 
the advantages of a change to decimal divisions. Much of the 
evidence of Mr. Bennoch is so sound and practical that I have thought 
it desirable to preserve it in the Appendix. 






IN NUMBERS, COINS, AND ACCOUNTS. 75 

rule given at the beginning of this article. Thus any person 
would see at once, after a moderate degree of practice in that rule, 
that £14 17s. 9|d. (old coinage), is £14, 8 royals (dimes), 8 
groats (cents), 9 farthings (mils) of the new coinage — at least 
within a farthing ; this would be written £14'889. Again £23*614 
of the new coinage, or £23, 6 royals (dimes), 1 groat (cents) 4 far- 
things (mils), would be seen by the same rule to be £23 12s. 3^d. 
(old coinage). 

"7. When the decimal coinage came to be completely established, 
the introduction of a decimal system of weights and measures 
would be very much facilitated, and its advantages would be seen."* 

And in his evidence before the Committee of the House of 
Commons, Professor De Morgan says : — 

"I am of opinion that considerably more than half of the 
trouble of money calculations would be saved (by a decimal 
system). An advantage connected with that would be, that the 
school arithmetic would make boys ready in business, which they 
are not now ; for with their imperfect learning of the decimal 
system, and their halting between two systems, most men of 
business will tell you that boys do not come from school very well 
prepared in business arithmetic. I have heard of a banker who, 
when asked what a boy who was to enter his bank should do at 
school to prepare himself in arithmetic, answered, ' For goodness 7 
sake, let him do nothing ; don't trouble yourself about him, and 
when he comes to us we will teach him what he has to do. If he 
can add up pounds, shillings, and pence, that is the only thing we 
can hope for from school-teaching.' " 

And again : " I think that, taking all the schools in the 
country, commercial as well as classical, and considering in how 
many of them reading, writing, and arithmetic form the great 
mass of what is taught, I am not putting it too high when I say 
that arithmetic forms the fifth part, in time, of all the primary 
education given in the country, that is, 20 per cent, of all the 
primary education. I think that is under the mark. I am sure I 
am putting the evils of the present system rather low when I say 
that they cause one-fourth of that time to be uselessly employed, 
that is to say, l-20th part of all the time spent in primary educa- 
tion in this country I consider to be thrown away by the present 
system of coinage, weights, and measures."f 

* " Companion to Almanack for 1841, p. 20. 
f Minutes of Evidence, p. 66. 



76 THE DECIMAL SYSTEM, 

The question of the decimal point is one of some interest. The 
decimal point is that which, as Professor De Morgan remarks, " is 
to be employed not merely as a rest in a process to be useful in 
pointing* out afterwards how another process is to come in, or 
language is to be applied, but making it the final and permanent 
indication, as well as the way of pointing out where the integers 
end and the fractions begin, as of the manner in which that 
distinction modifies operation." # So in its application to English 
accounts the decimal point must be placed where the pounds sterling 
terminate, and the fractional parts of the pound begin. Every 
figure placed to the left of the decimal point represents pounds 
sterling, — every figure to the right, some decimal portion of the 
pound sterling. There have been divers ways of marking the 
point of division. Stevin used one dash for decimal units, two for 
decimal tenths, three for decimal hundredths, thus — 2146 8'2"5"'. 
Napier uses a comma in his quotient as a rest, thus— 2146,825, but 
presents his answer in the same form as Stevin. Briggs, whose 
arithmetic was published in 1624, leaves a space between the in- 
teger and the fractions, and draws a line under the decimals, thus — 
2146 825. In 1623, Johnson, in his " Arithmatick," employed this 

rude form of notation— 2146 | 825. Oughtrede adopted both the 
vertical and sub-horizontal separators, thus — 2146 1 825. Gunter, 
though he sometimes employs Briggs' underline, seems to have 
abandoned it for the simple point, 2146*825, whichhas maintained 
its ground to the present day. It may be worth considering whether 
a more marked division than a simple point, such for example as a 
perpendicular or vertical line might not be advantageously adopted. 
In ruled account books the division, would be already provided 
either by a double line or a line of different colour ; but as there 
may be some danger of confounding the decimal point with the 
comma used in the tripartite division of the integer, 2, 146 825, a 
more marked distinction than a simple dot might be adopted by 
those to whom the decimal formula are not familiar. A sloping line 
has been suggested, thus — 2,146 / 825, and it has also been proposed 
to introduce the letter £ between the pound sterling and its decimal 
parts, thus — 2,146£825. The probability is, however, that the 
point or full stop will be generally employed, and supersede all 
other modes of separating the integer from its parts. 

I cannot more appropriately conclude this chapter than with 



* Arithmetical Books, Introd. xxiii. and xxiv. 




WILLIAM DROWN. ESQ., M.P. 



IN NUMBERS, COINS, AND ACCOUNTS. 77 

the following extracts from the printed Keport of the Select 
Committee appointed "to take into consideration, and report to 
the House of Commons on the practicability and advantages, or 
otherwise, that would arise from adopting a Decimal System of 
Coinage :" — 

" The question being one which, from its peculiar character, and 
the importance of the principles involved in it, required to be examined 
with much care, it has been the object of the committee to obtain 
evidence of as varied a character as possible from witnesses whose 
opinions may carry duo weight with them, as respects not only the 
theoretical but the practical bearings of the subject. Amongst them 
will be found the representatives of the scientific opinion of the 
country in relation to a system of coinage based upon the decimal 
principle, together with others who, from their social position, their 
business occupations, or their interests in the question, have been led 
to examine into the practical inconveniences attaching to the existing 
system of coinage, and to seek for practical means of remedying 
them. 

"All the witnesses examined by the committee concur in the 
opinion that great advantages attach to a decimal system, as compared 
with the present system of calculation ; and the only points on which 
any difference of opinion was expressed by them relate to the precise 
basis which should be adopted, and the practical measures to be 
employed for introducing the decimal system, so as to produce the 
least amount of temporary inconvenience, and the smallest extent of 
unwillingness to encounter the change on the part of the classes who 
are the most likely to be affected by it. 

" With regard to the inconveniences of the existing system, the 
evidence is clear and decided. That system is shown to entail a vast 
amount of unnecessary labour, and great liability to error, to render 
accounts needlessly complicated, to confuse questions of foreign 
exchanges, and to be otherwise inconvenient. 

" On the other hand, the concurrent testimony of the various 
witnesses is to the effect that the adoption of a decimal system would 
lead to greater accuracy, would simplify accounts, would greatly 
diminish the labour of calculations (to the extent of one-half, and in 
some cases four-fifths, according to Professor De Morgan, who has 
made the question his especial study), and, by facilitating the com- 
parison between the coinage of this country and other countries that 
have adopted the decimal system, would tend to the convenience of all 
those who are engaged in exchange operations, of travellers, and 
others. An important benefit would be derived in several depart- 
ments of the public service, and in every branch of industry, from the 
economy of skilled labour which would result from the proposed 



78 

change ; at the same time that the education of the people generally 
would be much facilitated by the introduction into our schools of a 
system so directly calculated to render easy the acquirement of 
arithmetic. 

" A further evidence of the value of a decimal system is to be 
found in the fact of its very general adoption in the different coun- 
tries of the world, not only in the case of money, but also as respects 
weights and measures. The committee are not aware of any instance 
in which a country, after adopting the decimal system, has abandoned 
it. The tendency, on the contrary, has invariably been in the direc- 
tion of a further adoption of the system, the most recent instance 
being that of Portugal, where the mode of reckoning has long been 
based on the decimal system, and where a decree has been published 
within the last few months, providing for the introduction of the 
French decimal metrical system of weights and measures. Dr. 
Bowring explained to your committee the decimal system that obtains 
in the vast empire of China, and produced an instrument, a description 
of abacus, there called the ' Swan Pan.' That instrument shows the 
ease with which a decimal system may be applied, and the great 
advantages which it confers, as is, in fact, practically proved by the 
extraordinary facility with which Chinese boys make any arithmetical 
calculations. 

" Even in this country, where the decimal system is not supposed 
to exist, the committee have ascertained that it is already practically 
adopted to a certain extent. The late Governor of the Bank of 
England has informed the committee that it has been found advisable 
in that establishment to employ a decimal system of weights in their 
purchases and sales of bullion, instead of the old system of troy 
pounds, ounces, pennyweights, and grains; and that great advantage 
has resulted from the change, and Parliament in the present session 
has passed an act to legalise the new weights. The Master of the 
Mint has also announced the intention of introducing the use of those 
weights at the Mint as soon as possible. Professor De Morgan 
mentions that many teachers, as well as himself, always use the 
decimal system in actual teaching, by giving their pupils a short rule 
for transposing the common money calculations into the decimal form, 
and then, when the answer is obtained, re-transferring them to pounds, 
shillings, and pence. The great waste of time entailed by its being 
necessary to perform these operations of transfer and re-transfer, in 
addition to the calculation itself, is obvious ; and yet the advantage of 
the decimal system is found to be so great, that, for the sake of 
employing it, it is worth while to incur the extra labour of those 
operations. 

" With regard to the other and more difficult part of the question 



IN NUMBERS, COINS, AND ACCOUNTS. 79 

referred to them, namely, the practicability of introducing the decimal 
system, it appears to the committee that the obstacles are two-fold in 
their nature. The first arises from the difficulty which is always 
found to exist in inducing the mass of the population to depart from 
standards with which they are familiar, and from modes of calcula- 
tion to the defects of which usage has reconciled them. The second 
obstacle arises from the necessity of re-arranging the terms of all 
pecuniary obligations, depending either on legal enactment or private 
contract, expressed in those coins which, in the event of a change in 
our monetary system, would cease to have legal currency. This 
second obstacle, although apparently the most practical and the most 
serious in its nature, is probably not so important in actual fact as 
the other, owing to its more tangible character, and the opportunity 
which it therefore presents of considering and grappling with its 
details. But an obstacle of so undefined a nature as a vague popular 
feeling, based upon habit and association, and not upon reason, cannot 
be dealt with on any general and abstract principles, and the committee 
therefore purposely abstain from seeking to fetter the discretion of 
the Executive on that part of the subject. 

" The committee have endeavoured to ascertain the probable 
feeling of the public, especially of the working-classes, in reference to 
the proposed change; first by examining witnesses who may be con- 
sidered to be well acquainted with their feelings ; and, secondly, by 
means of the analogy to be drawn from previous changes of a 
somewhat similar character. As respects the first point, several 
witnesses who have very extensive dealings with the poor, and some 
of whom are accustomed to take as many as 1,000 farthings per week 
over the counter, have expressed their opinion that if the farthing 
were altered from its present value (the g^th part of the pound 
sterling) to the 7555 th part of the pound, in accordance with the 
decimal subdivision, no prejudice would be raised against this slight 
decrease of four per cent, in the value of the farthing, provided they 
were made to understand that they could, on the other hand, get 25 
of the new coin for sixpence where they now get 24. All the traders 
examined also stated, as the result of their experience, that competi- 
tion invariably causes the quantities of the articles sold to adjust 
themselves without difficulty to the value of the money received for 
them. 

"The Committee have also taken evidence as to the difficulty expe- 
rienced on occasions when the coinage of any country has been 
changed, and would especially refer to the cases of the United States 
and of Ireland. In the former country the old system of pounds, 
shillings, and pence has been entirely superseded by the decimal 
system of dollars and cents, and no inconvenience appears to have 



80 THE DECIMAL SYSTEM, 

attended the change. The principal difficulty with which the Com- 
mittee have now to contend will be the substitution, in lieu of the penny, 
of a new copper coin, hereafter described, of which the present shilling 
will contain ten only instead of twelve. In the case of Ireland, where 
thirteen Irish pence make one English shilling, for which twelve 
English pence were substituted, a prejudice was originally felt on the 
part of the poorer classes, in consequence of their believing that as 
they only got twelve pence for a shilling where they formerly received 
thirteen, they sustained a loss of a penny in every shilling. .They 
soon found from experience, however, that the injury was imaginary. 

u The other difficulties to which the Committee have referred, viz., 
those of a practical character, arising from the necessity of a re-ad- 
justment of a large number of existing contracts and obligations 
based upon the present system of coinage, are not, in their opinion, 
insuperable ; but the precise point of view from which to consider 
them must, of course, depend in some degree on the exact system 
which may be adopted. 

" The first question to be decided is, what shall be the unit of the 
new system of coinage ; and the Committee have no hesitation in 
recommending the present pound sterling. Considering that the 
pound is the present standard, and therefore associated with all our 
ideas of money value, and that it is the basis on which all our exchange 
transactions with the whole world rests, it appears to the Committee 
that any alteration of it would lead to infinite complication and embar- 
rassment in our commercial dealings ; in addition to which it fortu- 
nately happens, that its retention would afford the means of intro- 
ducing the decimal system with the minimum of change. Its tenth 
part already exists in the shape of the florin or two-shilling piece, 
while an alteration of four per cent, in the present farthing will serve 
to convert that coin into the lowest step of the decimal scale which it 
is necessary to represent by means of an actual coin, viz., the 
thousandth part of a pound. To this lowest denomination the Com- 
mittee purpose, in order to mark its relation to the unit of value, to 
give the name of mil. The addition of a coin to be called a cent, of 
the value of ten mils, and equal to the hundredth part of the pound, 
or the tenth part of the florin, would serve to complete the list of 
coins necessary to represent the moneys of account, which would 
accordingly be pounds, florins, cents, and mils. 

* Other proposals, having in view the adoption of a different unit, 
have been brought under the notice of the committee. Of these, the 
one recommending the retention of the present farthing as the basis 
of a new system of coinage, leaving its relation to the existing penny 
untouched, presents the greatest amount of advantage. The large 
number of payments which are now expressed in pence would remain 



IN NUMBERS, COINS, AND ACCOUNTS. 81 

unaltered, and a great portion of those daily transactions in which 
the mass of the population are engaged, would be unaffected by the 
change; but when it is considered that the adoption of that alternative 
would, by adding lOd. to the value of the present pound, and a half- 
penny to that of the shilling, necessitate the withdrawal of the whole 
of the present gold coinage, and nearly the whole of the silver, and 
involve the alteration of the terms of all contracts and obligations 
expressed in coin of either of the latter metals, the committee would 
not feel themselves warranted in recommending the adoption of such 
a proposal. 

" The committee, therefore, are now in a position to resume the 
consideration of the practical difficulties in their way, and of the 
means by which those difficulties may be most readily overcome. 
The most important obstacles are those connected with the re-adjust- 
ment of obligations expressed in the penny (including its multiplies 
and sub-multiples), by receipts in which coin various portions of the 
public revenue are in great part raised, such as postage, newspaper, 
and receipt stamps, as well as many duties of customs ; in addition to 
the class of cases in which private interests are concerned, such as 
railway, bridge, ferry, and road tolls. To take an illustration, it is 
obvious that, if instead of charging a toll of one penny or four 
farthings, as at present, the nearest equivalent toll under the decimal 
system, viz., one of four mils, were substituted, the. change would 
involve a loss to the receiver of the toll of four per cent. ; while, on 
the other hand, raising the toll to five mils would involve a loss to the 
payer of 20 per cent. The payment is now the ^ 5 th part of a pound, 
and on the first of the foregoing suppositions it would be reduced to 
the ^th; on the latter, it would be raised to the 533th. In the case of 
all cumulative and gross payments, that difficulty will not be felt, and 
may be disregarded ; as the amount involved in the change, being 
always less than a mil in each case, is then inappreciably small in 
comparison with the total sum. 

" The case of the penny newspaper stamps presents no difficulty, as 
they are always sold to the newspapers in considerable quantities, and 
might be charged at the rate of 12 for 50 mils (the equivalent of the 
shilling), instead of one penny each as at present, the two rates of 
charge being identical. 

" The payment of the troops may be easily arranged in a similar 
manner, for although they are nominally paid at the rate of so many 
pence per day, the full pay of every man is drawn in advance each 
month, and any difference between the sum received by him each day 
under the decimal system, and that received under the present system, 
could be adjusted at the monthly clearance, which takes place even 
at present, for the purpose of settling any small balance. 

G 



82 THE DECIMAL SYSTEM, 

" The cases in which the payment of the penny is made in separate 
and isolated, instead of cumulative sums, present greater difficulty. 

" The charges payable to the public revenue for duties and stamps, 
are very generally expressed in pence, or fractions of a penny. 
Assuming that at the period fixed for the alteration of the coinage, 
no grounds should exist for an alteration of those charges, the 
object to be attained will be to secure the levy of an equal amount 
of revenue in the aggregate, without so far altering existing charges 
as to create public dissatisfaction, and without needlessly complicating 
the proceedings of the Revenue Departments. The committee'' are 
disposed to believe that these objects may be attained by such slight 
modifications of existing payments as will enable the payments for 
duties and stamps to be expressed by a whole number of mils, the loss 
upon any one head of revenue being compensated by the gain upon 
some other. 

" The case of the penny postage is the most important, and requires 
a special reference to be made to it. Various witnesses who have 
been examined on this subject, including Mr. Rowland Hill, have 
expressed an opinion that considerable discontent would be occasioned 
by any addition to the present rate, such as the adoption of a charge 
of 5 mils, whatever might be the benefit to the Exchequer, and they 
have proposed that the alternative should be adopted of substituting 
a rate of 4 mils. But the committee feel that, in arriving at a decision 
on this subject, it is necessary not to forget that, supposing the 
number of letters transmitted through the post to remain unaltered, 
the adoption of a charge of 4 mils would involve a loss of revenue 
estimated at .£100,000. Whether such a loss would be actually 
sustained must depend on whether or no the trifling diminution of 
charge on each letter would lead to increased correspondence, in 
accordance with the law that is found to prevail in the case of more 
extensive reductions. On the other hand, it is admitted that, apart 
from the fiscal and other practical considerations involved in the 
alteration of a duty which was reduced to its present rate of one 
penny in compliance with a popular demand, the establishment of a 
rate of 5 mils would be convenient, as representing an aliquot part of 
the coins of a higher denomination in the proposed decimal scale, and 
that that rate would probably have been adopted had a decimal 
system of coinage been in existence at the time when a uniform postage 
was established. The Committee apprehend that it must remain with 
Parliament to decide, upon the consideration of the respective 
advantages and disadvantages of the two rates as above indicated, 
whether the postage rate to be adopted under a decimal system shall 
be four or five mils. 

* The new penny receipt stamp is subject to the same observations. 



IN NUMBERS, COINS, AND ACCOUNTS. 83 

The committee would only observe, with reference to it, that they 
have no experience to guide them as to the probable receipts under it, 
as compared with the receipts under the much higher rates that have 
hitherto existed. 

" As respects those customs and other duties which are now levied 
at so much per lb., and which are the only cases of the kind that would 
be sensibly affected by the change to a decimal system, the committee 
are of opinion that all difficulty would be removed by charging those 
duties in future by the 100 lbs. 

" The chief remaining difficulty relates to charges payable to 
companies or private individuals, fixed by Act of Parliament at sums 
expressed in pence or fractions of a penny. Of this class are mileage 
charges received by railway companies, and tolls on roads, bridges, 
and ferries. Various suggestions as to the means of regulating these 
charges, should a decimal system be adopted, have been made to the 
committee, especially one whereby compensation to the owners of 
such tolls for the loss they would incur by the ultimate reduction in 
the charges, should be provided by sanctioning a small increase in 
those charges for a limited period. 

" It remains for the committee to consider the question of the coins 
to be employed under the decimal system of coinage, and the means of 
introducing that system. 

"As respects the coins, it will be necessary to withdraw from 
circulation certain of the coins at present in use, and to substitute in 
their place certain other coins, having reference to the decimal scale, 
before the decimal system can be considered as fully developed. The 
committee contemplate the retention under any circumstances of the 
present sovereign (1,000 mils), half-sovereign (500 mils), florin (100 
mils), and shilling (50 mils, or 5 cents). The present sixpence, under 
the denomination of 25 mils, might be retained, and the crown, or 
piece of 250 mils, of which few are in circulation, need not be with- 
drawn. On the other hand, it will be desirable to withdraw the half- 
crown, and the threepenny and fourpenny pieces, which are 
inconsistent with the decimal scale. 

" With regard to the coins not in actual existence at present, but 
which it will be necessary eventually to introduce, it appears to the 
committee that copper coins of 1, 2, and 5 mils, and silver coins of 20 
and 10 mils, will be required, to which should be added such others as 
experience may show to be desirable. It is important, .however, to 
bear in mind, that the smaller the number of the coins with which it is 
practicable to effect purchases and exchanges, the better. 

" The committee feel that a certain period of preparation, destined 
to facilitate the transition from the present to the new system, is in- 
dispensable. During such a transition period, various measures should 

G 2 



84 THE DECIMAL SYSTEM, 

be adopted with a yiew to prepare the way for ulterior changes, and 
to create in the public mind a desire for their completion. Several of 
the proceedings on the part of Her Majesty's Mint, which would ulti- 
mately become necessary, might be adopted at the present time without 
introducing any elements inconsistent with the existing system of 
coinage and accounts. The committee believe that no unnecessary 
delay should prevent the full introduction of the decimal system, and 
they recommend that the necessary preparatory measures should be 
entered on at the Royal Mint as soon as possible. 

" As respects the means to be employed for preparing the public 
for the introduction of the new system, the committee would refer to 
the very valuable and detailed evidence on the point given by the 
Master of the Mint, the Astronomer Royal, Professor De Morgan, and 
General Pasley. The committee recommend that all the silver coins 
hereafter coined should have their value in mils marked upon them, in 
order that the public might, at the earliest possible period, associate 
the idea of that system with their different pecuniary transactions. 
They further recommend, that all the copper coins that may be issued 
under the decimal system should also have their value in mils similarly 
marked on them. They think that it would familiarise the public with 
the new system of account, if some of the papers submitted to parlia- 
ment, and most generally referred to, were exhibited in the decimal as 
well as the ordinary form. 

" Supposing the decimal system to be introduced into this country, 
the question of its introduction into the British colonies naturally 
presents itself. That no indisposition is felt on the part of the colonial 
legislatures to entertain the question, may be inferred by the fact, that 
the legislature of Canada has just established a decimal currency in 
that country. 

" The attention of the committee has been incidentally directed, in 
the course of their inquiries, to the advantage in applying the decimal 
system to weights and measures as well as to coinage. This being a 
question not embraced in their order of reference, the committee do 
not feel themselves to be in a position to do more than express their 
sense of the importance of further inquiry into that interesting 
subject. 

" In conclusion, the committee, having well weighed the compara- 
tive merits of the existing system of coinage and the decimal system, and 
the obstacles which must necessarily be met with in passing from one 
to the other, desire to repeat their decided opinion of the superior 
advantages of the decimal system, and to record their conviction that 
the obstacles referred to are not of such a nature as to create any 
doubt of the expediency of introducing that system, so soon as the 
requisite preparations shall have been made for the purpose, by means 
of cautious' but decisive action on the part of the 'government. 



IN NUMBERS, COINS, AND ACCOUNTS. 85 

M The committee consider the present moment especially adapted 
for introducing the decimal system, in consequence of the prosperous 
state of the whole community, including those classes which would be 
more immediately affected by the change, and they feel the importance 
of not allowing such an opportunity to be lost. 

" They believe that the necessary inconvenience attending a tran- 
sition state will be far more than compensated by the great and per- 
manent benefits which the change will confer upon the public of this 
country, and of which the advantages will be participated in to a still 
greater extent by future generations. 

" 1 August, 1853." 



THE DECIMAL SYSTEM, 



CHAPTER VI. 

BRITISH SYSTEM OP COINS, WEIGHTS, AND MEASURES, AND PROPOSED 
MONETARY CHANGES. 

Nothing can be more striking than the contrast between the 
uniformity, precision, and significancy in the French system of 
coins, weights, and measures, and the irregularity, vagueness, .and 
confusion of the English system. Not only England, however, 
but almost every other European country, excepting France and 
Belgium (which has adopted the French system), presents some 
evidence of incongruities and absurdities in monetary and metrical 
designation, the original growth of ignorance and imperfect means 
of calculation ; but they have been allowed by habit and indolence 
to continue unreformed. The following extracts from Mr. John 
Quincy Adams' Report to Congress are full of instruction : — 

" In every system of weights and measures, ancient or modern, 
with which we are acquainted, until the new system of France, 
the poverty and imperfection of language has entangled the subject 
in a maze of inextricable confusion. The original names of all 
the units of weights and measures have been improper applications 
of the substances from which they were derived. Thus, the foot, 
the palm, the span, the digit, the thumb, and the nail, have been, 
as measures, improperly so called for the several parts of the 
human body, with the length of which they correspond. Instead 
of a specific name, the measure usurped that of the standard from 
which it was taken. Had the foot-rule been unalterable, the 
convenience of its improper appellation might have been slight. 
But in the lapse of ages, and the revolutions of empires, the foot- 
measure has been everywhere retained, but infinitely varied in its 
extent. Every nation of modern Europe has a foot-measure, no 
two of which are the same. The English foot, indeed, was adopted 
and established in Russia by Peter the Great ; but the original 
Russian foot was not the same. The Hebrew shekel and maneh, 
the Greek mina, and the Roman pondo, were weights— the 
general name weight improperly applied to the specific unit of 
weight. The Latin word libra, still more improperly, was 



IN NUMBERS, COINS, AND ACCOUNTS. 87 

borrowed from the balance in which it was employed : libra was 
the balance, and at the same time the pound-weight. The termg 
weight and balance were thus generic terms, without specific 
meaning. They signified any weight in the balance, and varied 
according to the varying gravities of the specific standard unit at 
different times and in different countries. When, by the debase- 
ment of the coins, they ceased to be identical with the weights, 
they still retained their names. The pound sterling retains its 
name many centuries after it has ceased to exist as a weight ; and 
after having, as money, lost more than two- thirds of its substance. 
We have discarded it, indeed, from our vocabulary ; but it is still 
the unit of moneys of account in England. The livre tournois of 
France, after still greater degeneracy, continued until the late 
Revolution, and has only been laid aside for the new system. The 
ounce, the drachm, and the grain, are specific names, indefinitely 
applied as indefinite parts of an indefinite whole. The English 
pound avoirdupois is heavier than the pound troy ; but the ounce 
avoirdupois is lighter than the ounce troy. The weights and 
m easures of all the old systems present the perpetual paradox of 
a whole not equal to all its parts. Even numbers lose the definite 
character which is essential to their nature. A dozen become 
sixteen, twenty-eight signify twenty-five, one hundred and twelve 
mean a hundred. 

" The indiscriminate application of the same generic term to 
different specific things, and the misapplication of one specific 
term to another specific thing, universally pervade all the old 
systems, and are the inexhaustible fountains of diversity, con- 
fusion, and fraud. In the vocabulary of the French system there 
is one specific, definite, significant word, to denote the limit of 
lineal measure ; one for superficial, and one for solid measure ; 
one for the unit of measures of' capacity, and for the units of 
weights. The word is exclusively appropriated to the thing, and 
the thing to the word. The metre is a definite measure of length ; 
it is nothing else. It cannot be a measure of oneTength in one 
country, and of another length in another. The gramme is a 
specific weight, and the litre a vessel of specific cubic contents, 
containing a specific weight of water. The multiples of these units 
are denoted by prefixing to them syllables derived from the 
Greek language, significant of their increase in decimal propor- 
tions. Thus, ten metres form a deca-metre ; ten grammes, a 
deca-gramme ; ten litres, a deca-litre. The subdivisions, or 



OS THE DECIMAL SYSTEM, 

decimal fractions of the unit, are equally significant in their 
denominations, the prefixed syllables being derived from the Latin 
language. The deci-metre is a tenth part of a metre ; the deci- 
gramme, the tenth part of a gramme ; the deci-litre, the tenth 
part of a litre. Thus, in continued multiplication, the hecto- 
metre is a hundred, the kilo-metre a thousand, and the myria- 
metre ten thousand metres ; while, in continued division, the 
centi-metre is the hundredth, and the milli-metre the thousandth 
part of the metre. 4 

" The same prefixed syllables apply equally to the multiples and 
divisions of the weight, and of all the other measures. Four of 
the prefixes for multiplication, and three for division, are all that 
the system requires. These twelve words, with the franc, the 
decime, and the centime, of the coins, contain the whole system of 
French metrology, and a complete language of weights, measures, 
and money."* \ 

" In the English system, every weight and measure is divided 
by different, and seemingly arbitrary numbers; the foot into 
twelve inches ; the inch, by law, into three barleycorns, — in prac- 
tice, sometimes into halves, quarters, and eighths, sometimes into 
decimal parts, and sometimes into twelve lines ; the pound avoir- 
dupois into sixteen ounces, and the pound troy into twelve, — 
so that while the pound avoirdupois is heavier, its ounce is 
lighter than those of the troy weight. The ton, in the English 
system, is both a weight and a measure. As a measure, it is 
divided into four quarters, the quarter into eight bushels, the 
bushel into four pecks, &c. As a weight, it is divided into twenty 
hundreds, of 1 12 pounds, or 2,240 pounds avoirdupois. The gallon 
is divided into four quarts, the quart into two pints, and the'pint 
into four gills. 

" In the French system, decimal divisions were prescribed by 
law exclusively. The binary division was allowed, as being com- 
patible with it; but all others were rigorously excluded, — no 
thirds, no fourths, no sixths, no eighths, or twelfths. But this 
part of the system has been abandoned, and they are now allowed 
all the ancient varieties of multiplication and division, which are 
still further complicated by the decimal proportions of the law. 
The nomenclature of the English system is full of confusion and 
absurdity, chiefly arising from the use of the same names to signify 

* Adams' Report, pp. 87, 88. 






IN NUMBERS, COINS, AND ACCOUNTS. 89 

different things ; the term pound to signify two different weights, 
a money of account, and a coin ; the gallon and quart to signify 
three different measures ; and other improper denominations, con- 
stantly opening avenues to fraud. 

" The French, nome nclature i possesses un iforroity. in- perfection, 
every word expressing the unit weight or measure which it re- 
presents, or the particular multiple or division of it. No two 
words express the same thing ; no two things are signified by 
the same word."* 

" The application of the new metrology to the moneys and coins 
of France, has been made with considerable success ; not, how- 
ever, with so much of the principle of uniformity as might have 
been expected, had it originally formed a part of the same project 
(the reform of weights and measures). But the reformation of 
the coins was separately pursued, as it has been with us ; and as 
the subject is of great complication, it naturally followed, that 
from the separate construction of two intricate systems, the adap- 
tation of each to the other was less correct than it would have 
been had all the combinations of both been included in the forma- 
tion of one great masterpiece of machinery. It is to be regretted 
that, in the formation of a system of weights and measures, 
while such extreme importance was attached to the discovery and 
assumption of a national standard of long-measure as the link of 
connection between them all, so little consideration was given to 
that primitive link of connection between them, which had existed 
in the identity of weights and of silver coins, and of which France, 
as well as every other nation in Europe, could still perceive the ruins 
in her monetary system then existing. Her livre tournois, like 
the pound sterling, was a degeneracy, and a much greater one, 
from a pound-weight of silver ; but it had scarcely a seventieth 
part of its original value. It was divided into twenty sols or 
shillings ; and the sol was of twelve deniers or pence. It had 
become a mere money of account ; but the ecu, a crown, was a 
silver coin of six livres, nearly equivalent to an ounce in weight, 
and there were half-crowns, and other subdivisions of it, being- 
coins of one-fourth, one-fifth, one-eighth, and one-tenth of the 
crown. There were also coins of gold, of copper, and of mixed 
metal called billon, in the ordinary calculations of exchange. 
Shortly after the adoption of the provisional or temporary metre 

* Adams' Report, p. 73. 



90 THE DECIMAL SYSTEM, 

and kilogramme, a law of 16th Vendemaire 2 (7th October 1793), 
prescribed that the principal unit, both of gold and of silver 
coins, should be of the weight of ten grammes. The propor- 
tional value of gold to silver was retained, as it had long before 
been established in France, at 15^ for one. The alloy of both 
coins was fixed at one-tenth ; and the silver franc of that coinage 
would have been worth about thirty-eight cents, and the gold 
franc a little short of six dollars. The law was never carried into 
execution. It was superseded by one of the 15th August 1794 
(28 Thermidor 3), which reduced the silver franc to five grammes ; 
and it was not until after a law of 7 Germinal 11 (28th March 
1 803) that gold pieces of twenty and forty francs were coined, at 
155 of the former to the kilogramme. 

" In the new system, the name of livre, or pound, as applied to 
money or coins, was discarded ; but the franc was made the unit 
both of coins and moneys of account. 

" The franc was a name which had before been in common use 
as a synonymous denomination of the livre. The new franc was 
of intrinsic value -g^ more than the livre. The franc is decimally 
divided into-decimes of Jq, centimes of -j-^, and millimes of yohq 
of the unit ; but the smallest copper coin in common use is of five 
centimes, equivalent to about one of the United States cents. The 
silver coins are of one- fourth, one-half, one and two francs, and of five 
francs ; the gold pieces, of twenty and forty francs. The proportional 
value of copper to silver is of one to forty, and that of billon to silver 
of one to four ; so that the kilogramme should weigh 5 francs of 
copper coin, 50 of the billon, 200 of the silver, and 3,100 of the 
gold coins ; and the decime of billon should weigh precisely two 
grammes. The allowances, known by the name of remedy for 
errors in the weight and purity of the coins, are of T ^ upon copper, 
which is only for excess : those upon the weight of billon are of 
tMo i u P on silver, y^gg for one-quarter francs, yiA_ f or one-half 
francs, and of 1 ^g , or one per cent., on one and two-franc pieces, 
and of 10 5 0b - for five-franc pieces: that of the gold coin is of 
Y o 4 00 - : — all, excepting the copper, allowances either for excess or 
deficiency. But the practice of the Mint never transgresses in 
excess; and the deficiency is always nearly the whole allowed by 
law. The remedy of alloy is of yo 7 oo, either of excess or defect, 
for billon ; of y^ for silver ; and of ^ww for gold. It is said 
that the actual purity of the coins, both of gold and silver, is 
within y^qq less than the standard. 



IN NUMBERS, COINS, AND ACCOUNTS. 91 

" The conveniences of this system are : — ■ 

" First, The establishment of the same proportion of alloy to 
both gold and silver coins, and that proportion decimal. 

"Secondly, The established proportions of value between 
gold and silver, mixed metal, and copper coins. 

"Thirdly, The adaptation of all the coins to the weights, in 
such manner as to be checks upon, and tests of each other. Thus 
the decime of billon should weigh two grammes ; the franc of 
silver, five; the two-franc piece of silver, and the five-centime 
piece of copper, each ten ; and the five-franc piece, fifty. The 
allowances of remedy disturb partially these proportions. These 
are practices continued in all the European mints, after the 
reasons upon which they were originally founded have in a great 
measure ceased. In the imperfection of the art, the mixture of 
the metals used in coining, and the striking of the coins, could 
not be effected with entire accuracy. There would be some 
variety in the mixture of metals made at different times, though 
in the same intended proportions, and in different pieces of coin, 
though struck by the same process, and from the same die. But 
the art of coining metals has now attained a perfection, that such 
allowances have become, if not altogether, in a great measure 
unnecessary. Our laws make none for the deficiencies of weight ; 
and they consider every deficiency of purity as an error, for which 
the officers of the mint shall be excused only in case of its being 
within T¥T , part, or about y^o, — for if it should exceed that, they 
are disqualified from holding their offices. Where the penalty is 
so severe, it is proper that the allowance should be large ; but, 
as obligatory duty upon the officers of the mint, an allowance of 
■- io-oo would be amply sufficient for each single piece, and no allow- 
ance should be made upon the average."* 

The account of the introduction of the decimal system of 
coinage into the United States of America, is thus given by 
Mr. Quincy Adams : — 

"At the close of our war for independence, we found ourselves 
with four English words, — pound, shilling, penny, and farthing, 
to signify all our moneys of account. But, though English words, 
they were not English things. They were nowhere sterling ; 
and scarcely in any two States of the Union were they repre- 
sentatives of the same sums. It was a Babel of confusion by the 

* Report, pp. 62—64. 



92 THE DECIMAL SYSTEM, 

use of four words. In our new system of coinage we set them aside. 
We took the Spanish piece of eight, which had alwaysjbeen the 
coin most current among us, and to which we__had_giyen a name 
of our own, — a dollar.* Introducing the principle of decimal divi- 
sions, we said, a tenth part of our dollar shall be called a dime, 
a hundredth part a cent, and a thousandth part a mille. Like 
the French, we took all these new denomination*- &oj__J_ie_X!_l__n 
language ; but, instead of prefixing them as syllables to the 
generic term dollar, we reduced them to monosyllables, and- made 
each of them significant by itself, without reference to the unit 
of which they were fractional parts. The French themselves, in 
the application of their system to their coins, have followed our 
example ; and, assuming the franc for their unit, call its tenth 
part a decime, and its hundredth a centime. It is ■ now nearly 
thirty years since our new moneys of account, our coins, and our 
mint, have -been established. The dollar, under its new stamp, 
has preserved its name and circulation. The cent has become 
tolerably familiarised to the tongue, wherever it has been made, 
by circulation, familiar to the hand. But the dime having been 
seldom, and the mille never, presented in their material images to 
the people, have remained so utterly unknown, that now, when 
the recent coinage of dimes is alluded to in our public journal?, 
if their name is mentioned, it is always with an explanatory 
definition, to inform the reader that they are ten-cent pieces ; 
and some of them which have found their way over the mountains, 
by the generous hospitality of the country, have been received 
for more than they were worth, and have passed for an eighth, 
instead of a tenth part of a dollar. Even now, at the end of 
thirty years, ask a tradesman or shopkeeper in any of our cities 
what is a dime or a mille, and the chances are four in five that he 
will not understand your question. But go to New York and 
offer in payment the Spanish coin, the unit of the Spanish piece 
of eight, and the shop or marketman will take it for a shilling. 
Carry it to Boston or Richmond, and you shall be told it is not 
a shilling, but ninepence. Bring it to Philadelphia, Baltimore, 
or the city of Washington, and you shall find it recognised for an 
eleven-penny bit ; and if you ask how that can be, you shall learn 
that, the dollar being of ninety pence, the eighth part of it is 
________ _ 

* Dollar; from Thaler (German), or Tallaro (Italian). The 
Spanish name is Duro, meaning hard. 






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IN SUiMBEHS, COINS, AND ACCOUNTS. 03 

nearer to eleven than to any other number ; and, pursuing still 
further the arithmetic of popular denominations, you will find 
that half eleven is five, or, at least, that half the eleven-penny bit 
is the five-penny bit, which five-penny bit at Richmond shrinks 
to fourpence halfpenny, and at New York swells to sixpence. 
And thus we have English denominations most absurdly and 
diversely applied to Spanish coins ; while our own lawfully esta- 
blished dime and mille remain, to the great mass of the people, 
among the hidden mysteries of political economy — State secrets."* 
* The key-stone to the whole fabric of the ancient English 
system of weights, introduced in the year 1266, was the weight of 
the silver penny sterling. This penny was the two hundred and 
fortieth part of the tower pound, the sterling or easterling pound, 
which had been used at the mint for centuries before the conquest, 
and which continued to be used for the coinage of money till the 
eighteenth year of Henry the Ejghth, 1527, when the troy pound 
was substituted in its stead. The tower or easterling pound 
weighed three-quarters of an ounce troy less than the troy pound, 
and was consequently in the proportion to it of 15 to 16. Its 
penny, or two hundred and fortieth part, weighed therefore 22\ 
grains troy ; and that was the weight of the thirty-two kernels 
of wheat from the middle of the ear, which, according to 
the statute of 1266, had been taken to form the standard measure 
of wheat for the whole realm of England. It is also to be 
remembered, that the eight twelve-ounce pounds of wheat, which 
made the gallon of wine, produced a measure which contained 
nearly ten of the same pounds of wine. The commercial pound, 
by which wine and most other articles were weighed, was then of 
fifteen ounces. This is apparent from the treatise of weights and 
measures of 1304, which repeats the composition of measures 
declared in the statute of 1266, with- a variation of expressions, 
entirely decisive of its meaning. It says, that ' by the ordinance 
of the whole realm of England, the measure of the king was 
made, — that is to say, that the penny called sterling, round, and 
without clipping, shall weigh thirty-two grains of wheat in the 
middle of the ear : and the ounce shall weigh twenty pence ; 
and twelve ounces make the London pound ; and eight pounds of 
weight make a gallon ; and eight gallons make the London 
bushel.' It then proceeds to enumerate a multitude of other 

* Adams', Report, pp. 55, 5G. 



94 THE DECIMAL SYSTEM, 

articles, sold by weight or by numbers, such as lead, wool, cheese, 
spices, hides, and various kinds of fish ; and, after mentioning 
nominal hundreds, consisting of 108, and 120, finally adds, 'It is 
to be known that every pound of money and of medicines consists 
only of twenty shillings weight ; but the pound of all other things 
consists of twenty-five shillings. The ounce of medicines consists 
of twenty pence, and the pound contains twelve ounces ; but, in 
other things, the pound contains fifteen ounces ; — and, in both 
cases, the ounce is of the weight of twenty pence."* * 

General Pasley makes the following remarks on the identity 
or close resemblance between the ancient monetary system of 
England and that prevailing on the Continent : — 

" The system of money established towards the close of the 
eighth century by Charlemagne, was not only used in France, 
Italy, and those parts of Germany which composed the dominions 
of that great monarch, but was also adopted in Britain and in 
the Christian part of Spain. All payments were estimated in 
reference to the libra, or pound-weight of silver, which was 
divided into twenty soldi, or shillings, and each shilling into 
twelve denarii, or pennies. These were the divisions of the 
pound of money ; but, for other purposes, the same pound was 
divided into twelve ounces, according to the system of the pound 
sterling of England,f the pound of Scottish money, the livre 

* J. Q. Adams' Report to Congress on Weights and Measures." — 
Washington, 1821, pp. 25, 26. 

f In England the term " sterling," originally " easterling," and in 
France the synonymous term "esterlin," were used to denote the 
twentieth part of the ounce, also called " penny " in England, and 
" denier," from denarius, in France. This term, whilst it became 
entirely obsolete in France, was by degrees applied not only to the 
penny, but to the pound in England ; and recently it has been used 
to denote the standard money of this country, in contradistinction to 
foreign or colonial money. For the use of this term in France, see 
Paucton's elaborate Treatise on Metrology, published in Paris in 
1780, who observes, after stating the royal or legal system of weights 
prevailing in France, that the then French pound (livre de marc) 
was anciently divided into 320 esterlins. Hence the pound of 
Charlemagne, of 12 ounces, must have been divided into 240 esterlins, 
and the common ounce of both those pounds must have been divided 
into 20 esterlins. See the 5th edition of ^Turner's History of the 
Anglo-Saxons, vol. 2, appendix II. 



IN NUMBERS, COINS, AND ACCOUNTS. 95 

of France, the libra of Spain, and the lira of some of the States 
of Italy, all of which were originally equal, or nearly so : and the 
marc, likewise common to all those countries, denoted a weight of 
eight ounces, being two-thirds of the above pound. Amongst the 
Anglo-Saxons, and for some time after the Norman conquest, it 
appears that there were only two coins in England, the most 
important although the smallest of which was the silver penny, 
which was not only the penny-coin, but the penny-weight of those 
times, being exactly the two hundred and fortieth part of the 
pound-weight of silver. The second silver coin alluded to was 
equal to the fifth part of the shilling ; but the shilling itself was 
not a coin, but a weight, and as such, it appears to have been 
applied to the weighing of bread as well as of money. The 
beneficial and simple system of absolute identity between weight 
and silver money, which thus prevailed over a great part of 
Europe, was not permanent. The standard pound of commerce, 
which in all probability was originally only twelve ounces, 
increased to fifteen ounces amongst the Anglo-Saxons, and to 
sixteen in France and Scotland, and eventually in England also ; 
whilst the local or market pounds in many parts of England and of 
Scotland, and I have no doubt in other parts of Europe also, in- 
creased to a much greater magnitude. I have not been able to dis- 
cover at what period the commercial pound of France, called livre 
de marc, and consisting of two marcs, or of 16 ounces, came into 
general use ; but it finally supplanted the pound of twelve ounces 
entirely, having been adopted by the French physicians in place 
of an apothecary's weight similar to ours, after the middle of the 
eighteenth century, when it was considered the only legal weight 
in France, excepting that, by a curious arrangement, silk was 
weighed by a pound of fifteen ounces similar to that of the Anglo- 



In the Assize of Bread and Ale, published in the collection of the 
Statutes of the Realm, and marked of uncertain date, but supposed to 
have been a statute of the 5th of Henry the Third, it is declared, that 
" when a quarter of wheat is sold for eighteenpence, then wastel bread 
of a farthing, white and well-baked, shall weigh four pounds ten shil- 
lings and eightpence ;" and thus it proceeds, giving a progressive 
scale of prices of wheat, and fixing the assize in proportion, until 
wheat shall rise to twenty shillings the quarter, when it is declared 
that the weight of the farthing loaf shall be six shillings and nine- 
pence three farthings. 



96 ' THE DECIMAL SYSTEM, 

Saxons. The aliquot parts of the French livre de marc were 
rather incongruous, the denier, the carat, &c., being used for 
money, which were not used for other purposes ; but, as applied to 
the wholesale and even to the retail dealings of commerce, the 
French system of standard weights, before the revolution, pos- 
sessed great advantages over those of England. It had only one 
ounce and one pound ; and the multiples of the latter were the 
most convenient that could have been desired, namely, the 
' quintal,' or hundredweight of 100 pounds, and the ' millief,' or 
thousand weight of 1,000 pounds."* 

Of an attempt made by the French government during the 
revolution to introduce a decimal system of weights and measures, 
Mr. J. Q. Adams gives the following account : — 

"In the year 1790, the present Prince de Talleyrand, then 
Bishop of Autun, distributed among the members of the Consti- 
tuent Assembly of France, a proposal founded upon the excessive 
diversity and confusion of the weights and measures then pre- 
vailing all over that country, for the reformation of the system, 
or rather for the foundation of a new one upon the principle of a 
single and universal standard. After referring to the two objects 
which had previously been suggested by Huyghens and Picard, — 
the pendulum and the proportional part of the circumference of 
the earth, — he concluded by giving the preference to the former, 
and presented the project of a decree: — First, that exact copies of 
all the different weights and elementary measures used in every 
town of France, should be obtained and sent to Paris : Secondly, 
that the National Assembly should write a letter to the British 
parliament, requesting their concurrence with France in the adop- 
tion of a natural standard for weights and measures, — for which 
purpose, commissioners in equal numbers from the French Aca- 
demy of Sciences and the British Royal Society, chosen by those 
learned bodies respectively, should meet at the most suitable 
place, and ascertain the length of the pendulum at the 45th de- 
gree of latitude, and from it, an invariable standard for all mea- 
sures and weights : Thirdly, that after the accomplishment, with 
all due solemnity, of this operation, the French Academy of Sci- 
ences should fix with precision the tables of proportion between 

* "Observations on the Expediency and Practicability of Simpli- 
fying and Improving the Measures, Weights, and Money," &c, 8vo, 
1834. 



TN NUMBERS, COINS, AND ACCOUNTS. 97 

the new standards and the weights and measures previously used 
in the various parts of France; and that every town should 
be supplied with exact copies of the new standards, and with 
tables of comparison between them and those of which they were 
to supply the place. This decree, somewhat modified, was adopted 
by the Assembly, and, on the 22nd of August 1790, sanctioned 
by Louis the Sixteenth. Instead of writing to the British Parlia- 
ment themselves, the Assembly requested the king to write to the 
king of Great Britain, inviting him to propose to the parliament 
the formation of a joint commission of members of the Royal 
Society and of the Academy of Sciences, to ascertain the natural 
standard in the length of the pendulum. Whether the forms of 
the British constitution, the temper of political animosity then 
subsisting between the two countries, or the convulsions and wars 
which soon afterwards ensued, prevented the acceptance and exe- 
cution of this proposal, it is deeply to be lamented that it was not 
carried into effect. Had the example once been set, of a concerted 
pursuit of the great common object of uniformity of weights and 
measures, by two of the mightiest and most enlightened nations 
upon earth, the prospects of ultimate success would have been 
greatly multiplied. By no other means can the uniformity, with 
reference to the persons using the same system, be expected to 
prevail beyond the limits of each separate nation. Perhaps when 
the spirit which urges to the improvement of the social condition 
of man shall have made farther progress against the passions with 
which it is bound, and by which it is trammelled, then may be the 
time for reviving and extending that generous and truly benevo- 
lent proposal of the Constituent National Assembly of France, and 
to call for a concert of civilised nations to establish one uniform 
system of weights and measures for them all. The idea of associ- 
ating the interests and the learning of other nations in this great 
effort for common improvement, was not confined to the proposal 
for obtaining the concurrent agency of Great Britain. Spain, Italy, 
the Netherlands, Denmark, and Switzerland, were actually repre- 
sented in the proceedings of the Academy of Sciences to accom- 
plish the purposes of the National Assembly. But, in the first 
instance, a committee of the Academy of Sciences, consisting of 
five of the ablest members of the academy and most eminent ma- 
thematicians of Europe, Borda, Lagrange, Laplace, Monge, and 
Condorcet, were chosen, under the decree of the Assembly, to report 
to that body upon the selection of the natural standard, and other 

H 



98 

principles properfor the accomplishment of theobject. Their report 
to the Academy was made on the 19th of March 1791, and imme- 
diately transmitted to the National Assembly, by whose orders it 
was printed. The committee, after examining the projects of a 
natural standard, the pendulum beating seconds, a quarter of the 
equator, and a quarter of the meridian, had, on full deliberation, 
and with great accuracy of judgment, preferred the last ; and 
proposed, that its ten millionth part should be taken as the standard 
unit of linear measure; that, as a second standard of comparison 
with it, the pendulum vibrating seconds at the 45th degree of 
latitude should be assumed ; and that the weight of distilled water 
at the point of freezing, measured by a cubical vessel in decimal 
proportion to the linear standard, should determine the standard 
of weights and of vessels of capacity."* 

In reference to the proposal of a consultation with foreign 
nations for a general reform of the existing systems of weights 
and measures, a measure which hopeful philanthropy may now 
anticipate at no very remote period, Mr. Adams says: — 

" Although it is respectfully proposed that Congress should 
immediately sanction this consultation, and that it should com- 
mence, in the first instance, with Great Britain and France, it is 
not expected that it will be attended with immediate success. 
Ardent as the pursuit of uniformity has been for ages in England, 
the idea of extending it beyond the British dominion has hitherto 
received but little countenance there. The operation of changes 
of opinion there, is slow ; the aversion to all innovations, deep. 
More than two hundred years had elapsed from the Gregorian 
reformation of the calendar, before it was adopted in England. 
It is to this day still rejected throughout the Russian Empire. 
It is not even intended to propose the adoption by ourselves of 
the French metrology for the present. The reasons have been 
given for believing that the time is not matured for this reforma- 
tion. Much less is it supposed advisable to propose its adoption 
to any other nation. But in consulting them, it will be proper to 
let them understand, that the design and motive of opening the 
communication is, to promote the final establishment of a system 
of weights and measures, to be common to all civilised nations."f 
On the application of a decimal system to thermometers, Mr 
Adams says: — 

J. Q. Adams' Report, pp. 49, 50. f Report, p. 92. 



IN NUMBERS, COINS, AND ACCOUNTS. 99 

n The divisions of the barometer had always been marked in 
inches and lines. The application to it of the decimetre, its 
multiples and divisions, had for observation and calculation the 
usual conveniences of the decimal arithmetic. The graduation of 
the thermometer had always been arbitrary and various in different 
countries. The principle of the instrument was everywhere the 
same, — that of marking the changes of heat and cold in the atmo- 
sphere, by the expansion and contraction which they produced 
upon mercury or alcohol. The range of temperature between 
boiling and freezing water was usually taken for the term of 
graduation ; but by some it was graduated downwards from heat 
to cold, and by others, upwards from cold to heat. By some the 
range between the terminating points was divided into 80, 100, 
150, or 212 degrees. One put the freezing, and another the 
boiling point at 0. Reaumur's thermometer, used in France, 
began with for the freezing point, and placed the boiling point 
at 80. Fahrenheit's, commonly used in England, and in this 
country, has the freezing point at 32, and the boiling point at 
212. The centigrade thermometer, adopted by the new system, 
begins with the freezing point at 0, and places the boiling point at 
100 : its graduation, therefore, is decimal, and its degrees are to 
those of Reaumur as five to four, and to those of Fahrenheit as 
five to nine."* 

The immense preponderance of evidence before the Parlia- 
mentary Committee is in favour of the retention of the pound 
sterling as the unit or integer of account, and for its division into 
a thousand parts. And the reasons are obvious. 

The pound sterling is one of the best known and most ancient 
moneys of account. From the time of the Conquest down to 
the time of Edward I., it represented one pound of standard 
silver, weighing 12 ounces troy, so that the value and weight of 
the shilling was then exactly the twentieth part of a pound of 
silver, and the penny the twelfth part of the shilling. Successive 
acts of legislation lowered the value to the present standard, 
which has been finally fixed, by what is called Reel's Act, at 
£3 17s. 10|d. per troy ounce of gold. 

There is an almost universal desire that, while the pound 
sterling should be kept as the basis of our accountancy, its name 
and value should remain unchanged as the unit of the cur- 

* Report, p. 62. 

H 2 



100 THE DECIMAL SYSTEM. 

rency and accounts of the nation, and no proposal for its deci- 
malisation is so reasonable as that which suggested that it shall 
in future be divided into one thousand instead of nine hundred 
and sixty parts. In 1838, Mr. J. Parry, in a paper read before 
the Numismatical Society, advocated the adoption of this system 
of decimal division, which indeed affects the copper coinage 
alone, and which will be only felt by the people as giving to 
them 50 of the new farthings, or mils, to the shilling, instead 
of 48 as at present, and 25 to the sixpence instead of 24. 

The pound sterling had ceased to be represented in the coinage 
from the reign of Charles II. till the year 1816; for though the 
guinea first coined by Charles II., in 1675, was intended to 
represent 20 shillings, it constantly fluctuated in value, and 
was fixed, in 1717, by Sir Isaac Newton, then master of the 
Mint, at 21 shillings, at which value it continued till it was 
superseded by the sovereign. The pound sterling, in the time 
of Elizabeth, had weighed 7 dwts. and 4 grains. It was reduced 
in the time of James I., first to 6 dwts. and lOf grains, and next 
to 5 dwts. and 20^ grains. In the time of Charles II., when its 
value was raised, it weighed only 5 dwts. and 9£ grains. Such 
had been the gradual growth in the value of gold as com- 
pared with silver, that the proportionate value of the two metals 
was, in the 43rd of Elizabeth's reign, of fine gold to fine silver, 
10-905 ; in the beginning of James I.'s reign, 12-109 ; in the 15th 
of Charles II., 13-485 ^ and, as established in the 3rd year of 
George I., 15-209. It is well worthy of note, that the enormous 
production of gold in California, Australia, and other parts of 
the world, has hitherto affected the relative value of gold and 
silver much less than had been anticipated. The greater porta- 
bility of gold will always recommend it as a preferable in- 
strument of exchange; and the displacement of silver from 
circulation by the greater influx of gold, leads to a diminished 
demand for silver, which has served to counteract the influence 
which the greater importation of gold would otherwise have 
exercised upon its market value. It is well known, that no 
one can be compelled to receive as a legal tender more than 
forty shillings in silver; and it has been contended by some 
high authorities, such as Locke and Harris, that there would be 
convenience in our adopting silver instead of gold, by making it 
a legal tender to any amount ; but, as Lord Liverpool says, 
with much good sense, — "In rich countries, where great and 






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IN NUMBERS, COINS, AND ACCOUNTS. 101 

extensive commerce is carried on, gold is the most proper metal 
to be employed as the measure of property and instrument of 
commerce. And, in such countries, gold will in practice become 
so, with the general consent of the people, not only without the 
support of law, but in spite of any law that may be enacted to 
the contrary." It would be utterly impossible to conduct the 
daily trading affairs of the metropolis by the medium of silver 
coins alone. In the Bank of France there are great numbers of 
facteurs and assistants employed solely in weighing and counting 
the silver coins which pass through that establishment. In 
England, the vexations and delays attendant upon legalising 
silver currency beyond a moderate amount, would be absolutely 
intolerable. Even gold becomes nearly unmanageable in large 
transactions ; and, but for the facilities of checks upon bankers, 
bank notes for the larger amounts, and the assistance which the 
clearing house gives for settling all balances between the Bank of 
England and the bankers, and between the bankers themselves, 
the vast operations of exchange in London could hardly be got 
through. 

The name originally given to the guinea was the unit, — a very 
convenient designation, as it then represented the real unit, or 
integer of English coinage and account.* It took the name of 
guinea in consequence of the large supply of gold which was 
furnished to the Mint, by the Royal African Company, from 
the Guinea coast. From the time of its introduction to the 
great re-coinage of silver money in 1717, the guinea fluctuated 
in value, as against English silver coins, from 30s. to 21s., at 
which last value it continued in circulation till superseded by 
the coinage of sovereigns in the reign of George III. 

The pound sterling is of all coins and integers of accountancy 
perhaps the most extensively, not to say universally, known. It is 
the groundwork of our exchanges with all trading nations, and 
its value could not be changed without intolerable inconvenience 
and perturbation of commercial relations. It has the recom- 
mendation of a higher antiquity, a larger uninterrupted possession 
of the field of commerce, than any other unit of exchange. The 
name pound (jpondus, Latin), with its synonyme libra, has the 
strongest hold upon the languages and associations of the trading 

* The dollar of the United States bears on its edge, " One Dollar 
or Unit — Hundred Cents." 



102 THE DECIMAL SYSTEM, 

world. The word libra, as used by the Latins, means equally 
a weighing machine, and a weight (pound) ; the ascertaining which 
being the most common object of the scale, probably £ave its 
name to the machine itself, as it is clear the existence of specific 
weights must have preceded the use of the instruments, in fixing 
and regulating those weights. Generally, the libra represented 
the pound- weight either of gold, silver, or other metal. The 
pound of pure silver, whose primitive value may be considered as 
representing nearly four times its nominal value of our present 
currency, has in various parts of the world been subject to a 
succession of depreciations, either by altering the size of the coins 
which represented its value, or adulterating the metal of which 
they are composed. Thus the pound sterling represents 20s. ; 
the lira Toscana, 1\ d. ; the Genovese, about Sd. ; the livre Tournois, 
about 9} 2 d. ; while the lira Reggiana was only 3^d. y and the lira 
Modenese only two-thirds of that of Reggio ; the livre of Venice 
only 2\d. 

Sir John Herschers detailed reasons for the adoption of the 
pound stei'ling as the unit of account, are unanswerable : — 

" I think we must adopt the pound sterling. 

44 There are four other systems which have been proposed. 
There is, first, the Ducat system, which takes the half pound as 
its unit. I call it the Ducat system ; some speak of Royals — some 
of Victorias ; it is no matter, provided only it is not called a 
pound, for if you call it a pound, all manner of objections apply 
to it. 

" This has some very taking points. It preserves the shilling 
as the silver unit — the poor man's unit, as it has been called : it 
requires only doubling to change pounds into ducats. It would 
admit of a copper coin to represent its tenth part — a copper cent, 
which is a real advantage. 

" On the other hand, it has, in my opinion, fatal objections. 
It would double the numerical announcement of debts, taxes, 
liabilities of all kinds, rents, and prices ; but what is of more real 
consequence, and is in my mind unanswerable, is, that the bulk of 
our gold circulation cannot possibly consist of ten-shilling pieces. 
It is impossible to coin enough of them in a given time to meet 
emergencies. Now the bulk of your gold coinage must consist of 
your gold unit. It would never do to have the one great element 
of all our reckonings thinly scattered among larger pieces, as our 
half sovereigns are now among the sovereigns. It would be, in 
short, a mere money of account. 




PROFESSOR AIRY. 



IN NUMBERS, COINS, AND ACCOUNTS. 103 

" Next comes the Florin system, which would reckon all in 
florins and cents of florins. This makes the pound a natural 
decimal multiple; — and so far good. But it assumes a silver 
monetary standard, whereas, for good or for evil, for better or 
for worse, we are married to a gold one. I do not mean to say a 
silver standard would not be better ; I believe it would : and I 
believe a binary standard — half silver, half gold, at the option of 
either party to insist on — would be better than either ; but gold is 
our standard of value, and we are lashed on to it, and must be 
carried along with it, toss as it may. 

"Then comes the Shilling system. It has no one point to 
recommend it but its copper dime. The sovereign must be called 
a twenty- shilling piece ; the penny must be demonetised; and we 
are landed in a system having no relation to any other in Europe, 
or elsewhere. 

" The Penny system is a little better. It would give us a franc 
not very far from the French, and a pound of 200 pence, which 
was the old Saxon pound of Ethelbert. I took occasion not very 
long ago to suggest this for a Canadian pound; but it is quite 
visionary as applied to England. 

" So, I conclude, we must stick to the pound. It is a national 
institution ingrained into all our notions, and I hold it impossible 
to oust it. The true office of the ten-shilling piece is to break 
the sovereign, and lessen the amount of silver necessary to be 
kept up.' 1 * 

If additional reasons were required to show the desirableness 
of retaining the pound sterling as the integer, those given by Pro- 
fessor Airy would be irresistible : — 

" I can scarcely conceive it possible, except by the most violent 
and offensive measures, to change the principal money of account 
from its present value of the pound sterling. Every estimation of 
large, and even of very moderate sums, is formed by the pound. 
I do not attach great importance to such things as the national 
debt, 'or the rental of the country ; but the price and rental of 
private estates, the salaries of offices, the annual wages of servants, 
down to those of the lowest female servant — in larger matters, 
the expense of constructing a railway or sailing a ship ; — all are 
estimated by pounds. An alteration of the value of the pound 
would unhinge every estimate and every contract in England. I 

* Minutes of Evidence, p. 90. 



104 THE DECIMAL SYSTEM, 

say advisedly every contract, for the shilling is inseparably con- 
nected with the pound; and every real contract which is not 
ostensibly made by the pound, is made by the shilling. To this 
class belong an infinity of shop purchases, and an infinity of 
weekly wages of workmen, occasional servants, and the like. If 
pence enter into these matters, it is merely as aliquot parts of 
the shilling, which can be supplied quite as well by the decimal 
division of the pound. 

" No important contract whatever, between man and man, is 
so made as to depend for its amount on the exact value of the 
penny. It is true that a Liverpool merchant may sell cotton per 
pound, or a Suffolk farmer may sell clover seed per pound, at 
prices below one shilling per pound, and therefore expressed on 
the existing system by pence. But he sells, not a single pound, 
but tons, and therefore the pence serve the purpose simply of 
subordinate parts of a shilling, and are expelled from the account 
before it is brought to the state of payment. The same would be 
done if any other scale of copper coinage below the shilling, as 
that of decimals from the pound, were in common use. 

" Many small articles in the retail trade are sold by the penny ; 
balls of string, apples and oranges, seats in an omnibus, and the 
like. The principle of adjustment here, is a struggle between 
the desire of selling many, and the desire of making a large profit 
on each article. The adjustment is a very rough one, and will be 
made as easily on one scale as on another. It possesses no sort of 
permanence, being altered from hour to hour. 

" In a word, I may say that every habitual estimate, and every 
long, or permanent, or important contract, depends on the pound. 
The things which depend on the penny are insignificant, even to 
the lowest classes."* 

To the pound sterling, indeed, the most distinct and definite 
ideas attach — whether on small or large amounts. Mention a 
pound, five pounds, ten pounds, fifty pounds, a hundred pounds, 
a thousand pounds, ten thousand pounds, and your meaning is 
comprehended by everybody. But those who would make far- 
things, pence, or shillings, the integer or basis of account, — and 
each denomination has had its advocates, — forget that to speak of 
a hundred, or a thousand farthings, pence, or shillings, is to convey 
only a vague idea of value to the mind of the hearer. It should 

* Minutes of Evidence, p. 30. 






IN NUMBERS, COINS, AND ACCOUNTS. 105 

be remembered, that all the machinery of compound calculation 
is but an instrument for converting the smaller into the larger 
denomination, — farthings into pence, to assist their being rendered 
into shillings, and from shillings into pounds. The relations of 
the lower denominations to a pound sterling, and in so far as a 
single pound sterling is concerned, may be intelligible enough ; 
but beyond a pound they become complicated and entangled to 
the common understanding. And even within the range, it may 
be doubted if a majority of the labouring classes could answer off 
hand, and without the process of a mental calculation, how many 
pence go to a pound, or, still less, how many farthings ! 

An exact representation of the new proposed system of keeping 
account in decimals, the pound sterling being the integer, may be 
seen in an old English book, by Richard Witt, published in 1613 
and called " Arithmetical Questions, &c. &c, Briefly Resolved by 
means of certain Breviats ;" of which Professor De Morgan says, — 

" Decimal fractions are really used ; the tables being con- 
structed for ten millions of pounds, seven figures have to be cut 
off, and the reduction to shillings and pence, with a temporary 
decimal separation, is introduced when wanted. For instance, 
when the quarterly table of amounts of interest at ten per cent, is 
used for three years, the principal being £100, (page 99), in the 
table stands 137,266,429, which, multiplied by 100, and seven 
places cut off, gives the first line of the following citation : — 



The Work. 



66,429 
2,858 
4,296 



(" £ 1,372 

Facit \ sh. 13 

[d. 3 

Giving £1372 135. 3c?. for the answer. And the tables are ex- 
pressly stated to consist of numerators, with 100 for a deno- 
minator." * 

In the division decimal next to the pound I should have been 
glad to have seen the word dime employed instead of florin, to 
designate the tenth of a pound. The word disme (decime) is that 
by which the idea of a decimal system was first popularised, and 
ushered in (as it deserved to be) with a loud trumpeting forth of 
the miraculous value of the system — giving light from smoke, 

* A reprint of this work, by T. Fisher, London, 1634, duodecimo, 
is in the Royal Society's Library. 



106 



THE DECIMAL SYSTEM, 



born of a Divine Author, and worthy of being celebrated with a 
golden voice, in a hundred tongues, to a hundred ears, "and 
through all ages in perpetual praise."* 

There is an English translation by Richard Norton, 1608, the 
title of which is " Disme, the Art of Tenths," or Decimal Arith- 
metike, invented by the excellent mathematician Simon Stevin.f 

Dismes are frequently mentioned with reference to our re- 
venues in the early records of the Exchequer. They are some- 
times called Tallage of Tenths, and the tolls or duties paid by 
merchants were also called dismes. \ 

The objection to the word florin is its vagueness of significa- 
tion, and its conveying no decimal idea whatever. The only florin 
known to English numismatic history, is a gold piece, of the 
value of six shillings, coined by Edward III., which soon disap- 
peared from circulation, was adopted by none of his successors, and 
is rarely found even in large collections. The ancient florin of Italy, 
and the existing florins of Austria and Holland, represent value 
by no means corresponding to the tenth of the pound sterling. 
Though the issue of the florin has been of immense value in 
introducing and popularising a decimal system, the name of the 
coin has been obstructive, and is a cause of much confusion in 
our intercourse with foreign countries. It were much to be wished 
that the old English word dime, now re-established in the United 
States to represent the tenth of a dollar, should be legislatively 
sanctioned in this country as the tenth of a pound sterling. 

Evelyn says : — " Florins were coined in gold, in the reign of 
Edward III., by certain Florentine moneyers who were employed 
in England."§ From these, no doubt, they took their name. The 

* " Non fumum ex fulgore sed ex fumo dare lucem 
Cogitat, ut speciosa dehinc miracula promat. 
Sume unum e multis, quid non Decarithmia praestat 
Divinum scriptoris opus? cur non ego si vel 
Aurea mi vox sit, centum linguae, oraque centum, 
Omni aetate queam laudes persolvere dignas." 

Decarithmia La Disme, p. 132. logins Tornus, Phi- 

lomates, appended to Gerard's Translation (French) 

of Stevin's Mathematical Works. 

f Dr. Peacock mentions that the early Dutch edition has " De 

Thiende Leirinde alle Reckeninger," Gouda, 1626. Tenths, teaching 

ail reckonings. De Morgan, pp. 26, 27. 

t Madox's Exchequer, p. 503. § Evelyn on Medals, p. 4. 



IN NUMBERS, COINS, AND ACCOUNTS. 107 

association of the name of the coin with the country of the coiners 
having completely passed away, the propriety of again introducing 
it may well be doubted. 

The coin which is now most required to complete the instru- 
ments of decimal currency, is the piece which is to represent 10 
mils (2-|rf. of the existing currency), or one hundredth part of the 
pound sterling. The name of cent, being monosyllabic, intelli- 
gible, and descriptive, will probably be adopted without much hesi- 
tation. I am not of opinion that either the dime or cent will 
become coins of account, though of the greatest importance for 
facilitating the settlement of all trading transactions, and for 
spreading a knowledge of the decimal currency. The cent should 
be a silver coin — it would not be perceptibly smaller than the 
silver 3d. If made of copper, it would be too unwieldy to be popular. 
The experiment of coining copper twopences was made in the 
reign of George III. ; but they found no acceptance from the 
subject, and soon ceased to circulate. It has been proposed that 
the cent should be of mixed metal, — which is objectionable, from 
the great facilities which would be given to fraud and adulteration, 
which nourish in all countries where coins of great alloy are in 
vogue. 

There has been an expression of contradictory views as to the 
convenience or inconvenience of the mil, or thousandth part of a 
pound, as the smallest coin of accountancy or of exchange. Some 
are of opinion that it is unnecessarily small, and have grounded 
that opinion upon the fact, that the farthing, whose value is some- 
what greater than the mil, is almost wholly excluded from the 
present system of accountancy, and that no banker or merchant 
has a column in his books for any sum less than a penny. Others 
maintain that the mil will not be a sufficiently small element of 
account, and that where articles such as cotton are sold by the 
pound, and the subdivision of the penny into sixteenths is become 
a commercial usage, the mil will be too large a coin for the 
convenience of merchants. When a decimal system of coinage 
and accounts shall have been established, there can be little doubt 
of its being followed by decimal weights and measures ? and their 
combination will lead to a reconstruction of all the operations of 
commerce. Cotton, instead of being sold at so many pence and 
subdivisions of a penny per lb., will be contracted for at so many 
mils per 100 lb., — not only making the transaction one of easy calcu- 
lation, but allowing a much more minute valuation of the commo- 



108 THE DECIMAL SYSTEM, 

dity. Meanwhile, as the farthing has been found sufficiently small 
for all purposes of currency, and, in fact, is seldom demanded, the 
mil, whose value is less than a farthing, may be accepted as suffi- 
ciently minute for the common purposes of life. The attempts to 
introduce a smaller coin, whether in the shape of half or quarter 
farthings, have, though made on more than one occasion, met 
with no encouragement. Moreover, though the division of a 
farthing is sometimes employed in accounts, the coin is very 
rarely, seldom or ever, required for the purposes of payment* All 
things considered, the mil will be found neither too large nor too 
small for the minimum coin ; — but if, for any purposes of minute 
accountancy, a lesser element is required, another column repre- 
senting the tenth of a mil, or the ten thousandth part of a pound 
sterling, may be employed in harmony with, and subserviency to, 
the decimal system which it is proposed to establish. 

Whatever be the coins in circulation, there is no reason that 
any other denominations should be used in accountancy than 
pound and mil. The Americans have eagles and dimes, but in 
accounts they only employ dollars and cents. The French have 
Napoleons and deniers, but they only use francs and centimes in 
their book-keeping. In Russia, though they have sundry coins 
in gold, platinum, and copper, yet accounts are always kept in 
rubles and copecks ;* so in Holland, notwithstanding their ducats, 
crowns, and stivers, yet guilders and cents form the sole account- 
ancy. In China, candereens and mace, being the decimal divisions 
of the ounce, are constantly used in conversation, but they do not 
figure in their accountancy. There would be considerable conve- 
nience from the introduction into common parlance of the words 
cents and dimes, as representing the decimal parts of the pound 
sterling ; but they need no more be money of account than the 
groat or the guinea. The florin or dime being a new coin, could 
not be paid without some name or other, and the coin of ten mils, 
which is needful to complete the decimal series, will be probably 
called a cent, though there is no reason it should be specially 
designated in the columns of account books. 

Whatever be the form in which accounts are kept, whether only 
in two divisions, £1, 525 mils, the pound sterling and the mil; or 
in three £1, 5d. 25wi., the pound, the dime (florin), and the mil; 
or in four — £l, 5d. 2c. 5m., i. e., the pound, the dime, the cent, and 

* A copeck is the one-hundredth part of a ruble. 



IN NUMBERS, COINS, AND ACCOUNTS. 109 

the mil ; — the principal coins will each represent a multiple or a 
division of 10 as regards the adjacent column — i. e., the cent will 
be lOmils, the dime 10 cents, thepound 10 dimes ; or, in other words, 
the pound will be a thousand mils, or 100 cents, or 10 dimes ; the 
dime will be 10 cents, or 100 mils ; the cent will be 10 mils. These 
will be the sole moneys of account, though the auxiliary coins in 
circulation may represent, as they would probably do, 1,000 mils and 
500 mils in gold, 100 mils (the dime), 50 mils (the half dime), and 
25 mils (the quarter dime) in silver, and 1 and 2 or 5 mils in copper ; 
the cent, or new coin of 10 mils, whose value would be 2f d. of our 
present money, would be the only novelty ; but it would at the 
same time be the great instrument of popular education and 
initiation into the decimal scale, and the demand of the new coin 
would probably grow with a perception of its usefulness. As 
regards books of accounts, there is no reason why the ruling for 
£ s. d. should not serve for pound and mils, — thus, £1 J 10 J 6 
would be written 1 [ 5 | 25. 

We cannot dismiss this part of the subject without some refe- 
rence to those familiar coins, shillings, pence, and farthings, which 
will cease to be coins of account when a decimal system is lega- 
lised. The shilling, no doubt, will retain its name, and perhaps 
its popularity, and, as throwing no impediment in the way of 
the new accountancy, may probably be issued from the Mint for 
generations to come. And as habit has so strong a hold on the 
mental associations, and the language of a people does not sud- 
denly or easily accommodate itself to change, or submit to the law 
which legislative authority may impose, it is likely that the mil, 
notwithstanding its altered value, will be called a farthing, two 
mils a halfpenny, and four mils a penny, for many a long year. 
And the evil will not be great, for though decimal names would be 
invaluable allies in giving currency to a decimal system, they are 
not a necessary part of such a system, and their introduction 
must be of slow progress. When J. Quincy Adams wrote his 
interesting report, the word dime, though coined on every piece 
representing the tenth of a dollar, had little hold upon the public 
mind, and had not incorporated itself with the popular idiom. I 
am assured that a great change has already taken place in the 
United States, and that the education of two generations has suc- 
ceeded in giving to the word dime the stamp of general acceptation. 
Names once familiar to English ears have passed into oblivion 
with the objects they betokened ; roses, spurs, laurels, marks, harps, 



110 THE DECIMAL SYSTEM, 

riders, nobles, angels, guineas, groats, testoons, mites, and a mul- 
titude of similar designations, are now only to be found in records 
of departed time, familiar though they once were as household 
words, and forgotten now, except in tales and tradition, as though 
they had never been. 

Down to the time of Edward the First, the pound of silver 
(troy 12 ounces), containing 11 oz. 2dwts. of fine metal, was coined 
into 240 pennies, or 20 shillings. The weight of the silver coinage 
was diminished by a succession of reductions down to 1816, when 
the pound troy was coined into 62 shillings. From that period to 
the present, the pound is coined into 66 shillings, so that the 
augmentation upon the primitive value amounts to 330 per cent. 
The additional 4 shillings represent the seignorage which the sove- 
reign appropriates on the coinage of silver. Yet more extraor- 
dinary than this depreciation are the changes upon Scotch coin- 
age. The pound of gold represented, in the reign of Robert II. 
(1371), £17 12s. Scotch : in the time of Charles I. (1633), £492 
Scots were coined from the same weight — an augmentation of 
nearly 2,800 per cent., or, in other words, that the pound Scots 
in the 17th century had only one twenty-eighth part of its intrinsic 
value in the 14th. 

The shilling, schilling, or skilling, called escalin in some 
parts of the Netherlands, represents twelve pennies or pfennings. 
The soue, sol, soldo, or suldo, which is its equivalent in southern 
languages, is also divided into twelve denarii, dineros, or deniers. 
It is worthy of notice, that though the depreciation of the coinage 
of England from its primitive value, as represented by its ancient 
names, amounts to more than two- thirds, the depreciation (with 
the exception of China, where the cash still represents about 
50 per cent, of its original value, viz., the thousandth part of the 
tael or ounce of pure silver) is far less in England than in other 
parts of the world, — the shilling of France being about one-half 
of a penny ; that of Italy one-third of a penny. 

Shillings, though constantly spoken of as the twentieth part 
of the pound sterling, were first coined by Henry VII., in the 
eighteenth year of his reign, when the front face was laid aside 
in our coinage, and the profile substituted. Henry VIII. and 
Edward VI. partially resumed the front face ; but from the time 
of Mary the profile portrait has continued in use, generally 
shifting from right to left on the advent of a new sovereign. 

There is in a curious old book — a big and heavy bcok 



IN NUMBERS, COINS, AND ACCOUNTS. Ill 

printed in the year 1600* — a versified description of the aliquot 
parts of a shilling : — 

" A farthing first findes forty-eight, 

An halfpenny hopes for twenty-four, 

Three farthings seeks out sixteen straight, 

A peny puis a dozen lower; 

Dicke Dandiprat drewe eight out deade; 

Twopence tooke six, and went his way j 

Tom Trip-and-goe with four is fled, 

But Goodman Grote on three doth stay j 

A testime only two doth take : 

Moe parts a shilling cannot make." 

The author, Thomas Hylles, who calls himself in his title-page 
" A Well-wisher to the Mathematicals," must have been a facetious 
pedagogue. 

The penny is a sort of continuation of the Roman denarius, 
which has penetrated into Oriental language as dinar, denier 
(French), danaro (Italian), dinero (Spanish), dinpeiro (Portu- 
guese), having in the three last and several other languages 
become the representative of the general idea of money or 
monetary value. Penny, penning, pfennig, though the initials are 
changed, preserve enough of the original root to render it probable 
they have been derived from the same source. The letter d is 
frequently rejected or modified in words derived from the Latin ; 
and, pronounced as we pronounce it, did not exist in Greek at all. 
It is a letter wanting in many alphabets, such as Finnish and its 
ramifications, and cannot be clearly uttered by any of the Celtic 
race. 

There are few coins, if any, of which so long, so uninterrupted, 
and so interesting a series, exists as the English penny. Repre- 
sentations of pennies from the Anglo-rSaxon period will be found 
in the accompanying illustrations. They not only exhibit the 
diminishing intrinsic value of our silver currency, but are illus- 
trative -of the state of art at different epochs of our history. 

The Roman denarius, a coin which continued current for more 
than six centuries, down to the time of Constantine I., was 
originally a decimal coin representing ten asses. After the last 
Punic war its value was varied to sixteen asses: Augustus 
reduced its value to twelve, but it mounted again to sixteen, 
though it frequently bore the worth of ten. 

* De Morgan, " Arithmetical Books," p. 31. 



112 THE DECIMAL SYSTEM, 

The denier of France remained, through many changes, an 
integral part of the monetary system of France, down to the 
introduction of the decimal francs and centimes. The denier, 
like the penny, was the two-hundred-and-fortieth part of the livre 
or pound. In the time of Charlemagne it weighed from 28 to 30 
grains. Charles the Bold raised it to 32 grains. It fell by suc- 
cessive adulterations down to 6^ grains in the time of St. Louis 
(1226). The small copper coins of France, which were super- 
seded by the decimal coinage, represented various values-^-from 
2 up to 36 deniers. 

The copper penny was first introduced in the reign of George III. 
Its utility is very doubtful. It is inconvenient from its size and 
weight. Copper twopences, still more huge and ungainly, were 
also issued in the same reign. They are now seldom seen — never 
as currency, and rarely even as curiosities. 

Farthings, or fourthings, no doubt had their name from the 
habit of cutting pennies into four parts, — a usual practice in the 
Anglo-Saxon times. Pennies cut accurately into halves (half- 
pennies), and fourths (farthings), are constantly found among 
Anglo-Saxon coins. In the Anglo-Saxon version of the Gospels, 
fourthling is twice used. — (Matt. v. 26, Luke xxi. 2.) 

A simple mode of ascertaining the number of farthings in any 
amount of pounds sterling, is to multiply by 1,000, and deduct 4 per 
cent, from the quotient. This operation is now frequently practised, 
and saves much labour. Persons receiving large amounts in copper 
currency, instead of undertaking the operose toil of adding up 
the number of farthings and pence, and then going through the 
various divisions of 4 for the farthings, 12 for the pence, and 20 for 
the shillings, would find it an easier task to consider the shilling as 
representing 50 farthings instead of 48, and the pound sterling 
1,000 instead of 960. 

£ s. d. 
Thus 1,206 10 6 in Decimals would be 1,206,525 
20 Deduct 4 per cent. 48,261 



24,130 1,158,264 

12 



289,566 
4 



1,158,264 
A saving of 11 out of 30 figures, or rather more than a third. 



IN NUMBERS, COINS, AND ACCOUNTS. 113 

A curious and instructive Table was laid before Parliament, 
by Mr. Kirkman, showing the number of customers which were 
served in Liverpool, at a popular tea and grocery establishment, 
during a day, the number of articles bought, the money ex- 
pended, — the average purchases not exceeding 2^6?. Mr. Kirk- 
man stated that he thought there would be no difficulty in recon- 
ciling the working classes to a decimal system, and that it would 
soon recommend itself; he believed that a coin lower than a mil 
would not be desirable. This Table is given on the next page. 

Of our current silver coins the most obstructive to a decimal 
accountancy are the half-crown, the fourpence, and the threepence, 
pieces which, however they may facilitate payments, are connected 
with complications and loss of time even in our existing mode of 
keeping accounts. Association has given to the half-crown a tolerably 
distinct value in the mind even of the least instructed, who know 
that eight of them make a pound sterling ; but there are multi- 
tudes among the people who, if asked how many threepences orfour- 
pences go to a pound sterling, would be unable to answer. And, 
as regards the present plan of book-keeping, every odd number of 
half-crowns requires two figures at least to record them, and necessi- 
tates the employment of two columns, and the division of the pence 
column by 12 to be carried on to the shilling; so in all cases except 
where four or fours is the multiple of the 3c?., or three and threes 
of the 4c?., two columns would have to be used. In decimal enu- 
meration the halfcrown would be represented by three figures, 
125, a very inconvenient number ; and though the multiplication 
of even quantities of half-crowns would assume a decimal form, the 
retention of the half-crown, from its resemblance in value to the 
dime or florin, is undesirable. As regards the 4d., which re- 
presents decimally 16 mils, and the Zd. 12 mils, these sums 
would be inconvenient in accounts, and ought undoubtedly to be 
superseded by a new coin of the value of 10 mils, which coin 
would become indeed the principal source of popular instruction 
in the introduction of a decimal system ; and its relative value to 
the mil, to the dime (or florin), and to the pound sterling, being 
once fairly established in the public mind, every difficulty growing 
out of ancient prejudices and usages would speedily pass away. 



STATEMENT of One Day's Transactions at a Shop in the Tea 
and General Grocery Trade, in a low part of Liverpool. 





£ "3 


«• 


is 


£ "2 


£ 2 




£ 2 




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THE DECIMAL SYSTEM. 115 



CHAPTER VII. 

PROGRESS OF PUBLIC ACCOUNTANCY IN ENGLAND. 

It is by no means irrelevant to the subject of the present 
volume to refer to the progress made in public accountancy from 
the rude system which prevailed in the Anglo-Saxon and Norman 
periods of our history. The introduction of a decimal system 
will — next to the employment of the English language, Arabic nu- 
merals, and book-keeping by double entry — be the most important 
step towards facilitating the records and insuring the accuracy of 
all accounts of income and expenditure. 

Book-keeping by double entry, or by what is called the 
Italian method, and which has become now the almost universal 
system of bankers and merchants, was one of the natural improve- 
ments growing out of the use of the Arabic numbers, the intro- 
duction of which so facilitated all the operations of exchange. It 
was only in 1832 that the Commission of Public Accounts recom- 
mended its universal employment by the various departments of 
receipt and expenditure. Under the direction of Sir Henry Par- 
nell, the expenditure of the army and the navy service was sub- 
jected to a sound and mercantile system of record and control ; 
and the complete success of the experiment in these great depart- 
ments has prepared the way for a general reform of the public 
accountancy. The period is now at hand in which the payment 
of the gross revenue into the Exchequer will lay the foundation 
of great additional securities for the investment or appropriation 
to the public service of all sums raised by the taxation of the 
people. 

The Exchequer is one of the most ancient institutions in this 
country. It was the place of receipt and payment of the royal 
revenues. The antique forms which existed before the. Conquest 
were preserved down to the time of William the Fourth, and the 
Exchequer still exists as a constitutional control upon the public 
accountants, its administration having been greatly reformed, and 
the cost of the establishment much reduced. It is still charged, 
as of old, with a general supervision of the application of the 

I 2 



116 THE DECTMAL SYSTEM, 

public money, and is bound to see that the revenues are appro- 
priated as directed by Acts of Parliament. The Bank of England 
is now the principal receiver of the State revenues, but it pays no 
warrants issued by the Treasury, or by any department of Go- 
vernment, until the Exchequer has reported that such warrants 
are sanctioned by legislative authority. Some account of the 
Exchequer, and of the mode formerly in use for receiving and 
paying the public moneys, will serve to illustrate the great im- 
provement which has taken place in the system of national ac- 
countancy ; and it may excite astonishment to learn, that the rude 
and barbarous forms employed in days of arithmetical ignorance 
should have been maintained even down to the present genera- 
tion. 

The ancient Exchequer* of England was similar to that of the 
Normans, and is supposed to have been introduced by the Con- 
queror, as no mention is made of an Exchequer in times pre- 
ceding the Conquest ; but soon after that event it is frequently 
mentioned by historians and in records.*!* The great officers who 
presided at the Exchequer were all, or most of them, new, that is, 
had different .functions from those of the great officers of the 
king's court or palace in the English or Anglo-Saxon times. J 



* It is said to have been called the Exchequer, from the chequered 
cloth, resembling a chess-board, which covered the table, and on 
which, when the accounts were made up, the sums were marked and 
scored with counters. 

In the ancient "Dialogue concerning the Exchequer," Book I., 
chap, i., written probably in the time of Henry II., the Exchequer is 
described as " a square board, of about ten feet in length and five in 
breadth, fixed up in the shape of a table, for people to sit round, with 
a border of about four inches high all round it, to prevent anything 
falling off, and a cloth, bought in Easter term, marked with black 
squares, distant from each other about a foot or a span, laid upon 
the Upper Exchequer, and was like a chess-board. In the squares, 
counters were regularly placed." 

And the " Dialogue" farther states that the cashier carried his coffer 
of silver from the Under to the Upper Exchequer, to be examined by 
weight and combustion ; therefore the offices of Weigher and Melter 
seem rather to belong to the Upper Exchequer.— See "Dialogue," 
Book I., chap. iii. and chap, vi., under the heads " Cashier " and 
" Melter." 

f Madox (folio), 120, 121. 

X lb. 127. Williams' " Ancient Exchequer of England," p. 1. 



IN NUMBERS, COINS, AND ACCOUNTS. 117 

When the Exchequer was held at Westminster, there were two 
principal rooms for the barons to sit in ; one was called Scacca- 
rium, or Scaccarium Baronum — it was so called in the times of 
Henry II. and III. ; the other was called Thalamus, or Thalamus 
Uaronum, a sort of council chamber.* Sometimes the greater 
Scaccarium was called Scaccarium in Solio, the throne-like 
Exchequer. The barons had also certain chambers in the King's 
Palace or Exchequer ; but whether for lodgings or for other pur- 
poses, does not appear.f It is stated in the "Dialogue of the 
Exchequer," Book I., chap, vii., that the Usher of the Upper 
Exchequer not only took care of the door of the apartment in 
which the Exchequer was kept, but had also the care of the 
Council Chamber, which was situated near the apartments of the 
Exchequer. The barons met there when any doubtful matter 
was proposed to them at the Exchequer which they chose to de- 
bate apart ; but their chief reason for retiring thither was, that 
they might not hinder the accounts from being proceeded with. 
If any doubtful question arose it was referred to them, j 

When any money was to be paid into the Exchequer by the 
sheriff or other person, the proper place was at the Receipt or 
Lower Exchequer, at the office of the Tellers, where it was entered 
in a book ; this entry was immediately transcribed on a slip of 
parchment called a bill or tellers' bill, and thrown down a pipe 
into the Tally Court, where a Tally§ was struck or levied. A 

* Coke, in his 4th Inst., p. 112, says, that "about the end of 
Edward I. this Court was new built, and, therefore, in 2 Edward III. 
it was called the New Exchequer. Four score and one persons 
(whereof the Abbot of Westminster and forty -eight of his monks 
were part) brake into the Receipt, and robbed therefrom £100,000. 
This occasioned the new building of both parts of the Exchequer, the 
old being ancient and weak." 

f Madox, 129—131. X Williams, pp. 1, 2. 

§ The system of recording events, especially numbers, by cutting 
notches in wood— as the tallies of the Exchequer were cut — is one of 
very general practice where the art of writing is little cultivated or un- 
known. Barrow, in his "Travels in South Africa," says of the 
Kaffirs, " Their only chronology is kept by the moon, and is regis- 
tered by notches in pieces of wood. It seldom extends beyond one 
generation till the old series is cancelled, and some great event, as the 
death of a favourite chief, or the gaining of a victory, serves for a 
new era." — i. p. 218. 



118 THE DECIMAL SYSTEM, 

tally was a stick (generally of hazel) prepared by an officer called 
the Tally Cutter, or Cutter of the Tallies ; on the tally notches 
were cut, indicating the sum in the Teller's Bill, a large notch for 
M (or £1,000), a smaller notch for C (or £100), a smaller still 
for X (or £10), and so on for pounds, shillings, and pence. The 
Clerk of the Pells entered the bill with the teller's name, in order 
to charge him therewith — this is called the " Pell of Receipt :" 
in addition to which, the tally writer, who was afterwards Auditor 
of Receipt, also wrote the sum on two sides of it, then i* was 
cleft from the head to the shaft through the notches, one part of 
which was called a tally, the other a counter- tally (or tally and 
foil) ; one of the parts was retained by the Chamberlains, the 
other part was given to the party paying in the money, and was 
his discharge for that amount in the Exchequer of Account 
when joined by the Joiners, whose business it was to fetch away 
the foils from the Chamberlains' chest when parties claimed 
allowance on their tallies ; and the bill was filed by the auditor, 
who also entered the same, by which he saw what every teller 
received, and made certificate thereof to the Lord Treasurer.* 

Four volumes have been printed of the earliest records of the 
public accounts, from parchments in the custody of the Record 
Commission. The earliest of these is of the second year of Henry 
the First. Then follow the rolls of the second, third, and fourth 
years of Henry the Second. They extend in almost unbroken 
continuity from the twelfth to the nineteenth century. They 
consist of a number of Rotulets (Rotulas) fastened together at the 
head. The Rotulets are each formed of two membranes — the width 
is fourteen inches. The writing is in the large square character. 
The membranes are for the most part written on the front and 
dorse.f 

As a specimen of the manner in which the early public accounts 
were kept, I have taken a copy of a portion of the first parch- 
ment skin, being one of the documents called the great Rolls of 
the Pipe, of the first year of the reign of Richard the First 
(1189-90):— 

HONOR WILLI DE VESCI. 

Nicholas de Morewich redd comp de ccc 7 q a t xx 7 vn li vm s 7 
11, d. de firma Honoris Willi de Vesci. In thro cc 7 XLiili 7 v s 7 vi d. 

* Gilbert, 137, 138. 

t Hunter's " Great Rolls of the Pipe," 8vo. 1844. 



IN NUMBERS, COINS, AND ACCOUNTS 



119 

vii s 7 mi d. Et 



Et in Elem const 7 Decim p maneria in denar x li 7 
p blado Prebendario3 appliatoji anno ti K 7 11 s. 

And so on. The rolls proceed to give in detail the manner 
in which the whole sum of £327 8s. 2d. was expended, less 
the £242 5s. 6d. paid into the Treasury. At the foot of each 
account are the words 



Et quiet' est. 
And he is discharged. 



In thro librauit. 
Paid into the Treasury. 

The following is an account of the receipts of public revenues 
for one lordship, as collected by Nicholas de Morewich, on the 
Pipe Roll, bearing the date of the first year of Richard the First, 
and of the manner in which the receipts were expended or paid 
into the Exchequer.* The second and third columns are transla- 
tions and explanations of the Latin account : — 



Extract from a 
Pipe Roll, 1 Etc. I. 

Honor Willi efe 
Vesci. 

Nichols de More- 
wich redd comp de 
ccc 7 qH xx. 7 
villi. 7 viii s. 7 11 d 
de firma Honoris 
Willi de Vesci. 



Chabge, 
Explanation. 

Honor of William 
de Vesci. 

Nicholas de More- 
wich renders his ac- 
count of 300 and 4 
score and 7 pounds 
8 shillings and 2 
pence for the farm 
of the Honor of 
William de Vesci. 



Charge. Discharge. 



£. s. d. 



387 8 2 



\. s. d. 



Discharge. 

In thro cc 7 xlii li ) Paid into the Trea- ) 
7 v s. 7 vi d. j" sury 2421. 5s. Qd'. ) 

Et in Elem Const 1 Also paid the set- 
7 Decim p maneria tied alms and tythes 
in denar x li 7 vn s. I on account of the 
mi d. manors; in money, 

J 101. 7s. 4d. 



242 5 6 



10 7 4 



Et p blado Preben- "j Also for the corn 
dario3, appliato h | of the Prebends, 
anno vi u 7 11 s. J appraised at 61. 2s, 



'\ 



6 2 



Williams, pp. 6Q, 67. 



120 



THE DECIMAL SYSTEM, 



Et Monialib' de 
Gisnes, n s 7 vi d 
in redditu salis, q 
hnt p amiu. 



Also for the nuns 
of Guisnes,for their 
annual rent of salt, 
2s. 6c?. 



Et p pannis xx frm [Also for clothes for ] 
Prebendar 7 11 In- | 20 friars and 2 re- f 



clusar lxxiv s. 



[ cluses, 74s. 



2 6 



3 14 



Et in Quiet tre Ric. 
falconar qa ht anno 
q° servit de minis- 
tio suo vi s. 7 viii 
d. qa h anno serui- 
uit. 



' Also for quittance 
of the land of Rich- 
ard the Falconer, 
who served his own 
office, 6.9. 8c?., which 
he is allowed when 

L he so serves. 



6 8 



Et in manio de 
Malton li li 7 xvn 
s 7 x d. de qM^, 
Galfr Haget de" 
responde. 



leb 3 



Also for the manor 
of Melton, 51Z. 17s. 
10c?., which Gef- 
fery Haget ought 
to answer. 



Et in defalta red- f Also in default of ] 
dit' militu p War- j the rents of the ' 
da de Alnewick, j Knights of the Ward j 
xxxviii s 7 xi d. [ of Alnwick 38s. lie?. J 



51 17 10 



1 18 11 



Et in defalta red- 
dit' tre de Burden 
qamat'Alani Goher 
disronau i curia ee 
dote sua xxx s. 



Abo in default of 
the land of Burden, 
which the mother 
of Alan Goher 
proved in court to 
I be her dower. 



Also in livery of 
residntis in Castde I one chaplain resi- 
Alnewick xxx s 7 1 dent in Alnwick 
v d. I Castle, 30s. 5c?. 



Et in libat 1 Caplli f 
de J 



Et in libat Eustach 
de Vesci H'edis 
ei' d Willi de anno 
integro liiii 1! 7 
xv s. set q' libs die 
in s. p br. R. 



Also in livery of 
Eustace, the heir of 
the said William, for 
one year, 54? 15s., 
at the rate of 3s. 
per day, by the 
King's Writ. 



1 10 



1 10 5 



54 15 



Et deb xii li 7 f And he oweth 12?. 1 

xvtii s. Id redd I 18s., and afterwards I 

comp de eod debito. | rendered account of j 

I the same. J 



IN NUMBERS, COINS, AND ACCOUNTS. 1*21 

In thro ix li. Et I" Paid into the Trea- 1 

deb lxxviji s. \ sury, 91. ; and then [ ... 900 

[ owed 78«. j 

Idreddcompdeeod [" And afterwards 
debit o. | rendered account of 

j. said debt. 

In thro libavit. f Paid it into the ) q i » a 

( Treasury, 78s. J ' * * 6 18 ° 

Et quiet' est. ...And he is quit. ... ... 387 8 2 

Some curious accounts of the usages of other days, in reference 
to the Exchequer, have been preserved. 

Coke, in his 4th Inst., p. 104, states, that the Lord Treasurer 
of England was appointed by the delivery of a white staff, but 
that in former times he was appointed by having delivered to 
him "the keys (golden keys) of the Treasury; when treasure 
failed, the white staff served him to rest upon, or to drive away 
importunate suitors; but, as Treasurer of the Exchequer, he 
was appointed by Letters Patent." It may here be observed, 
that the Secretary of State is appointed by the delivery of the 
signet, but he has also Letters Patent, under which he receives 
his salary, but no one will say he holds two offices. 

However, in process of time he was called Lord High Trea- 
surer and Treasurer of the Exchequer. The following quotation 
from the " Black Book" of the Exchequer* will show the great 
ceremony observed on the Earl of Godolphin taking possession of 
his office a century and a half ago. 

" Monday, the 11th day of May 1702, the Right Hon. Sydney 
Lord Godolphin having had the staff of Lord Treasurer delivered 
to him by Queen Anne on Sunday the 10th instant, on the 11th 
he came, about the hour of ten in the morning, to the house of 
Lord Halifax, the Auditor of the Receipt of the Exchequer, 
where he was attended by many Earls, Barons, Privy Councillors, 
the King's Attorney and Solicitor- General, and other persons of 
quality"; they being assembled in the two great rooms, were 

* The " Black Book " is so called from its binding. It contains 
divers authentic entries, chiefly relating to the Receipt of the Exche- 
quer, such as oaths of office, admissions of officers, &c. In it is entered, 
also, a celebrated treatise on the ancient constitution and practice 
of the Exchequer, called " Dialogus de Scaccario ;" and various 
other entries and memoranda, from an early period to 1755. 



122 THE DECIMAL SYSTEM, 

treated with chocolate, &c, by the said Lord Halifax. The pro- 
ceedings began from thence ; a great number of gentlemen in 
swords and coats, pell mell, the Clerks of the Treasury, Auditors 
of the Exchequer, Secretaries, Officers, &c, and amongst them 
the officers of the Exchequer, having no gowns (who should have 
marched in their proper places if they had had gowns) ; then the 
Usher of the Exchequer in his gown, the Clerk of the Pells, 
Clerk and Tally-writers' Clerk in gowns, the Tally-cutter, the 
Deputy Clerk of the Pells, the two Deputy Chamberlaius, the 
Marshal of the Exchequer, the auditors, viz., the Lord Halifax, on 
the right hand of Mr. Lowndes, the Secretary to the Lord Trea- 
surer, Lord Treasurer's Sergeant-at-Mace, the Lord Treasurer ; 
on his right and left, and behind, several Lords, as the Lord Pre- 
sident of the Council, Lord Privy Seal, &c, all pell mell. Thus 
they proceeded along the Inner Court up the great stairs of the 
Exchequer in the corner of the Palace-yard, by the Tally-court, 
down the stone-steps into Westminster Hall, by the Common 
Pleas bar — when my Lord Treasurer made his obeisance to the 
Judges of that Bench — so up towards the Chancery bar ; and 
about the middle of the Hall made two obeisances, one to the 
Lord Keeper, sitting in the Court of Chancery, the other to the 
Court of Queen's Bench, whence they proceeded up the Hall into 
the Court of Chancery, the officers filing off at the bottom of the 
steps, except the Marshal of the Exchequer, and the Sergeant- 
at-Mace, with the Lords, where he took the oaths to the Queen ; 
after which he came back, with the Lord Keeper on his right- 
hand, and the said officers before him, by the Common Pleas bar, 
where they both made their reverences to the Judges, so up the 
stone-stairs into the Exchequer. The Barons being sat, my Lord 
Keeper went into the Court, placing himself on the right of the 
Lord Chief Baron ; the Lord Treasurer was by the Marshal, and 
his own sergeant conducted to the outside of the bar, with the 
Sergeant-at-Mace on his left, when my Lord Keeper made a neat 
speech, signifying his Lordship's great abilities — that he had two 
offices, that of Lord High Treasurer by delivery of the staff, and 
that of Treasurer of the Exchequer by patent ; after which my 
Lord's patent was read by one of the clerks of the King's 
Remembrancer's office. Then his Lordship was conducted into 
the Court, where was a cushion provided, on which he knelt whilst 
the oaths of his respective offices were administered to him by the 
Lord Keeper. After which he was conducted to his place on the 



IN NUMBERS, COINS, AND ACCOUNTS. 123 

left of the Lord Keeper, and his patent delivered to him by the 
Lord Keeper ; which done, the Lord Keeper departed the Court, 
and the Lord Treasurer sat to hear motions some little time, after 
which he departed the Court, when he should have taken posses- 
sion of the King's Remembrancer's Office, Treasurer's Remem- 
brancer, Pipe, and other the offices on that side of the Exchequer, 
before he walked thence ; but he was conducted in the same 
order, accompanied to the Tally Court, where were placed 
cushions for him in the middle thereof, and two for the Cham- 
berlains on each side of the block, the two Deputy-Chamber- 
berlains in each corner, the Lord Halifax, Tally-writer, and 
his clerks on the right-hand, below the senior Deputy Cham- 
berlain ; the Deputy Clerk of the Pells and his clerk below the 
junior Deputy Chamberlain ; then the Usher of the Exchequer 
just within the door, and the Tally-cutter without the Court ; 
the Chancellor of the Exchequer on the Lord Treasurer's left ; 
several Dukes and Earls round the Court, the Barons of the 
Exchequer on the outside of the bar, with the Attorney and 
Solicitor- General. When all were come in, a bill was thrown 
down from the tellers' offices, a tally prepared, writ on, struck, 
and examined by the proper officers ; then his Lordship withdrew 
thence, after having had the great keys of the Treasury presented 
to him by the Auditor, and he delivered them to him again ; then 
he went into the Auditors', Pells', and Tellers' Offices-, and 
viewed the cash in the last of them, the Barons of the Exchequer, 
Attorney and Solicitor- General, with the Dukes, Earls, &c, 
attending him to each office. After which he went back again to 
the other side of the Exchequer, to take possession of the several 
offices there, which he should have done before he came to the 
receipt side ; and after retired to his house," &c. 

The intervention of the Exchequer in matters of coinage is 
thus described : — 

" The trial or assay of money is technically called the Trial of 
the Pix, from the box in which the coins selected for that purpose 
are contained. In Ruding's ' Annals of the Coinage,' it is stated 
that the modern practice is for the Master of the Mint to present 
a memorial, praying for the trial of the pix ; upon which the 
Chancellor of the Exchequer moves the Sovereign in Council, 
who commands the trial to be holden. The members of the Privy 
Council are accordingly summoned. A precept is likewise 
directed by the Lord Chancellor to the Wardens of the Gold- 



124 THE DECIMAL SYSTEM, 

smiths' Company, to nominate a competent number of sufficient 
and able freemen of their company, skilful to judge of and to 
present the defaults of the coins, to be of the jury. This num- 
ber is usually twenty-five, of which the Assay Master of the Com- 
pany is one. 

" No coin whatever is issued from the Mint until a portion of 
it has been assayed by the Queen's Assayer. When that process 
has been gone through, one coin of each denomination is placed in 
what is called ' the Pix,' meaning box, chest, or casket ; ^hen so 
deposited, this box is sealed with three seals, and secured with 
three locks, the keys being separately kept by the Master of the 
Mint, the Chancellor of the Exchequer, and the Queen's Assayer ; 
the pieces of coins so secured are given to the jury to assay and 
compare with the trial plates, which are kept in the ancient 
Treasury in the Chapel of Edward the Confessor, in the cloisters 
of Westminster Abbey, the keys of which, and of the box in which 
the trial plates are deposited, are now in the custody of the 
Comptroller of the Exchequer and the Lords of the Treasury." 

It is, indeed, scarcely credible, that the perplexing and 
entangled manner of keeping accounts by the Roman numerals, 
in the same t>arbarous style which was practised before the Nor- 
man Conquest, was maintained at the Exchequer almost down to 
the present day ; and the introduction of the English language 
and the Arabic numerals was successfully resisted by no less a 
personage than Lord Granville, on the ground, that if the bar- 
barous usages of our ancestors were reformed, it would be diffi- 
cult to understand the accounts, and the records of departed 
time ; and hence he argued for the necessity of perpetuating a 
uystem of complication, confusion, and imperfection, not on the 
common plea of the superior wisdom of our ancestors, but in full 
acknowledgment and appreciation of the ignorance which was 
originally instituted and had continued to reign triumphant 
among the Exchequer records. 

In addition to the strange and absurd system of Exchequer 
book-keeping, tallies continued to be used down to the year 1782. 
It was only in the year 1831 that the Committee on Public Accounts, 
of which I was the Secretary, recommended the utter and imme- 
diate abolition of the ancient system, and the adoption of the 
Arabic numerals and the English language. It was in conse- 
quence of this change that, in the year 1839, the tallies were 
ordered to be burnt, a conflagration which led to the destruction 



IN NUMBBRS, COINS, AND ACCOUNTS. 120 

of both Houses of Parliament — the Exchequer in which the 
tallies were kept having formed a part of the ancient edifice of 
St. Stephen's. Far more serious consequences than were ever 
anticipated were thus produced by the introduction of the new 
and improved system of accountancy at the Exchequer. To it 
we owe those splendid edifices which are now the seats of British 
legislation, and in their grandeur and beauty we may find 
some consolation for having been, as one of the principal authors 
of the Exchequer Report, the unintentional incendiary of that 
old sanctuary whose eloquent words and legislative influence have 
so often agitated and ameliorated the world. May a grander 
pile accomplish even loftier destinies ! 

Many of the ancient forms and usages of the Exchequer are 
preserved even to our own time, and afford various illustrations 
of the habits of our forefathers. The following is an account of 
a tenure custom, as it was observed in the present year, in con- 
nection with the presentation of the Sheriffs in the Court of 
Exchequer. The chopping the sticks and counting the six horse- 
shoes and sixty-one hob-nails have probably reference to amounts 
due to the Crown on account of the tenures in question : — 

" The Lord Mayor, accompanied by several members of the 
Court of Aldermen, the Sheriffs, Under Sheriffs, and other cor- 
porate officers, then proceeded in state from Guildhall, via Cheap- 
side, Ludgate-hill, and Bridge-street, taking water at Blackfriars- 
Bridge, and proceeding in the city barge to Westminster, where 
they were met by the High Constable of that important city. 

" On their entering the court, which was much crowded, a 
number of ladies being present, the Cursitor Baron took his seat 
on the bench. The Baron wore his scarlet robes, as did also the 
Sheriffs and Recorder their scarlet robes, as also the Lord Mayor, 
with his collar of SS. 

" The Lord Mayor and Sheriffs, and other civic functionaries, 
having taken their position within the bar, — 

" The Recorder, addressing the Cursitor Baron, then related 
Mr. Sheriff Wire's personal history and civic position, together 
With the connection of Mr. Wallis with the City. 

" The Cursitor Baron having referred to the ceremonial as 
having existed for several hundred years, concluded by signifying 
the approbation of her Majesty to the appointments the citizens 
had made ; and by wishing health and strength to the Sheriffs to 
discharge their onerous duties. 



126 THE DECIMAL SYSTEM, 

" The Recorder then read the warrant of attorney from the new 
Sheriffs to receive and execute all writs, &c, and prayed that it 
might be recorded. 

"The Queen's Remembrancer read the warrant, which the 
learned Baron ordered to be recorded. 

" The Recorder also read the warrant for the late Sheriffs to 
account, as also the Under- Sheriffs, they having placed in their 
stead Mr. G. K. Potter and Mr. Thomas Cleobury ; and this ter- 
minated the ceremony of the Sheriffs' presentation. 4 

" Proclamation was then made by the Crier of the Court for 
the service, as follows : — 

" 4 Oyez ! Oyez ! Oyez ! 

"'Tenants and occupiers of a piece of waste ground called 
" The Moors," in the county of Salop, come forth and do your 
service, upon pain and peril that shall fall thereon ! ' 

" Alderman Moon, as the senior Alderman below the chair, 
then cut one faggot (small twigs) with a hatchet, and another 
with a bill-hook. 

" The Crier then made a proclamation : — 

"'Oyez! Oyez! Oyez! 

" ' Tenants and occupiers of a certain tenement called ' The 
Forge,' in the parish of St. Clement Danes, in the county of 
Middlesex, come forth and do your service ! ' 

" Alderman Moon then counted certain horse-shoes and hob- 
nails, and was questioned by the Queen's Remembrancer thus : — 
4 How many have you ? ' ' Six shoes.' Then the Alderman 
counted the nails : — ' How many have you ? ' ' Sixty -one nails — 
good number.' 

" The Recorder having invited the Cursitor Baron to dinner at 
the London Tavern, the civic cortege returned." 

Mr. Nichols, in the "Gentleman's Magazine" for October 
1804, vol. lxiv., p. 965, describes the custom as performed in that 
year, and adds this explanation : — " The ceremony on this occasion, 
in the Court of Exchequer, which vulgar error supposed to be an 
unmeaning farce, is solemn and impressive; nor have the new 
Sheriffs the least connection either with chopping of sticks or 
counting of hob-nails. The tenants of a manor in Shropshire are 
directed to come forth and do their suit and service ; on which 
the senior Alderman below the chair steps forward and chops a 
single stick, in token of its having been customary for the tenants 
of that manor to supply their lord with fuel. The owners of a 



IN NUMBERS, COINS, AND ACCOUNTS. 127 

forge in the parish of St. Clement (which formerly belonged to 
the City, and stood in the high road from the Temple to West- 
minster, but now no longer exists) are then called forth to do 
their suit and service ; when an officer of the court, in the presence 
of the senior Alderman, produces six horse-shoes and sixty-one 
hob-nails, which he counts over in form before the Cursitor Baron, 
who, on this particular occasion, is the immediate representative 
of the Sovereign." 

Mr. Sheriff Ho are, in the journal of his Shrievalty, 1640-41, 
in his own handwriting, says : — " The senior Alderman present 
cut one twig in two and bent another, and the officers of the court 
counted six horse- shoes and hob-nails. This formality, it is said, 
is passed through each year, by way of suit and service for the 
citizens holding some tenements in St. Clement Danes, as also 
some other lands ; — but where they are situated no one knows, nor 
doth the City receive any rents or profits thereby." 

The Court of Exchequer, be it observed, is the legal court of 
accounts ; and, moreover, pursuant to the charter 32 Henry III., 
the high officers of the City are, on their appointment, to be pre- 
sented to the Sovereign, or, in the absence of Majesty, to the 
Sovereign's Justices or Barons of the Royal Exchequer. 

So many references to the Exchequer are to be found in 
Shakspeare, that some have supposed he must have been a clerk 
in that office. The process of examining the public accounts is 
recorded in one of his sonnets : — 

" She may detain, but still not keep her treasure. 
The audit, though delayed, answered must be : 
And her quietus is to render this." 

Sonnet cxxvi. 

There is the stoppage of the public money — the delay in pass- 
ing the account till certain answers are obtained to justify the 
audit — and the rendering the correct account is followed by the 
quietus, .exactly as was practised in the Exchequer Court : — 

" For she hath no exchequer now but his." 

Sonnet lxvii. 

" To make their audit at your Highness' pleasure." 

Macbeth. 
Again, 

"What acceptable audit canst thou have ?" 

Sonnet iv. 



128 THE DECIMAL SYSTEM, 

Again, 

" Called to that audit by advis'd respects." 

Sonnet xlix. 

" Nor need I tallies thy dear love to score." 

Sonnet cxxii. 

* When he himself might his quietus make 
With a bare bodkin." Hamlet, Act hi. 

" Some younger brother would have thanked me, . 
And given my quietus." Gamester, Act v. 

" It were a sin to disquiet him, since he carries his quietus est with 
him." Cletus' Whimsies, p. 166. 



IN NUMBERS, COINS, AND ACCOUNTS. 129 



CHAPTER VIII. 

NUMERALS OF DIFFERENT NATIONS. 

It would be quite impossible — even were the present occasion 
a fit opportunity — to explore, still less to exhaust, those vast fields 
of investigation which are open to any one who seeks to trace, 
through the infinite variety of language and symbols, the modes 
adopted by different nations for communicating ideas of numbers 
and quantities. I have thought it might not be wholly without 
amusement or instruction if I selected some of the most pro- 
minent and characteristic peculiarities which present themselves 
in various parts of the inhabited globe ; and without encumbering 
these pages with redundant and superfluous matter, it appeared 
not undesirable to connect and preserve in them some materials 
which might prove of more general and diffusive interest than 
would seem directly connected with an inquiry into the history 
and advantages of a decimal system. There is, however, more of 
association and affinity between the various branches of human 
knowledge, than the careless or the thoughtless inquirer may 
imagine. The multifarious developments of progress and civilisa- 
tion are closely allied to each other ; and though it can hardly be 
expected that many will concern themselves in the discussion of all 
the topics upon which this volume touches, it may be hoped that, 
to some readers at least, they will recommend themselves, and be 
suggestive of pleasing and useful objects of research. 

Man is born with, and carries about him, instruments of nota- 
tion, and weighing, and measuring, which serve for the common or 
everyday purposes of life. Most of these have passed into habitual 
language in the various idioms of the world, representing num- 
bers, quantities, and proportions, with more or less accuracy, but 
generally with considerable approximation to the truths 

* Sir J. E. Tennent has given us the following memorandum illus- 
trative of the remark in the text : — 

" As an illustration of the expedients resorted to by the Singhalese 
to describe measures of distance in the absence of any standard or terms 
by which to define it, I may mention to you, that in my travels through 

J 



130 THE DECIMAL SYSTEM, 

In India, govista, or the cries of a cow— i. e., the distance at 
which the lowing of a cow can be heard — is equal to two keg, or 
8,000 cubits. A goshpada, cow's foot, is a measure representing 
what the impression of a cow's foot will hold. 

The classification of numerals or decimal multiplications, or a 
progression in tenfold proportions, would naturally grow from the 
employment of the fingers as counting instruments, and is to be 
traced to the remotest records of history, and over a vast extent of 
the inhabited world, both in the words and the symbols employed. 
Every step in the lower gradations enables us to form clearer con- 
ceptions of the higher. Proceeding from ten units to ten times 
ten, we immediately perceive the value of a hundred, — which 
being thoroughly understood, another multiplication by ten helps 
us accurately to estimate a thousand, and so onward. The nu- 
meration by twenties has equally its foundation in nature, every 
human being having not only ten fingers, but ten toes ; and it 
will be found that a vicenary scale is employed, not only in con- 
nection with, but sometimes, as by the ancient Mexicans, sepa- 
rately from, the decimal progression. 

Examples 'will also be discovered of a quinary scale, or reck- 
oning by fives, in the spoken languages of many rude tribes, as in 
written signs for numerals. Some ancient nations adopted a new 
series of characters at the quinary stage, as i, v, x among the 
Latins, and "i* V by the inhabitants of Palmyra. A binary system, 
or counting by twos, presents its own explanation in the many 
combinations of pairs which the human frame presents, — such as 
two eyes, two ears, two nostrils, two arms, two legs ; but a multi- 
plication by two increases the power of numbers too slowly to 
be available for the higher purposes of arithmetical calculation. 

Humboldt has very properly remarked, that if we consider the 
source of the various numerals, we shall find everywhere a 
great resemblance in the nature of their developments. The 



the more unfrequented portions of Ceylon, I constantly heard, in 
reply to my inquiries as to short distances, that I was within " a dop'.* 
cry " of it, — or that it was still " a hoo " off, or a loud hoo, as the case 
might be, — a hoo meaning the sound a man's voice exerted to the 
utmost in shouting that sonorous monosyllable, and thus denoting the 
distance at which it could be heard. The dog's cry, in the same man- 
ner, meant a shorter distance, or such as a bark of a dog could ex- 
tend over." 



IN NUMBERS, COINS, AND ACCOUNTS. 131 

last is generally only a wider extension of the first. Thus, if, as in 
many branches of the Malayan stem, the number 5 is represented 
by (lima) the hand (5 fingers), it might be anticipated that for 
the number 2, words meaning Avings, arms, eyes, and so on, would 
be employed. Of such symbols no doubt many have been for- 
gotten, and will be no more restored to use. Nations appear soon 
to have discovered that a variety of signs for the same number was 
not only a superfluity but an inconvenience, and likely to lead 
to misunderstandings. Hence synonymes for the same numbers 
growing out of the same language, are of rare occurrence, though 
some examples are to be found in the dialects of the southern 
seas. Nations alive to the powers of language must, long before 
trained to form an accurate estimate of numbers, have felt the 
desirableness of establishing clear notions, and of fixing a general 
standard, — and the more this feeling prevailed, the less would be 
the desire to retain in the names of the numerals the primitive idea 
of its value, and thus, as the original meaning became less and less 
discernible, the words would be rendered by merely conventional 
sounds." 

The word stone, for 14lb. in English, is no longer associated 
with its vague and normal meaning, which undoubtedly was the 
weight of a stone, of a generally understood size, in a particular 
locality. Some of the associations of definite numbers with unde- 
fined ideas, are remarkable. Out of the Sanskrit root yu, — mean- 
ing gathering together, or union, — come pra-yuta and ni-yuta, which 
express equally a hundred thousand and a million, — while a yuta 
which means " detaching" or "disuniting," is used for ten thousand, 
a decimal division of the larger number. 

Though the richness and precision of a language in arithmetical 
terms is undoubtedly an evidence of the civilisation and advance- 
ment of the people employing them, such richness cannot always 
be referred to as a standard of civilisation, or accepted in itself 
alone as all-sufficient proof of superior intellectual cultivation. 
One language, for example, possessing high capabilities for express- 
ing high numerals, may continue little changed where those who 
speak it have been declining in the scale of civilisation ;< — another 
language, wanting such facilities of expression, may be spoken by 
an advancing nation, and not easily lend itself to the introduction of 
novel terms. This is not alone the case with respect to numerals ; 
for, as regards languages generally, there are many which, " neither 
in the perfectness of their grammar, nor even in their copiousness, 

j2 



132 THE DECIMAL SYSTEM, 

appear to have any certain relation to the state of civilisation of 
the people by whom they are spoken."* There existed in France, 
for instance, from the reign of Louis XIV., quite a passion for pre- 
serving what was called the purity, or, to speak more truthfully, 
for cherishing the poverty, of the language by the repudiation of 
all novelties in words. Necessity has broken down many barriers. 
Improvements in science, especially in the field of modern investi- 
gation and discovery, have compelled the introduction of many 
terms for which no representative could be found in the dictioriary. 
Thus, in spite of repudiation and hostile criticism, new words 
become nationalised. The English language affords a noble 
example of still progressive advances in richness and efficiency. 
Its ever-increasing vocabulary, representing and adapting itself 
to all the demands of growing civilisation, fit it admirably for the 
great mission it has to accomplish as the instrument of the widest 
intercourse, and thus the mightiest ally of the interests of peace, 
commerce, and happiness, through the most populous regions of 
the world. 

No portion of the field of language presents more curious 
results, both ojf affinityf and dissimilarity, than do the various 
numerals. It may be generally said, that the least civilised races 
have almost invariably taken the names for the higher numbers 
from the more civilised with whom they have come into communica- 
tion. Thus the words mil and million have found their way into a 
great variety of idioms, between which words for numerals of lower 
value there is not the least affinity. The word lak is of very 
extensive use in the regions of Eastern Asia, generally meaning 
100,000, but sometimes, as in Sumatra, implying only 10,000, — 
and in the Newar district of Nepaul, laksee means a million. The 
words of high numeral value in Sanskrit are found in many 
languages, associated with decimal notation indeed, but with very 
different value in several other idioms. The Chinese word wan 
(10,000), which is found in almost all the dialects of that vast 
empire, is employed, with slight variation, iwrian, to denote 1,000 
in Manchuria. Alp, which represents 1,000 in several of the 

* Peacock, p. 377. 

f The numeral 3 is exactly the same (tri) in the Sanscrit, Erse, 
Welsh, Armoric, and Cornish languages. A close resemblance to the 
word may be traced through most of the European, and many of the 
Asiatic tongues. 



IN NUMBERS, COINS, AND ACCOUNTS. 133 

languages of the nations bordering on the Nile, means 10,000 in 
the Amharic, being a language of close affinity.* As we proceed 
into the higher ranges of figures, our notions become less and less 
distinct. The English word myriad presents to many minds an 
undefined or erroneous idea of its value. 

The Spaniards have adopted a singular word for million, — 
cuento, — a tale, a story, a fiction. It is not found as a numeral 
anterior to the introduction of the Arabic system of notation. 
The Portuguese have the word Gonto, with a similar meaning, also 
of modern introduction. 

Though the ceremonial forms of language generally only 
influence phrases of courtesy, and are principally exhibited by 
a greater elaboration of words, there are some languages where 
the same words for numerals cannot (without offence) be applied 
to superiors, as to equals. Among the Javanese, ja or siji is the 
word for one; but in the language of ceremony, it is needful to add 
tungil ; — and one becomes satungil meaning one standing by itself. 
Though the common word for ten is puluh, in addressing a supe- 
rior, doso, a numeral of Sanskrit derivation, must be employed. 

There are not wanting poetical forms of expression even in 
the dry regions of arithmetical figures. Some of the tribes of 
South America, instead of inquiring, " How many years have you 
lived ?" ask, " How often has the algarroba blossomed since your 
birth ? " Some reckon by the phases of the moon, and the 
numerals of some are reputed to be described by the names of 
flowers, whose petals represent the number in question. The 
lotus plant was, in consequence of its fruitfulness, deemed the 
symbol of millions ; while the centifolium represented hundreds, 
and the cinquefoil fives. The ancient Egyptian character for 1,000 
is a lotus leaf in its stalk, which is supposed to denote, that the 
fruit of the lotus bears thousands of seeds.f Among the Abipones, 
five is denoted by a word which signifies an animal's hide, which 
has spots of five colours upon it. So some of the Brazilian Indians 
call the months by names of native fruits ; and others designate them 
bywords implying the return of the various seasons. In Thibet, the 
word is the same for year and leaf (spring). Indian's, on their 



* Peacock, pp. 376-7. 

f Champollion Gramm. Egypt, i., p. 230. See also Humboldt, 
Verschiedenheit des menschlichen Sprach-baues," p. 437. 



134 THE DECIMAL SYSTEM, 

travels, speak of the twenty-four hours, or days, as rests : instead 
of saying, " I shall be three days absent," they say, " I shall rest 
three times before I return." Among the Arabs, a common mode 
of denoting a mile, is so far that you cannot distinguish a man 
from a woman. Hussein Khan, in reporting his victories, said, 
" I have destroyed more enemies with my own hand, than there 
are hairs on my beard," — and his beard was distinguished for its 
size.* 

There is considerable affinity between the Sanskrit* and 
Persian, the Greek and Roman numerals, — with their derivations, 
such as the Romaic, French, Italian, Spanish, Portuguese, Romance, 
the Catalan, and Wallachian ; — between these, and all the branches 
of Gothic and Scandinavian roots — such as High and Low Dutch, 
Anglo-Saxon and Frisian, Icelandic, Swedish, and Danish — 
between these, again, and the ancient Sclavonic, with its de- 
scendants, the Russian, Polish, Servian, Bohemian, Illyrian, 
Hydriote, — with the Celtic varieties, such as Gaelic, Erse, Welsh, 
Armorican, Manx, and Cornish.f 

The resemblance which exists between the numerals and 
a few other words in this great body of languages, has led many 
writers to the hasty conclusion, that all languages descend from 
one primitive or common language — once universal — and from 
which the whole human family have derived their various idioms 
— changed, modified, and separated, by the progress of time. 

But it may be laid down as a general principle, that where no 
intercourse has existed between nations, no affinity will be traced, 
either in the words, or the construction, or the general character 
of their languages ; and when any marked analogy exists, it must 
be received as undoubted evidence of inter-communication. 

If any two languages be examined, taken from localities 
wholly separated from one another, the comparison between tluin 
will strike not by any resemblance whatever, but by their extra- 
ordinary variety. 

* "Cameron's Travels in Georgia, Circassia," &c, vol. i v 
t Dr. Peacock (" Arith.," p. 372) classes the Armenian among the 
Sclavonic tongues, with which it has no affinity: only two of its nume- 
rals — ut (8) and inn (9) — resemble those of other nations. He also 
speaks of the Biscayan as a Celtic language, which it is not: only 
one of its numerals, set (6), bears any likeness to the group above 
referred to. 



IN NUMBERS, COINS, AND ACCOUNTS. 135 

Compare, for example, any language spoken in the remoter 
parts of Eastern Asia with that of any nation of Western Europe, 
and, neither in its numerals nor in any other word, will be found 
even an accidental resemblance, with the exception of those 
earliest utterances of infancy, such as ma-ma, pa-pa, fa-fa, ba-ba, 
which are generally employed to exhibit the paternal, maternal, or 
filial relations ; and the words, such as ku-ku (cuckoo), by which 
an animal may be represented by its voice ; or words like hiss or 
roar, which have an affinity with the sounds they designate. 
Even the old joke, that the word sack was preserved, at the dis- 
persion of the Tower of Babel, in every language, in order that 
every man might carry away his own property, will not bear 
examination, as, compared with the number of idioms in which 
the word is not found, the number of idioms in which it is found 
are exceedingly small. 

Again, if a language be taken from the interior of Africa, and 
compared with any spoken by the natives of America, or by any 
of the islanders of the Pacific, no analogy whatever will be found. 
Only one example is recorded of great resemblance between the 
numerals of races essentially different, and between whom inter- 
course can hardly have been supposed ever to have existed, viz., 
those of the African Mandingoes and an extinct American tribe, 
the Nanticocks, on the banks of the Chesapeak.* But the 
evidence of similarity may well be doubted, and the disappearance 
of the Nanticock nation deprives us of the means of investigation. 
No such resemblance, or anything like it, is traceable between 
any of the American- Indian and African languages which we are 
able to compare with one another. 

As far as our knowledge and experience extend, the number 
of languages spoken is not increased, but diminished, by the pro- 
gress of time, by intercourse between different races, and by the 
influence of civilisation. So far from inquiry leading to proofs 
that the many languages now used are traceable to one or a few 
sources, we shall find, that the farther we look back to the records 
or traditions of the past, the greater will be the number of idioms 
of which traces are discoverable. Conquests, so far from intro- 
ducing new languages, tend to the absorption of many dialects 
into one. We have undoubted evidence that in ancient Greece 
there were many languages, which have wholly disappeared. In 

* Barton, as quoted by Dr. Peacock, p. 373. 



130 THE DECIMAL SYSTEM, 

Italy, a great variety of tongues were spoken, of whose existence 
we are assured, but of whose characteristics we know nothing. 
Many languages were spoken in Spain, of which Strabo speaks, and 
probably only one of them (the Biscayan) has survived to our 
days. In France, it is but in Britanny we find the remains of a 
single specimen of the languages spoken in ancient Gaul. In Eng- 
land we have seen the ancient language of Britain driven into the 
county of Cornwall, and perishing there within the memory of man ; 
while the inroads of the modern English into Ireland, Sco^and, 
Wales, and the Isle of Man, will undoubtedly, in a few generations, 
wholly extirpate the remains of the ancient Erse, Gaelic, "Welsh, 
and Manx. Just before the French Revolution, not three quarters 
of a century ago, three-fourths of the population of France spoke 
various idioms, — the Provencal, the Languedocian, the Gascon, 
the Walloon, the Bas Breton, — which are already invaded and 
undermined on every side, and will certainly be supplanted ere 
long by the literary language of Paris. In Spain, the Catalan, 
the Valencian, the Gallician, and the Euscara, or Bascuence, are 
gradually fading before the growing influence of the Castilian 
tongue. In Germany, Luther's translation of the Bible has 
generalised the High Dutch dialect, and every generation sees the 
decay of the multitudinous idioms which have their hold among the 
least instructed of the Teutonic races. The all but total extinction 
of the Dutch language in the State of New York, the progress of 
the English tongue in Canada, in Florida, and Louisiana, are re- 
markable evidence, most visible to our own senses, of the sub- 
jugation of the idioms of minorities to those of greater numbers. 
The Arabic language — the instrument of Mussulman influence — 
has not only greatly modified, it has in many cases wholly super- 
seded, other languages ; and, with the Arabic language, Arabic- 
numerals, and a system of decimal notation, have been very widely 
spread. The Malays, more adventurous and active than most of 
the tribes of the Indian Archipelago, have made their language 
the instrument of intercourse through the vast tropical regions 
with which they have had intercourse. No man can estimate how 
many languages have been utterly extirpated by the conquests of 
the Spanish and Portuguese races in the southern countries of 
America, and by the Anglo-Saxon conquerors in those of the north. 
The more barbarous the country — the less the communications 
between the people — the greater will be the variety of languages 
spoken. We have no accurate knowledge of the multitudinous 



IN NUMBERS, COINS, AND ACC0UNT8. 137 

idioms used in the various regions of Australia ; but we know 
that every separate tribe had an idiom of its own. In the same 
district of Paraguay, in South America, no less than thirty lan- 
guages were spoken. On the coast of California, in an extent of 
500 miles, seventeen varied tongues were used.* We possess a 
catalogue of more than 150 other languages on that continent, 
and the list is very imperfect. 

In a small district tM the western coast of Africa, we have the 
numerals of thirty-one languages ; and, on the eastern coast, 
between Mozambique and Abyssinia, we have those of fifteen."}" 
It is not always easy to draw the lines of distinction between 
dialects and languages. Some would contend for placing Dutch 
and German, Danish and Swedish, Spanish and Portuguese, in the 
same category ; others would draw the lines of separation between 
English and Lowland Scotch, — between the idioms of Yorkshire, 
Devonshire, and Northumberland ; but it may be stated with 
tolerable certainty, that there are about 3,000 languages in the 
world so distinct and separate, that in no two of them could an 
ordinary conversation be carried on by persons who had not been 
accustomed to the use of both. 

I have ventured upon these observations of a somewhat general 
bearing, before tracing some of the peculiar characteristics 
languages as connected with their various modes of reckoning. 

We are told that there are tribes of Indians in Brazil who 
reckon by the joints of the finger, and whose numerals do not go 
beyond three. Beyond this, they always use a word signifying 
many.% Some of the African languages are also reported to be 
wholly deficient in the means of defining any high numbers, 
except by general terms. || In America, the tribe of the Purys 
has the three numerals — 1 omi, 2 curisi, and 3 prica, or many. 
There is a point of fine observation in Dickens' " Haunted 
Man," where he speaks of the poor savage boy — " The chemist 
laid a few shillings, one by one, in his extended hand ; to count 
them was beyond the boy's knowledge ; but he said ' One' every 
time, and avariciously looked at each as it was given, and at the 

* Dobritzhoffer's "Abipones," and Humboldt on New Spain; 
quoted by Dr. Peacock, p. 372. 

f Bowdich's " Ashantee," and Salt's " Abyssinia." Peacock, p. 372. 
X Spix and Martin's Travels, i. p. 387. 
|[ Lichtenstein, ii. p. 610. 



138 THE DECIMAL SYSTEM, 

donor." It is said that in the idiom of theBotucudos there are only 
two numerals, one meaning unity, mocenam ; the other, multitude, 
uruhu. No doubt the power of accurately estimating and cor- 
rectly expressing any considerable numbers, is one of the most 
striking evidences of civilisation ; and complications of words 
in the expression of small amounts must be deemed evidence of 
great intellectual inferiority. The Abipones say initara for 1, 
inoakd 2 ; but for three they use inoaka yik aimi, or two and 
more, that is, with an addition.* * 

Crantz, in speaking of the numeration of the Greenlanders, 
says it is so imperfect, that they have difficulty in getting beyond 
the number of their fingers, which they always employ in reckon- 
ing : 1 is called attausek, 2 arlaek, 3 pingajuah, 4 sissamat, 
and 5 tellimat. When they have reached this point, they begin 
by the fingers of the other hand, and call 6 arbennek ; but they 
then repeat for 7, 8, 9, and 10, the words employed before for 2, 3, 
4, and 5. They call 11 arkanget, and 16 arbarsanget, counting 
their toes as they count their fingers; and for 20 they say innuk, 
a man, meaning all the fingers and toes of a man. For 100, 
some go so far as to say 5 men ; but generally numbers above 20 
are held to b*e uncountable. In the same way, the inhabitants of 
Nootka Sound repeat the same words when they reckon above 5. 
The example of the Abipones is a fair picture of what takes place 
among almost all uncivilised nations, and such as I have often 
witnessed in my intercourse with them. Ask an Abipone " How 
many ?" and if the number be small, he will raise as many fingers 
as denote the number, and only exclaim " Leyer iri — Look !" 
but if the number be five, he will say " Hanamegen !" the fingers 
of one hand ; if 10, " Lanamrehegem," the fingers of both hands ; 
if 20, " Lanamirhegem cat gracherhaka anamichirihegem," the 
fingers and toes of both hands and feet. But between the 5, the 
10, and the 20, he will probably attempt no definition. If the 
Abipones have to describe a number of horses, they will point 
out the space they would occupy standing side by side. When a 
quantity in question is very great, they will take up a handful of 
grass, or of sand, and shew it, as exhibiting an innumerable 
amount. But their notions of number are always vague and inac- 
curate ; and in reporting amounts, they are never to be trusted.f 

* Balbi's Ethnographical Atlas, Nos. 497 and 501. 
f Dobritzhoffer, ii., p. 202-3. 



IN NUMBERS, COINS, AND ACCOUNTS. 139 

Sometimes, when the number exceeds three, an Abipone will 
lift up his finger and shout " Pop !" many ; or " Chic legyekalipi," 
cannot count them; and where only ten soldiers were drawn 
out in a line, the crowds shouted " Voaliripi," very many men ; 
" Latenk naueretape !" multitudes are come. In translating the 
ten commandments, the missionaries found it necessary to use 
after the word first, or foremost — and yet another — and yet an- 
other; for the tenth they employed the terms, latest or hind- 
most.* Even the Chinese, who are very precise in matters of 
accounts, employ very loose terms in general conversation: they 
say " several tens," " several hundreds," " several thousands :" 
they neither have themselves, nor do they convey to others, any 
clear notions of number or quantity. 

Another American tribe, the Guaranos, are unable to proceed 
beyond the number 4 : they have for 1 petey, 2 mokoy, 3 inbohassi, 
4 irundy; but they reach the number 8 by repetition — mokoy-mokoy, 
being another form for 4 ; inbohassihassi, 3 and 3 = 6; irundy- 
rundy, 4 and 4 = 8. Beyond this they call numbers ndipapahabi, 
meaning " not to be counted." The missionaries, however, tried 
to introduce the Spanish numerals up to 1000. They report, that 
the Guaranos learnt music, drawing, and painting ; but that, after 
all the trouble taken in teaching them figures, nobody could trust 
a Guarano in his report as to numbers, his ideas being always 
vague and confused, f They used, according to some authorities, 
inbo or po-petei, one hand for 5 ; po-mokoy, two hands for 10 ; inbo- 
mbiabu, hand-foot, for 20. j 

Among the aboriginal Brazilians there existed the same in- 
firmity as to calculation. Their dialect stopped at three : 1 was 
ojepe, 2 mocoi, 3 mogapyr, which have a remarkable resemblance 
to the Guarano dialect. They also called five umbo, the word 
for hand. The Portuguese priests assisted them with Portuguese 
words, and introduced decimal divisions. They learnt to employ 
dez for 10, ojepe papaqaba, meaning "one enumeration or count- 
ing," for 100 ; dez papaqaba, 10 countings, = 1000. For 5 they 
were in the habit of lifting up their hands and saying " Ojepe 
xe po," like my hand; for 10, "Xe po," my hands, lifting both 
hands ; for 20, " Xe po, xe pi," my hands, my feet. For 13 they 

* Dobritzhoffer, p. 204. f Balbi, p. 490. 

t Hervas' Arith., p. 16. 



140 THE DECIMAL SYSTEM, 

say " Xe po, mocapir cembyra," literally, my hands and three 
more. 

The description of the manner of reckoning among the Tara- 
humara Indians (Quadalajara), resembles much that which has been 
just described. " When they reckon, the Tarahumaras are careless 
about words, but employ their fingers, toes, and joints of their 
fingers, to designate numbers. For 10 they exclaim " Macoek," 
and exhibit their two hands with the fingers separated ; for 20 
they strike their ten fingers against their two feet ; for 4 they 
show the three joints of the forefinger, and one joint of the 
second finger; for 12 they bend in the thumb; — and thus the 
joints of the four fingers exhibit the desired number." They 
sometimes employ grains of maize, small stones, or cut notches 
in sticks, and they have the following words for their numerals : — 1 
pile, 2 oca, 3 brica, 4 naguoca (a repetition of 2), 5 mariki, 6 
pusaniki, 7 kichao, 8 ossanaguoc (2 fours), 9 kimacoe (1 from 10), 
10 macoe, — and are said to possess a decimal progression, though 
seldom used in conversation.* 

" The people on the Orinoco," says Gilj,f " have numerals, but 
avoid using them. If they wish to convey an idea of great num- 
bers—as, for example, ' I saw multitudes of turtles,' or a ' great 
many armed Caribs,' — they pull about the hairs of their head, and 
put on a look of stupefaction." On the . Maranbam river, La 
Condamine says, " The arithmetic of the Jamei does not go beyond 
the number three ; and however incredible it may appear, other 
South American natives exhibit the same incompetency, and have 
only learnt higher numerals, with European words, from the 
Catholic missionaries." The intricate combinations for conveying 
ideas even of simple units, as exhibited in the Orinocan dialects, 
easily explain their unwillingness to use such lengthened and 
elaborate terms: — 1 is tevinitpe; 2, ac-ciache; 3, ac-ciluove ; 4, 
ac-ciachemnene or ac-ciachere-pene, 'two-twos;' 5, amgnaitone, 
which means a full hand ; 6, itacono amgna-pond tevinitpe, or ' one 
from the other hand;' and so on up to 9. For 10, amgnd aceponare, 
that is, ' both hands.' For 1 1 they stretch out both hands, and 
point to one toe, saying, puitta-pona tevinitpe, which is, ' one from 
the foot;' 16 is itacono puitta pona teventpe, 'one from the other 
foot ;' 20, tevin itoto, ' one man,' meaning ten fingers and ten toes ; 

* P. M. Stetfel, as quoted by Murr, i., p. 369. lb. 349. 
t Chap, xxvii. book ii. p. 332. 



IN NUMBERS, COINS, AND ACCOUNTS. 141 

21, itacono iioto jamgnar-bonct tevinitpe, * one taken from another, 
man ;' 40, acciache itato, 4 two men ;' 100 being 4 five men.' " * 

The Manipuri Indian numerals are — 1, papeta ; 2, avanume ; 3, 
apechivd ; 4, apechipachi (i.e., 3 and 1) ; 5, papeta capiti (i. e., one 
hand) ; 6, papeta jand, paaria capiti purena, ' take one from the 
other hand ;' 10, apa numerri capiti, ' two hands.' But this nation 
does not employ the same numerals for different objects. They 
sometimes modify the noun : — 1 day is mapuchia pecumi ; 2 days 
apucunuine ; 3 days, apeche-pucu. The ex-missionary G. M. 
Forueri says of the Jaruris — " They have only five numerals — 1, 
caneanie ; 2, gnoeni ; 3, tarani ; 4, chevveni ; 5, cani-iccimo, which 
last, as it signifies a hand, can scarcely be deemed a numeral ; for 6, 
7, &c, they say one, two, &c, from the other hand; for 10, 
jord-iccibo, ' all two hands ;' 15, a foot; 16, one from the other foot , 
20, a man ; and beyond 20, they make heaps of grain of 20 each,f 
but do not employ words." 

Lichtenstein speaks of the difficulty of obtaining from some 
of the African races any words for numbers, or other symbols 
than the exhibition of their fingers. From the Bechuanos, he 
reports, he could not learn the words for either 5 or 10. Van 
der Kemp, who lived long among some of the tribes, says he 
could never ascertain the word for 8. But it is worthy of 
remark, that though it is quite impossible to obtain from a Kaffir 
any expression which defines such numbers as 11, 12, and so on, 
they will take charge of a large flock of sheep or oxen, and, with 
absolute certainty, detect the loss of any one, — such is the 
power of habit. The arithmetical faculty being never called into 
action, remains inert and dormant, while that of observation or 
recollection being in daily exercise, is alert and active. Of the 
Botocudoes we are told that they have two numerals : they use 
moke-nam for one, hentiatd for two, urrehu for more or many ; 
to express other numbers, they apply to their fingers and their 
toes for aid.| 

Marks of decimal notation are found among nations and lan- 
guages the most rude and imperfect. The Huron tongue is so 
poor as to have no adjective, no abstract noun, no active verb : 
it can express no negation without an absolute change of the 
word ; and yet it possesses a numeral language sufficiently regular, 

* Gilj, passim. t Hist, de l'Orin. : iii., ch. xlviii. 

% Prince of Neuwied's Travels, ii. part viii. p. 41. 



142 THE DECIMAL SYSTEM, 

the name for 10 being assou — for 100, egyo tiwoissan — and for 
1000, assou attevoignavoy. Among the tribes of Upper Canada, the 
Indians of the Delaware, the ancient inhabitants of Virginia, and 
the neighbourhood of New York, and most of the tribes of Central 
North America, numeral systems equally complete are to be 
found.* 

A common mode among rude people, whose powers of language 
are feeble, is to adopt a quinary system, making the number five 
the starting point for the higher digits. There are, howevef, cases 
in which 5 -f- 1 being used for 6, and 6 + 1 for 7, new words or new 
combinations are found for the numbers 8 and 9. In the Ende 
language, 5 is lima ; 6, limasa, or 5 -}- 1 ; 7, limazua, 5 + 2 ; 
8, ruabutu, 2x4; 9, trasa ; 10, sabulu. The forms by which the 
numbers above five are expressed, are various and capricious. 
Among the inhabitants of New Caledonia, every numeral from 
1 to 10 begins with the syllable pa ; but 6 pdnimgha, 7 pdnim-roo, 
8 pdnim-ghin, and 9 pdnim-bai, are made by adding 1, 2, 3, and 
4, to 5, and 10 is parooneek, or 2 X 5. In the Tanna, the word 
five is dropped, and 6, 7, 8, and 9, are represented by ma-riddee 
more one ; mfl-carroo, more two ; ma-kakdr, more three ; and ma- 
kafd, more four ; while ten is expressed by karirrom-harirrom, 
meaning five, five. The Koriaks of Kamtschatka, and several of 
the tribes of Eastern Asia, make the numerals from 6 to 9 by 
combinations of five with the lower figures from 1 to 4, but they 
have almost all an independent word for 10 ; and there are many 
examples where the words for 8 and 9 are complicated, those for 
10 are simple. Among the Greenlanders, the same words are used 
for 2 and 7 — arlaek, 3 and 8 — pingajuah, 4 and 9 — sissamat, and 5 
and 10 — tellimat, the sole distinction being, that when the lower 
numbers are meant, the left hand is raised, and when the 
higher, the right hand.f The same words are employed for 12 
and 17 as for 2 and 7— for 13 and 18 as for 3 and 8— for 14 and 19 
as for 4 and 9 ; but in order to distinguish this, they point first 
to the toes of the left, and then of the right foot. There is a 
variation between the numbers — 1 attausek, 6 arbennek, 11 
arkangit, and 16 arbasangik, each serving to show the begin- 
ning of a new series of fives. For 20, the word innuk, or man 
(ten toes and ten fingers), is used ; for 40, innuk arlaek, men two ; 

* Peacock, p. 379. 

f Peacock, p. 386. Crantz's Greenland, vol. i., p. 208. 



IN NUMBERS, COINS, AND ACCOUNTS. 143 

but beyond twenty they hesitate in using any other term than 
words implying that the number is not to be counted. Humboldt 
gives similar examples among the South American races.* 

The Esquimaux are less advanced than the Greenlanders. 
They use the fingers of the left hand with facility for reckoning 
up to five, but in employing the right hand, they generally make 
some mistake before they reach seven, and beyond nine they hold 
up both hands. If 15 or 20 are required, they point to the hand 
or hands of another person, but do not refer to their own feet. 
When they are perplexed with any number beyond 10, they gene- 
rally say oonooktoot, which means something undefined. 

There are many native tribes, not only on the American conti- 
nent, but descended from the ancient inhabitants of the West 
Indian islands, whose numerals only extend to 4, and who use 
their fingers alone — having no words in their language to express 
higher amounts. One of the races of Paraguay calls 4 geyenk 
uate, meaning the foot of the emu, which has four claws ; and 
5 necuhalek, which is the name of a skin remarkable for having 
five distinct colours. The poverty of language is often remark- 
ably exhibited in the want of special words for numerals. In the 
Caribbean, where the words for fingers and toes mean " the 
children of the hands and of the feet," the phrase for 10 is clwn 
oucabo raim, or " all the children of the hands." The Achaguas 
on the Orinoco, call 5 abacaje, " the fingers of one hand ;" 10, tucha 
macaje, " all the fingers ;" 20, abacaytacay, " all the fingers and 
toes ;" 40, incha matacacay, " two men's fingers and toes." The 
Zamucoes call 5 " the hand finished ;" 6, " one of the other hand ;" 
10, " the two hands finished;" 11, " foot one ;" 20, " feet finished."t 
Many of the natives of Australia have only the three first 
numerals, and either raise their hands to express a greater 
number than three, or use a phrase meaning multitude. Among 
the ancients, it was a joke against a stupid fellow that it took him 
infinite pains to reckon up to five; and in the well-known 
passage of Aristotle, before referred to,t in which, after saying 
that almost all nations, barbarous and civilised, used the decimal 

* Vues des Cordilleres, p. 253. Peacock, p. 586. 

f Vues des Cordilleres, p. 253. Peacock, 390. 

J Movoi ds apiB/iovai rdiv Qpaicuiv y'svog ri elg TtTTapa, did to, uxrirep 
ra TraiSia, firj dvvavSai \ivi\[ioviVEiv iirnzokv, \ir\§i xpriaiv firjdivbg 
elvai ttoXXov avrolg. 



144 THE DECIMAL SYSTEM, 

notation, he excepts a tribe of Thrace, declaring they could not 
count beyond 4. 

Though words, as instruments of counting the high numbers, are 
often wanting among rude nations, a decenary or decimal system 
is often adopted when other auxiliaries than words are employed. 
The Guaranoes calculate by heaps of maize of twenty grains each, 
and mingle 2, 3, 4, or more heaps, when they mean to denote 40, 
60, 80, and so forth, — the excess of the scores being expressed by 
the usual numbers. In Sumatra, the natives make a knot* on a 
string to represent 100,— and we are told, that, in reckoning money, 
every tenth, and sometimes every hundredth piece is set aside. In 
reporting numbers of men or of horses, the Abipones marked out 
the space which they supposed the numbers would stand upon. 
Humboldt says he never met with a native Indian who, if asked 
his age, would not answer indifferently 16 or 60, — not always 
from the want of numerals, but from the very indistinct associa- 
tions of numbers with words. Thus, as Dr. Peacock remarks, we 
have generally great reason to distrust the authority which gives 
to particular words a definite numeral interpretation, especially 
in the higher figures. * 

The works of Humboldt throw much light upon several of 
the languages, both modern and ancient, of the central parts of the 
continent of America. The Aztecs, or ancient Mexicans, appear 
to have possessed the most complete system of vicenary numerals 
both in words and signs. Up to 20 the numbers were represented 
by dots. A small flag represented 20, which, if divided by two cross 
lines and half coloured, represented half twenty, or 10 ; and, if three 
quarters coloured, 15. The square of 20 (400) was represented 
by a feather, because grains of gold enclosed in a quill were used 
as money, — or a sign for purposes of exchange. A figure of a sack 
indicated the cube of 20 (8,000), and bore the name of xiquipilli, 
which was given to a kind of purse that contained 8,000 grains 
of cocoa. These symbols were repeated twice, thrice, and to denote 
multiples by 2, 3, and grouped together, — both the common sym- 
bols to denote any compound number. The first nine digits 
were — 

12545 6 7 8 9 

ce ome jei nahui macuilli chicuace chicome cliicuei chiculmnhui 
6+1 5+2 5+3 5+4 



* Marsden's Sumatra, p. 192. Peacock, pp. 390, 391. 



IN NUMBERS, COINS, AND ACCOUNTS. 145 

In which a new quinary modification will be seen in the use of 
the prefix chi. The third form from 10 upwards — 

10 11 12 13 

matlactli matlactli oz ce matlactli omotne matlactli oz jei 
10+1 10+2 10+3 

At 20 a new form of notation began. 

20 30 100 

pohualli cem pohualli oz matlactli macuilli-pohualli 
or one 20+10 5x20* 

cem-pohualli. 

The fingers being universally used as calculating instruments, 
decimal notation was the result. When ten had been counted, 
it was necessary to begin the reckoning anew, in order to employ 
them for higher numbers. There are few languages in the 
world in which a word is not to be found for ten, but there are 
many languages in which words for all the units between one and 
ten are not to be discovered. I remember, when I was at Kandy, 
the capital of Ceylon, I met with a Yeddah — one of the abori- 
ginal race of that island, who represent the lowest stage of 
human civilisation. They build themselves no houses, but live 
like beasts in caves, or monkeys among the trees of forests seldom 
or never explored by cultivated man. They do not dress their food, 
nor cover any part of their bodies with garments. The man I 
conversed with had been convicted of murder ; but as it was found 
utterly impossible to associate with his answer any idea of guilt 
or responsibility, the judge very properly objected to subject him 
to the rigour of the law, and, instead of being executed, he was 
condemned to perpetual imprisonment. He was not able to 
reckon up to Jive, — but the word for hands was associated with the 
ten fingers upon the hands, though for any number between 4 and 
9 he had no word in his language."]" 



* Vues des Cordilleres, pp. 241 and 251. Peacock 388. 

t Sir J. Emerson Tennent, whose diligent inquiries into all sub- 
jects connected with Ceylon give much value to his communication, 
informs me that — 

" The Veddahs are a race of harmless savages, who inhabit the 
forests in one of the eastern districts of Ceylon, between the moun- 
tains of Ouva and the sea. Their origin and history are unknown ; 
but they are probably a remnant of tHe aborigines driven into their 

K 



146 THE DECIMAL SYSTEM, 

Among some of the American Indians there are distinct words 
for the ten digits — then compound words from eleven to twenty ; 

wilds many centuries ago by the Malabar invaders of the island, and, 
from some unaccountable cause, they have never returned to civilised 
life. They live by hunting, and are expert in the use of the bow. 
They lodge in caves, under the shelter of over-hanging rocks, and fre- 
quently sleep in the trees out of the reach of the bears and other wild 
animals. Fruits, roots, and grain they consume when they ca$ pro- 
cure them ; but they subsist chiefly on birds, fish, honey, and the 
products of the chase. They dry deer's flesh and carry it for barter 
to the confines of the inhabited country, whither some of the travelling 
Moors resort with clothes, axes, and arrow-heads, to be exchanged 
for dried meat, ivory, and bees-wax. In these transactions the wild 
Veddahs are rarely seen by the strangers ; in the night they deposit 
what tbey bave to offer in barter, and intimate, by established signals, 
the description of articles which they require in exchange, and which, 
being left the following evening at the appointed place, are carried 
away before sunrise. 

" Their language contains some words so similar to the more ancient 
Singhalese, that the civilised natives are enabled to communicate with 
them, though With difficulty; but Mr. Mercer, who held for some years 
an official appointment in the vicinity of their forests, told me that not 
only is the language of the Veddahs almost unintelligible to the Singha- 
lese generally, but so imperfect in itself, that much of their communi- 
cation with each other is conveyed by signs, grimaces, and guttural 
sounds, which bear scarcely a resemblance to articulate words. 

" This race are unable to count beyond the first few numerals. A 
Veddah who had been found guilty of murder, is now undergoing a 
long imprisonment in the gaol at Colombo, where he learned to 
count his own fingers ; but he has never been able to advance fur- 
ther, and seems bewildered by the unaccustomed idea of any numbers 
beyond. 

" Mr. Atherton, the Government agent at Batticaloa, was employed 
by the Government to induce these untamed creatures to become 
located in villages, and betake themselves to cultivating the ground ; 
and he has to a great extent succeeded in several instances. He 
verified to me the statement of their incapacity to comprehend the 
smallest combination of numbers ; and I remember, in illustration of 
this, that he mentioned to me an instance in which he had given 
twelve arrows to a Veddah to be divided between himself and two 
others ; but so helpless was he that, after spreading them out on the 
ground, he failed in every attempt to reduce them to three equal 
portions." 



IN NUMBERS, COINS, AND ACCOUNTS. 147 

a new series begins at 400, and another at 8,000. In Yucatan * the 
numerals are — l,hun; 2, ca; 3, ox; 4, can; 5, ho; 6, nac; 7, uuc; 
8, uaxac; 9, bolou ; 10, lahun; 20, te AaJ; 400, hun bak; 8,000, 
fam jm'c; 100 is expressed by five times twenty, ho-kal; 1,000 by 
twice four hundred, plus ten times twenty, or by 200 from 1,200, 
lahu-y-ox-bak. The Mexican hieroglyphics are in accordance 
with the numeration of the spoken language. They have dis- 
tinct characters for the numerals 1, 20, 400, and 8,000, and these 
are sufficient to express any number. The unit is represented by 
a small circle, 20 by a standard shaped as a parallelogram, 400 by 
a feather, and 8,000 by a purse supposed to contain so many 
grains of cocoa. Although the number of units from 1 to 19 is 



[ I 



generally represented by so many small circles, yet in the same 
manner as they had uncompounded names for the numerals 5, 10, 
and 15, they had also an abbreviated and direct way of represent- 
ing their numerals. This consisted in dividing the parallelogram 
or hieroglyphic for twenty, into four squares, which, according as 
they were coloured, represented either 5, 10, or 15. It seems 
also that they occasionally represented the numeral 200 by half a 
feather. The year 1854 would be thus expressed: — 

The mode of counting by 20, 400, and 8,000, had a practical 
influence. Bernal Diaz, when speaking of the Indian armies, 
counts them by so many xiquipillis, or bodies of 8,000 men. It is 
not improbable that they were divided into battalions of 400 men 
each— these again subdivided into squads of 20 men— and that the 
hieroglyphic of 20 represented originally the banner or standard of 
each such squad. A load (cargo) of dresses, cloaks, &c, consisted 
of twenty such articles.f 

The decimal and vigesimal divisions are found in many 
and completely distinct languages, as points round which 
varieties of expression are grouped to convey the ideas of num- 

* Gallatin, cited in Pott, Zahlmethode, &c, p. 93. 
f Gallatin. 

x 2 



148 THE DECIMAL SYSTEM, 

bers adjacent to those divisions. In Anglo-Saxon, when the 
numerals reach towards 100, its adjacency is pointed out, and 
hund seofortig is 70, hund eahtatig is 80, hund nigontig 90. Tyn 
(10) is from the verb tynan, to inclose, meaning the number that 
can be inclosed by the fingers. " Forty stripes less one" is the 
biblical form for 39. In the Malay, sambilan, meaning "one taken" 
(from ten), signifies 9, while 99 is expressed by kovang asa sa- 
rdtus, " wanting one of a hundred." In Danish, 30 and 40, Iredive 
and fywetive, are 3 and 4 times 10. Twenty is the frequent mdex 
to greater amounts, as 60 and 80 ; tre sinds tyve, fir sinds tyve, 3 
times 20, and 4 times 20 ; while 50, 70, and 90, halv tre sinds 
tyve, halv fier sinds tyve, halv fern sinds tyve, mean half the 
third, fourth, and fifth 20. So in Icelandic, halft fiorda hun- 
drada, half four hundred, means 350 ; halft fertngr, half the 
fourth ten, 35; halft sextogr, half six ten, is 55. The form of 
stopping an expression midway, as it were, existed among the 
Greeks,* as it does among the Germans, Scandinavians, and even 
among the Scotch, who frequently, instead of saying it is half- 
past 9, or half-past 10 o'clock, say it is half 10, or half 11. 
The Laplanders, whose numerals do not go beyond 100, say for 
11, auft nubhe lokkai, 1 to the second 10; for 23, golm goaalmad 
lokkai, 3 to the third 10, and so forth. The Finlanders, for 14, 
use words signifying "the 4 in the second 10." f 

In the long series of English numerals, there is only one break 
in the simple process of decimal notation, and that is, in the num- 
bers eleven and twelve. The first nine units have distinct and 
separate words — then comes the decimal ten, which, with the 
units, the sole exception being that of eleven and twelve, the 
meaning of which is leave one and leave two (with 10), or rather, 
one leave or two leave, from the Gothic ainlif and tvolif \ go up to 
one hundred, thence to thousands, millions, billions, and so on- 
wards by multiplications, which even go beyond the powers of 

* *2/3d<yiov i\\iiTaKavTov— seventh half-talent = 6£ talents. 

t The irregular formation of these numerals may be traced through 
the different Gothic dialects. For eleven the ancient German had in 
the genitive einlif, and in the dative einlivein; the old Saxon had eleven ; 
the Anglo-Saxon endlufan; the Swedish has ellofva ; the Danish 
elleve; the German eilf or elf; — the Gothic word for twelve was thus 
declined — tvalif nom., tvalibi gen., tvalibim dat. ; Anglo-Saxon tvelf 
dat. tvelf um. Swedish, tolf; Danish, tolv ; German, zwalf 

t Peacock, p. 381. 



IN NUMBERS, COINS, AND ACCOUNTS. 149 

record and of conception. The vigesimal form is sometimes used, 
and maintains its hold possibly, more than for any other reason, 
from its having been adopted in the English translation of the 
Scriptures, and especially as occurring in some of the most fre- 
quently quoted texts of the Bible — as, for example, " The days 
of our years are three-score years and ten ; and if by reason of 
strength they be fourscore years, yet is their strength labour and 
sorrow."* 

Like the Latin, many languages preserve the genders in the 
first two or three digits. The Lithuanian and the Lettish have 
the masculine and feminine forms up to the number 9, but with 
several breaks. In the Lettish, all the units except three, 
represent the masculine and feminine genders. 

In the ancient Gothic, several of the numerals have genders, 
and some of them are declinable : — 

1 mas. dins ; fem. dina ; neut. din, dinata. 

2 „ tvdi ; „ tvos ; „ tva. 

3 „ threis; „ thrijos; „ thrija. 

4 no. ac. fidvor; dat. fdvorim. 

5 fimf. 

6 saihs. 

7 sibun* 

8 ahtdu. 

9 no. ac. niun ; gen. rdune. 

10 taihun. 

11 dinlif. 

12 no. ac. tvalif; dat. tvalibim ; gen. tvalibi. 

14 fidvortaihun. 

15 no. ac. fimftaihun ; dat. fimftaihunim. 

20 tvdi-tigjus (two decades) j dat. tvdim-tigum. 
30 thrins-tiguns. 
100 taihun — taihund (10x10). 
1,000 thusundi. 
10,000 taihun thusundjos. 

On the declension of numerals, Grimm says :— " The number 
one in all idioms of Gothic origin is regularly declined as an 
adjective of the first declension: — 

Gothic — dins, aina, dinata {din). 
Old German — einer, elnu, einaz. 

* Psalm xc, 10. 



150 THE DECIMAL SYSTEM, 

Old Saxon — en, en, hi. 

Anglo Saxon — an, an, an. 

Old Frisian — en, en, en. 

Old Norse — elnn, eln, eitt ; gen. eins, einnar, etns. 

Middle High German — einer, einiu, einez. 

Middle Dutch — en, en, 3n. 

Middle English— awe, dne, tine. 

Modern German — einer, eine, eines. 

Modern English — one. 

Swedish — en, en, Ht. 

Danish — hi, in, it* 

For two : — 

Gothic — n. d. a. ivdi tvos, tva; tvdim, tvdim, tvdim ; 
tvans, tvos, tva, in the adjectival form. In John viii. 17, 
tvaddji occurs in the genitive form ; and in Luke ix. 3, 
tveihnos, for tvos, in the accusative feminine. 

The Anglo-Saxon had tvegn mas., and tvd fem. and neuter. 
The numeral was also declined, gen. tviga and tvegra, dat. tvdm ; 
tvig is also found in the accusative. In the German anciently, 
zwene or zween, zwo and zwei. We had formerly in English, as 
will be found 'in the common version, twain as well as two. The 
Germans, like ourselves, now only employ one form, zwei, the 
neuter ; but the masculine, feminine, and neuter will be found in 
Luther's Bible, zween Ebraische manner, Exod. ii. 13 — lt zwo werden 
mahlen auf der Miihle," Matt. xxiv. 31, where the adjunct women 
is not even introduced. (See also Matt, xviii. 8, 9, &c.) The 
Gothic, Anglo-Saxon, and ancient German, had inflections to 3, and 
several of the lower numerals; but in all the modern descen- 
dants of the Gothic root, whether in the Teutonic or Scandina- 
vian branches, no inflection is now retained, except in the nume- 
rals 1 and 2, and in the two in the Swedish language alone ; — so 
much has simplicity of expression progressed with civilisation. 

The old northern word her, or army, is used for 100 ; enflocke, 
a flock, means 4 persons; folk (a crowd of), people, is a word 
for 40. Morgen (morning), a common measure for land in 
German country, meant the quantity that could be ploughed 
before mid-day. 

The Welsh language has some peculiarities. From 11 to 15, 
the numerals proceed regularly: — 11, unarddeg, 1 -f- 10; 12, 

* Deutsche Grammatik, p. 760. 



IN NUMBERS, COINS, AND ACCOUNTS. 



151 



deuarddeg,2 + 10; 13, triarddeg, 3 + 10; 14, pedwarddeg, 4+10; 
15, pymtheg ; but from 16 to 19, the elements are 15 and an added 
unit; 16 is unarbymtheg, 15 + 1 ; 17, dauarbymtheg, 2 + 15 ; 18, 
triarbymtheg, 3 -j- 15 ; 19, pedwararbymtheg, 4 -f 15. From 20 up- 
wards we count to every succeeding score, instead of by tens — that 
is, we express the same numerals as to the first 20, adding after each 
the words ar ugain, or " over twenty," as unarbymtheg ar ugain, 
1 + 15 + 20 for 36.* It is remarkable that the Welsh numerals 
were decimally carried into very large amounts — 100, cant; 1,000, 
mil; 10,000, myrdd; 100,000, rhiallu; 1,000,000, myrddiwn. The 
Bas Breton has some characteristic peculiarities in the formation 
of words expressing numerals: — 18 is tri-ouech, =3x6; 50, 
hunter Jtant, or half a hundred. Like the French, they count by 
twenties up to 80, and so from 80 to 100, using for 70, dek ha tri 
ugent (= 10 + 3 X 20) ; for 71, 11 + 3 X 22 ; for 80, 4 X 20; 
for 90, 10 + 4 x 20. In Erse and Gaelic, 31 is 11 over 20. 
Both languages preserve the vigesimal form : thus 40 = 2 x 20 ; 
50 = 10 4- 2 X 20 ; 60 = 3 X 20; 70 = 3 x 20 + 10. 

The numerals of the various Celtic dialects have all a decimal 
character, but resemble the Phoenician and some other oriental 
tongues in proceeding by twenties as far as 100, and not beyond 
that amount. Thus in — 



Welsh. 


Erse. 


Gaelic. 


1 un 


aon 


aon. 


5 pump 


cuig 


coig 


10 deg 


deic 


deich 


11 unarzeg 


aondeag 


aondeug 1+10 


15 pymtheg 


cuig deag 


ciiig-deug 


5 + 10 


5+10 


5+10 


16 unarbymtheg 


seact-deag 


sia-deug 




6+10. 


6+10 


20 ugain 


fitce 


fichead. 


30 deg ar ugain 


deic ar fichead 


deich thar fichead 

10+20 
fcoig fichid) 


100 cant 


cead 


] or [-5x20 
( ciad. ) 
( mile ) 


1000 mil 


mile 


] or [-10X100 
( deichceud ) 



* Pughe's Welsh Grammar, p. 108. 



152 THE DECIMAL SYSTEM, 

The Welsh is characterised by making the number 15 a point 
of departure for 5 ; 16 begins a new numeration ; 17 is deu ar 
bymtheg, 2 over 15; 38 is tri ar pymtheg ar ugain, 3 over 15 
over 20. 59 pedwar ar pymtheg ar deugain^ 4 over 15 over 
2 twenties. 

It is by no means my intention to present anything like a 
general catalogue of the numerals known to be employed in the 
various languages of the world. Though the materials towards 
a complete collection are augmenting from year to year^there 
yet remain many millions of the human family with whose means 
of communication we are but little acquainted ; and the selec- 
tions I have made from the languages of Asia, Africa, America, 
and Polynesia, are rather intended to awaken than to satisfy 
curiosity, and to exhibit, in various shapes, their peculiarities — 
especially with reference to the decimal system, to which allusion 
has been so frequently made in the course of our inquiries. They 
will serve to show how universal are the same elements of thought, 
which find an infinitely varied expression in words. These 
general resemblances of mental operations, — these wonderful diffe- 
rences in forms of speech, — are alike marvellous and mysterious. 
Could the multitudinous human races employ only one language, 
how vast would seem the distance between them and the brute 
creation ! but, furnished by the common Creator with powers to 
communicate in ten thousand modes of speech, these plastic organs 
of utterance — so subservient to the necessities and the enjoy- 
ments of existence — seem to remove us farther and farther from 
the inferior animals. And yet philanthropy cannot but breathe 
the prayer, that the distinction of languages may be gradually 
obliterated, and man become everywhere intelligible to his fellow 
man. Such seems, indeed, the tendency of things. One written 
language (the Chinese) is understood by more than one -third of 
the inhabitants of the globe. One spoken language (our own) is 
making its way, on the wings of commercial enterprise, from one 
region to another, and is becoming more and more the instrument 
of mercantile communication. Hundreds of idioms are dying 
away, absorbed in the influence of tongues, which are the principal 
depositories of the literature, the sciences, the progress, of an 
inquiring and advancing age. In Europe, no literary record 
anterior to the Christian era represents the language of, or would 
be intelligible to, any portion of the European people. Languages 
seem to perish like the races which have disappeared on the ad- 



IN NUMBERS, COINS, AND ACCOUNTS. 



153 



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IN NUMBERS, COINS, AND ACCOUNTS. 



155 



vancing cycles of time, — but, like the vestiges of these races, are 
full of instruction to successive generations. 

The specimens, then, which follow of the numerals of various 
nations, have been selected from those presenting many points for 
comparison and contrast. It would be a vain attempt to trace 
the origin either of all the primitive roots, or the various modi- 
fications to which they have been subjected; but the text will 
present many curious materials for investigation and inquiry, the 
development of which would be inappropriate here. 

The Thibet numerals are frequently cited as presenting an ex- 
ample of the simplest structure, and exhibiting the nearest ap- 
proach to arithmetical notation by local value.* 



1 cheic 


11 chucheic 


10+1. 


21 gnea cheic. 


2 gnea 


12 chugnea 


10+2. 


22 gnea gnea. 


3 soom 


13 chusum 


10+3. 


23 gnea soom. 


4 zea 


14 chuzea 


10+4. 


24 gnea zea. 


5 gna 


15 chugna 


10+5. 


25 gnea gna. 


6 tru 


16 chutru 


10+6. 


26 gnea tru. 


7 toon 


17 chutoon 


10+7. 


27 gnea toon. 


8 ghe 


18 chughe 


10 + 8. 


28 gnea ghe. 


9 goo 


19 chugoo 


10+9. 


29 gnea goo. 


10 chutumbha 


20 gnea chutumbha 


2x10. 




The groups of the first ten numerals (or 


digits) on pages 15 


and 154, present many curious points 


of contrast and comparisoi 


Chinese Tartary. 


Corea. 




Formoza. 


1 yga 


1 ho-djiin, ho-tun 


1 tat saat 


2 lianga 


2 fu-pu 




2 rauha 


3 ssanga 


3 sai 




3 tauro 


4 Sigg89 


4 nai 




4 hpat 


5 ugse 


5 ta-shu 




5 rima or hand 


6 lugse 


6 ji-shu 




6 nnum 


7 szugae 


7 ji-kii 




7 pytto 


8 baya 


8 ji-ta 




8 kauyphpa 


9 dshugae 


9 ja-hao 




9 matauda 


10 shy 


10 je 




10 kytti 


11 shy-ygae 








12 shy-lianga 








20 ul-shy 


20 shu-nui 






30 sung-shy 


30 shi-hau 






40 sig-shy 


40 ma-jii 






60 ug-shy 


50 shim 






60 lug-shy 


60 ji-shun 







* Peacock, p. 373. See Turner's Embassy to Thibet, p. 321, 
Cf. Klaproth's Asia Polyglotta, p. 352. 



156 THE DECIMAL SYSTEM, 

Chinese Tartary. Corea. Formoza. 

70 tzy-shy 70 ji-tuon 

80 bay-shy 80 ji-tun 

90 dschi-shy 90 ja-shiin 

100 ibai 100 jun 100 kautaughau 

1000 iwuan* 1000 zian (chinese) 1000 katanuaun t 

10000 wan (ditto) 

Some of the Caucasian numerals are very complicated. The 

Taguarish for 20 is caedz ; for 90, daec aemae tzuppaerucaedzuj 

(10-|-80); for \00, fondzucaedzy : for 1000, daec fondzucaedzy, 

10X100. The Circassian numerals are simple, and monosyllabic 

up" to 10— se 1, tu 2, she 3, ptle 4, chu 5, chi 6, ble 7, ga 8, bgu 9, 

pshe 10, sheh 100, min 1000. 

The Ostiak numerals present curious combinations : — 

1 chusem. 

2 ynem. 

3 dogom. 

4 syjem. 

5 chajem. 

6 ahjem, or chajem-chiisem — 5 and 1. 

7 ohnem, or chajem-ynem — 5 and 2. 

8 chajem-dogom, 5 and 3, or ynem boche chojem — 2 from 10. 

9 chajem-sysem, 5 and 4, or chusem boche chojem — 1 from 10. 

10 chojum. 

11 chusem chojum — 1 and 10. 

18 ynem boche agem — 2 from 20. 

20 agem. 

30 domga-sha. 

40 soluk-sha. 

41 soluk-sha an chogda. 
50 cholepky-sha. 

60 aha-chojum — 6 tens. 
70 ohna-chojum — 7 tens. 

80 ynem boche chojem chojum — 2 from 10 times 10. 
90 chusem boche chojem chojum — 1 from 10 times 10. 
100 kyshash, or ky. 
1000 chojem kyshash— 10 times 100.$ 
Of the Oedh-Ostiaks (Sable- Ostiaks), who are also called 
Denka, Klaproth, repeating Messerschnudts,§ says that many of 

* The roots of all these words are Chinese. 

f Asia Polyglotta, pp. 340, 380. 

J Asia Polyglotta, p. 171. 

§ Messerschnudt's "Tagebuch," 9th July, 1723. 



IN NUMBERS, COINS, AND ACCOUNTS. 157 

them could only reckon up to five, and that on reaching that 
number they began with one till they again reached five. 

The different tribes of the Jenisei have the following 
numerals : — 



i! 

H J I sis iiJll fi 

f.<J 1 ,S ! ill III II 1 1 

Sllill 1 u i III ililii s i 



j<3'. 



Ii 



«ifiiiiii i ii i in -Usui 1 1 



Ill » » I Jl llllllil 



! H3 i $i t all IK 



SCSI'S 



iJl'lllil I -if I IP llll!l J ri 




158 



THE DECIMAL SYSTEM, 





EASTERN RUSSIA. 


Kamtschatka. 


Tarakai. 


Jeso. 


1 syhnap 


shnepf 


sonezb, zinezf 


2 dupk 


tup 


zuzb, zuzf 


3 raph 


repf 


rezb, rezp 


4 yhnap 


inipf 


inezb, ynezf 


5 ahsik 


asheki, ashikinipf asaraneeof, assikine 


6 chguaehu 


juwambi 


juiwanbe, ywam 


7 aruaehu 


aruwauibi 


aruambe, aruwani 


8 duhpyhs 


tubishambi 


zujemambe, zubsam 


9 syhnahpyhs 


shnebishambi 


sinesambe, sinobsam 


10 upyhs 


wambi 


fambe, wambe* 


Motorish. 




Koibalish. 


1 om 




unera 


2 kydy 




syda 


3 nagor 




nagor 


4 deite 




tade 


5 shumblia 


sumula 


6 muktun 


muktuk 


7 kiibe 




s'eigbe 


8 knydeite 


syetade 


9 togos 




togos 


10 tchiun 




bet 


11 tchiun 


'op 


bedop 


12 tchiun- 


gide 


besyda 


15 tchium sumblia 


betmuktut 


20 kydy tchiun 


sydybet 


30 nagor- 


tchiun 


nagorba 


50 shumblia-tchiun 


ilich 


100 tchius 




dsoonf 




TUNGUS NUMERALS. 




1 mukonn. 






2 djuhr. 






3 ilann. 






4 degenn. 






5 t » ma. 






6 nunun. 






7 naddan. 






8 djapkull. 






9 ijogjin. 




* Asia Polyglotta, pp. 314-15. 


f Ibid., p. 159. 



IN NUMBERS, COINS, AND ACCOUNTS. 



159 



10 djann. 

11 mukonn-dje — one ten. 

12 djuhr-dje — two ten. 
20 djuhr-jarr — two tens. 
30 ilann-jarr — three tens. 
40 degenn-jarr — four tens. 

100 nemadje. 
200 djur-nemadje. 
1000 djann-nemadge — ten hundred.* 

As in many of the African languages, so in the Kurile islands 
of Japan, and on the coast of Kamtschatka, numbers are formed 
by deduction from the decimal points.f 

Various are the inventions by which the decimal points are 
made subservient to the purposes of numerals. The Knisteneaux, 
in order to count up to 20, add to the first 9 digits a word signi- 
fying "with," as peyac 1, peyac osap 11 ; for 21 they say, nishew 
mitenah peyac osap, or 2x10+1. So the Malays add bias, and 
the Javanese tolas, meaning complete, to the lowest numerals, in 
order to reach from 11 to 19. They have also several words with 
special meaning for some of the higher numbers, such as samas, one 
piece of gold meaning 400, — and dornas, two pieces of gold meaning 
800,]: — names originally associated, no doubt, with specific values. 



Send. 


Armenian. 


Georgian. 


Mingrclian. 


Suanian. 


1 ohn 


mi 


erti 


arti 


eshgu 


2 besh, bee 


jergu 


ori 


djin 


jern 


3 teshro, se 


jerjek 


sami 


sumi 


semi 


4 chetwere 


chors 


ot'chi 


ot'chi 


wortshtcho 


5 pianche 


hink 


chut'i 


chuti 


wochushi 


6 chshuesh 


wjez 


ekwsi 


apchshui 


usgwa 


7 hapti 


jeotu 


shwidi 


shgwit'i 


ishgurd 


8 ashte 


ut 


rwa 


ruo 


ara 


9 neo 


nen 


zchra 


chchoro 


chchara 


10 des 


dasn 


ati 


lirti 


jesht 


100 sete 




ase 


oshi 


asher § 




MONGOLIAN NUMERALS. 




Mongols beyond 


Chalcha 


Burietish. 


Olotish 


Olotish 


Walls of China. 


Mongols. 


Dsungaria. 


on the Volga. 


1 nige 


nege 


nege 


xege 


negen 


2 gojer 


chour 


koir 


chojur 


chojur 


3 churban 


gurba 


gurban 


gurba 


gurban 



* As. Pol., p. 286. 
t Peacock, p. 381. 



f Peacock, p. 380. 

§ As. Pol., pp. 74, 107, 122. 



160 



THE DECIMAL SYSTEM, 



Mongols beyond 
Walls of China. 

4 durban 

5 tabun 

6 dserchochan 

(dsirohn) 

7 dolochun 

(dolohn) 

8 naiman 

9 jisun, dsisun 
10 arban 

20 chosin 
30 chuchin 
40 duchin 
50 tabin 
60 dsiran 
70 dalan 
80 najan 
90 jar an 
100 dsachun 
(dsun) 
1000 nungcban 



Chalcha 
Mongols. 

durba 

tabu 

asurga 

dolo 

naima 

jusu 

arban 

chori 

quchi 

duchi 

tabi 

ddjava 

dala 

naje, naja 

jire 

dso 



Burietish. 
derbyn 
tabun 
ddj ergon 

dolon 

najaraan 

jihun 

arban 

koryn 

quchin 

duchin 

tabin 

ddj iron 

dalan 

najan 

jirin 

dson 



rainggamjangga minggan 



Olotish. 

Dsungaria. 

dorbo 

tabu 

surga 

dolo 

naima 

jesu 

arba 

chorin 

quchin 

duchin 

tabin 

ddjiva 

dalan 

naija 

jeren 

dzo 

minggan 



Olotish 
on the Volga, 
dorbon 
tabun 
surgan 

dolon 

naiman 

jesura 

arban 

chorm 

quchin 

dochin 

tabin 

ddjira 

dalan 

naijan 

jeren 

sulin 

minggan 



The following groups of numerals are employed in the various 
islands of the Indian Archipelago : — 



Kay an. 


Malayan. 


Javanese. 


Buges. 


1 ji 


sa 




sedi 


2 duo 


duwa 




duwa 


3 tulo 


talu 




tolu 


4 pat 


ampat 


pat 


opak 


5 lima 


lima 




lima 


6 anam 


anam 


nam 


bnong 


7 turyu 


tuju 




pitu 


8 saya 


dalapan 


wolu 


aruwa 


9 pitan 


sambilan 


sanga 


asera 


10 pulo 


puluh 


puluh 


sbpulo 


11 puloji 


sablas 


sawalas 


sopulo sedi 


20 




rongpuluh 




30 


talupuluh 






100 


ratus 




siratu 


1000 


C riwu ) 
( ribu ) 




sisobu 


10,000 


laksa 




silasa 


100,000 


katt 




saktti 



* As. Pol., p. 284. 



IN NUMBERS, COINS, AND ACCOUNTS. 



161 







20 duwa puluh 


kong piiluh 








30 


tiga puluh 


tahing puluh 








40 


ampat puluh 


pat puluh 








50 lima puluh 


limans puluh 




Kayan — Borneo 


60 


anam puluh 


nam puluh 


' 






70 tujuh puluh 


pitung puluh 








80 


dalopan puluh wolung puluh 






90 sambilan puluh sangang puluh 






, 100 ratus 


atus 




Kisa. Manatoto. Timuri. Eotti 


Sara. 


Ende. 


Mangavai. 


1 itaida 


nehi 


aida aisa 


aisa 


asa 


sa 


2 ror 


erua 


rua diia 


n'ua 


rua 


sua 


3 kal 


etalu 


tolo talu 


tanu 


talu 


talu 


4 ahka 


ch'aat 


haat haa 


hah 


wutu 


pa 


5 lima 


lema 


lema lema 


lema 


lema 


lema 


6 nain 


naen 


naen naen 


naen 


lema sa* 


1 ana 


7 iko 


beta 


hetu petu 


hetu , 


lema-rur 


if petu 


8 ah 


walu 


walu talu 


panu 


rua butuj alo 


9 hi 


sioh 


sioh sToh 


sioh 


turaasa 


sioh 


10 wali 


nulu 


rulu liulu 


bo 


buru,bulu puluh 


11 Ita-wali.ita 












1 ^ 10 + ] 






, 


, 




20 waroh 








bulu rua 


§ sua puluh | 


21 waroh. ita 












30 wali kal 












100 raho 


atus 


atus natun 


natun 


nasu 


ratuh 


1000 riun 




Tamati 




rewu 


RWU 


Tambora. Sambawa. 


(Temali). 


Serang. Tagala. 


Bisaya. 


1 seena 


satu 


rimoi 


takura 


isa 


isa, isara 


2 kalae 


diia 


remo diti 


dua 


dalava 


duha 


3 nih 


tiga 


raangi 


tolu 


tatlu 


tulu 


4 kude-in 


ampat 


rah a 


pat 


apat 


upat 


5 kukl-ih 


lima 


roma toha 


lira 


lima 


lima 


6 bata-in 


anam 


rava 


onan 


anim 


anum, unum 


7 kumba 


tuju 


tomdi 


titura 


petu 


petu 


8 koneho 


dalapan 


tofkangi 


dalapanti 


valu 


valu 


9 lali 


sambder 


l siyu 


sambilante 


siyam 


slam 


10 saroni 


pulu 


yagi 


putusa 


pulu 


pulu 


20 sisarone 


duapulu 


yagi romdide 


dua pulu 






100 simari 


atos 


ratu 


utun 


daan 


gatus • 


1000 




ribu 


rihune 


libu 


livu 


10,000 








laksa 


laksa 


100,000 










yuta 


yuta 



The Burmese numerals are : — 

12 345 6 7 89 10 

ta wheet thoun he nga khyouk khwon sheet ko tshay 



♦5-^1 f5 + 2 $2x4 §10x2 fl2xl0 



162 THE DECIMAL SYSTEM, 

They employ a sort of decimal accountancy, and pay all 
precious metals (like the Chinese) by weight, 
moo mal hkwe kyatatikas 
1000 = 400 = 200 = 100 = 1 priktha or vissom. 
The purity of gold is expressed by moos or tenths ; 10 moos 
and shay moo being esteemed pure gold.* 

POLYNESIAN NUMERALS. 



Marqnesa. Sandwich Islands. 


Fiji. 


Tonga. 


Maori. 


1 tahi 


kahi 


diia 


taha 


tahi * 


2 ua 


liia 


rua 


ua 


riia 


3 torn tu 


kolu 


tulu 


kulu 


toru 


4 ha, aha 


ha, aha 


ra 


fa 


wa 


5 fima 


lima 


lima 


nina 


rima 


6 ono 


ono 


ono 


ono 


omo 


7 hitu 


hiku 


pitu 


fitu 


witu 


8 vau 


valu 


walu 


valu 


waru 


9 iva 


iva 


tiva 


iva 


iwa 


10 ono hiiu 


umi 


tini 


ulu 


tekan 


100 uata 


uuta 


hanvaan aii 


raie 


1000 mano 


mano 


handolu afe 


-mano 


Caroline. 


Tnham. 




Pelew. 


Malagas!. 


1 tot 


asaha 




tong 


trai 


2 ru 


agiia 




oru 


riia 


3 tal, iol 


tulu 




othai 


telu 


4 tan 


tod-fud 




o'ang 


efatra 


5 lim, nim, lib 


lima 




ain 


dimi 


6 hoi 


gurum 




malong 


enina 


7 fiz, fuz 


fiti 




oweth 


fitu 


8 wal, wan 


giialu 




tai 


VOlll 


9 tihu 


sigua 




eten 


sivi 


10 seg, sik, sig 


manud 




makoth 


fulu 


100 sia pugu 


gatus 




20 olo-yuk 


11 iraiki ambi- 
nifulu 


1000 senses zele 


s'alan 




30 ok-a-thai 


12ruambinifulu 








40 ok-a-waugh 20 rua fulu 








50 ok im 


100 zatu 








60 ok gollan 


1000 arion 








70 ok-a-weth 


10,000 alina 








80 ok tai 


100,000 ketsi 




* 




90 ok a tui 










100 mak a dart 



* Prinsep's Useful Tables, p. 30-31. 



COINS, AND ACCOUNTS. 163 

One of the most extraordinary numeral forms is that of the 
Hawaian, where the unity is represented by kauna, or four; but 
instead of being multiplied by itself, it is multiplied by 10, and 
the different grades are thus represented :— 



4 integers 


= 


1 kauna 


= 


4 


10 kauna 


= 


1 kanaha 


= 


40 


10 kanaha 


= 


1 lau 


= 


400 


10 lau 


= 


1 mano 


= 


4,000 


10 mano 


= 


1 kini 


ESS 


40,000 


10 kini 


= 


1 lehu 


= 


400,000* 



The Arabic cardinal numerals are simple and declinable as 
masculine and feminine nouns from 1 to 10; — from 3 to 10 they 
may be employed either as adjectives or as numerals; — from 11 
to 99 they are indeclinable, but are distinguishable into the 
masculine and feminine genders. The word for 100 is feminine, 
— that for 1,000 is masculine, f 

The Arabs have introduced the names of the higher digits 
into several of the languages of Africa. In Darfour, the numerals 
are: — 1, dik; 2, au; 3, ihs; 4, ongall; 5, 6s; 6, 6szandik x (i. e., 5 
and 1),- 7, szebbe; 8, tmani; 9, nattise ; 10, uSje — where 7 to 9 are 
Arabic words; but their notation is decimal, 20 ueng-au (10x2;) 
100, jiri ; 1,000, Jiri-nga-uieh— 100 X 10. 

The Oceanic languages, which have no words in com- 
mon with those of any of the great continents, have the 
same quinary and decimal character which is found so generally 
diffused. 

In the Ende or Flores, the numerals are : — 1, sa; 2, zua; 3, telui 
4, wutu; 5, lima (hand); 6, lima-sa (hand and 1); 7, lima-zua 
5+2; 8, rua butu, 2x4; 9, tram; 10, sabulu.% 

The Australian dialect spoken in the neighbourhood of 
Sydney: — \,wagle; 2, bola; 3, broui; 4, karga; 5, blaoure; 6, 
blaourl-wagle; 5 + 1 ; 7, blaoure bola; 5+2; 8, blaoure broui, 5+3; 
9 ; blaoure-karga (5+4). 

The Tanna: — l,retti; 2, carru; 3, 7(dhar; 4Jtefa; 5,karirrom; 



* Chamisso Hawaian Language, p. 57. 

f De Sacy, Grammaire Arabe, i. 418, ii. 313, 

X Forster, p. 254, quoted by Balbi. 

L 2 



164 



THE DECIMAL SYSTEM, 



6, me-riddi ; (5 + 1 ;) 7,me-carru; (5+2;) 8, me-Uali&r, (5+3;) 

9, me kefa, 5+4; 10, liarirrotn-liarirrom, 5+5. * 

In New Caledonia : — 1, parai; 2, jparw ; 3,parghen; 4,parba\ ; 
5, panim ; 6, panimghi ; 7, panimru ; 8, panimghen ; 9, panwibai ; 

10, parunik. 

In this language, no doubt, the word joa prefixed to all the 
digits is a word denoting a numeral. The numbers from 6 to 9 
are all combinations of 5 with the lower units. The association of 
a prefix to words denoting numerals, obtains among many <jf the 
tribes in the Pacific ; — wa is adopted by several f: — 1, wanaet; 2, 
wadu ; 3, wakien ; 4, wdbay ; 5, wanaim ; 6, wanaim guic paig- 
nique ; 7, wanaimdu ; 8, wanaimgaiene ; 9 wanaivibait ; 10, wa- 
douninc. 

The Iddah, a language spoken at the confluence of the Tshad 
and the Niger, has a system of numeration perfect in its decimal 
character — 



1 nya 

2 edji 

3 eta 

4 ele 

5 elu 

6 efa 

7 eba 

8 edjo 

9 ela 

10 egua 

11 egua 'nka 

12 egua edji 

13 egua eta 

14 egua eli 

15 egua elu 

16 egua efa 

17 egua ebia 

18 egua edja 

19 egua ela 

20 dogu ogu 

21 ogu ngka 

22 ogu edji 



10+1 
10+2 
10+3 
10+4 
10+5 
10+6 
10+7 
10+8 
10+9 
10+10 

abbreviated 20+1 
do. 20+2 



23 ogu eta 

24 ogu ele 
30 ogwela 
40 ogweali 
50 ogwelu 
60 ogwefa 
70 ogweba 
80 ogweja 
90 ogweala 

100 ijeje abbreviated 

101 ijeje maya 

102 ijeje medji 

103 ijeje meta 

104 ijeje mele 

105 ijeje melu 

106 ijeje mefa 

107 ijeje mcba 
200 guake maya 
300 guake meta 
400 guake meli 
500 guake melu 

1000 itshha madji 



20+3 

20+4 and so forth 

10x3 

10x4 

10x5 

10x6 

10x7 

10x8 

10x9 



There has been lately published a collection of the numerals, 



* Cook's Third Voyage, ii., p. 364; and Balbi's Eth., 432. (Pott, 47.) 
f Balbi, p, 275. 



IN NUMBERS, COINS, AND ACCOUNTS. 



165 



from 1 to 10, of no less than 388 dialects and languages of Africa, 
and of these very many have separate words for 1 to 5, and com- 
binations of 5 with 1, 2, 3, and 4, to represent 6, 7, 8, and 9, but 
most have a simple word for 10. For example : — * 



The Felata (Soudan)— 

1 2 
go diddie 

6 7 
sowiego sowadie 


3 

tattie 

8 
sowatuttie 


4 
ni 

9 
sowanie 


5 

jowie 

10 

sapo 


The Felaps (Senegambia)— 

1 2 

enori kukaba 

6 7 

futuk enori futuk kukabo 


3 

sisaji 
8^ 
futuk sisaji 


4 

sibakir 

9 

futuk sibakir 


5 

futuk 
10 

sibankoni 


The Ballorn (near Sierra Leone) — 

12 3 

bul ting ra 

6 7 8 

meinbul meinting meinra 


4 

nenol 

9 

memuehol 


5 

mun 

10 

naung 


Benin (Bight of Benin) — 

1 2 

bo bi 

6 7 

tahu tabi 


3 

la 

8 

tala 


4 
nin 

9 i 
tenii 


5 

tang 

10 

te 


Igberra (on the Niger) — 

1 2 

anya ebba 

6 7 

sokkiloanya jokkirebba 


3 

eta 

8 
jokkireta 


4 
enna 
9 
jokkireuna 


5 

jokki 

10 

ikkewah 


Bongo (Gaboon) — 

1 2 

uoto baba 

■6 7 

batan a nota batan a baba 


3 

balali 

8 

batan a bala 


4 

banai 

9 

batan a banai 


5 
batan 

10 
dium 


Otam (Cross river) — 
1 2 
yokamoa beba 

6 7 
bitan ari yo bitan ari beba 


3 

beraru 

8 

bitan ari raru 


4 

bini 
9 
bitan ari bini 


5 
bittan 

10 
isaka 



Specimens of Dialects, &c, by John Clark : Green, 1489, 



166 THE DECIMAL SYSTEM, 

Several other African languages exhibit examples of decimal 
notation. The Dankali has, 

1234567 8 

eneki lamei siddehu ferei konoo lekei melhein bahhara 
9 10 11 

sagalla tabana tabbankeeneki 

and so up to twenty, which is labbdtana; 30, soddomo — 3x10; 
31, soddonhi eneki; 50, kontomoj 5x10; 100, bol ; ^1000, 
tubban a bol, 10x100.* 

The Galla numerals! are also decimally arranged : — 

1234567 8 9 

tok lama sadi afur shani tsha torba sadeti sagall 
10 11 12 

kudana kudatok kudalama, &c. 

20 is diktama, 2x10; 100, dibba ; 1,000, kuma. 

The Dongola numerals, in the Sennar kingdom, have a similar 
character : — 

12 3 4 5 6 7 8 9 

uerij dwi tuskij kemmisk dik gorik kdloda iddiige iiskodk 

10 11 12 20 50 100 

diimming diimmindoek dummindoe arrigk ir-ik immelwek 

1000 
ddnnalwe'k $ 

The pursuit of the decimal elements through the languages 
of the world, would occupy volumes. Though, as we have seen, 
there are examples in which the quinary power is the limit to 
calculation, yet ten, and additions or multiplications of tens, may 
be deemed the almost universally recognised arithmetical instru- 
ment. But there are many examples which might be added to 
those already given, where the word for ten is only the duplication 
of the word for five. There are several of the African languages 
in which there are separate and distinct words for the numerals 
up to 6 ; the numerals 7, 8, and 9, are combinations of 5 and 2, 

* Isenberg's Small Vocabulary of the Dankali language. Salt's 
Voyage to Abyssinia, Appendix xii. (Pott, 106-7.) 

f Krapf's Imperfect Outline of the Elements of the Galla 
Languages. (Pott, 106.) 

X Vater's Proben, p. 247. Balbi, N. 209, 210, 



IN NUMBERS, COINS, AND ACCOUNTS. 167 

5 and 3, and 5 and 4, as those used by the Manna people : — 
1, kidding ; 2, fidding ; 3, sarra; 4, nani; 5, soolo ; 6, seni; 7, 
soolo mo Jidding ; 8, soolo ma sarra; 9, soolo ma nani; 10, nuff. 
The Buntookoos have five monosyllables for the first five digits, 
while the following five are made up by combinations of the first : 
l,tah; 2, noo ; 3, sah ; 4, nah ; 5, taw ; 6, torata; 7, toorifeenoo ; 
8, toorifeessa; 9, toorifeena; 10, nopnoo. 

Some of the African languages have simple words for the 
numerals up to 6, but have combinations of 5 and 2, 5 and 3, 
5 and 4, for 7, 8, and 9, with a simple word for 10. 

The Susu :— 

1 2 3 4 5 6 7 8 

kiring firing sukung nani suli seni suli firing suli masakung 
9 10 

suli manani fu. 

The Mozambique has the combination of 5+1, 5+2, for 6 and 
7, but has simple words for the remaining digits. 

12 3 4 5 6 7 

moosa pili thara ssesse thana thanamoasa thanapili 

8 (5+3) 9 10 

thana ssesse looko mino komili ssesse. 

Many of the African languages make their numeral resting- 
place at 5, and start from thence with new combinations. The 
numerals of Lagoa Bay are : — 

1 chiugea 6 tanou na chengeva 5 and \ 

2 se-berry 7 tanou na tree-beere 5 and 2 

3 ni-rarou 8 tauou ni raron 5 and 3 

4 moo-nau 9 tanou na maunau 5 and 4 
6 thanou 10 koumau 

20 ma-koumau ma-bdere 10 by 2 
30 ma-koumau ma-varou 10 by 3* 

So in the Mozambique : — 

1 moosa 6 thana moasa 5 and 1 

2 pili 7 thana pili 6 and 2 

3 thara, ba-tatu 8 thana ssesse 

4 ssesse, me sana 9 looko 

5 thana 10 mino komili ssesse 

* "White's Journal," 1800, p. 72, quoted by Balbi, Atlas Ethno., 
No. 287. 



168 THE BECIMAL SYSTEM, 

Among the Feloops, as given by Mungo Park : — 

1 enory 6 footuck enory 5 and 1 

2 sickaba or cookaba 7 footuck cookaba 5 and 2 

3 sisajee 8 footuck sisajee 5 and 3 

4 sibakir 9 footuck sibakir 5 and 4 

5 footuck 10 sibankonyem 

The Ratongga* exhibits some very remarkable caprices : — 
1 yoko 2 beba 3 biraru 

4 binni 5 betta a 

6 betta nadi yoko (5+1) 

7 ossi yoko bin tsambi (8 — 1 ) 

8 iwambi 

9 issiokomancondaru (10 — 1) 
10 doridaru 

The forms of the Ludaf numerals are various : — 

1 aquiripo 6 aquesiato 

2 aquawe 7 aque se aur (5+2) 

3 aquaton 8 aque se anto (5+3) 

4 aqueni 9 aque se eni (5+4) 

5 aquato 10 aqua owe, i. e., 2 numbers 
in which the wdrd aqua obviously means a numerical substantive. 

The numerals of the Jolofs present more irregularities than 
those of almost any other rude people; They are found in 
Durand's "Voyage au Senegal" (Paris, 1807, vol. ii. p. 360), and 
are as follows : — 

Bene ------- l 

Gnare ------ 2 

Gnete 3 

Gnanette ------ 4 

Gnirome ------ 5 

Gnirome bene - - - - - 6=5 + 1 

Gnirome gnare - - - - - 7=5 + 2 

Gnirome gnete - - - - - 8=5 + 3 

Gnirome gnanette - - - - 9=5+4 

Foucq ------ 10 

Foucq ac bene - - - - - 11 =10 + 1 

Foucq ac gnare - - - - - 12 = 10 + 2 

Foucq ac gnete - - - - - 13 =10 + 3 

Foucq ac gnanette - - - - 14 =10 + 4 

Foucq ac gnirome - - - - 15 =10 + 5 

Foucq ac gnirome bene - - - 16 =10 + 5 + 1 

Foucq ac gnirome gnare - - - 17 =10 + 5 + 2 

Foucq ac gnirome gnete - - - 18 = 10 + 5 -f- 3 

Foucq ac gnirome gnanette - - - 19= 10 + 5 + 4 

* Bagoon River. f Dahomy. 



IN NUMBERS, COINS, AND ACCOUNTS. 169 

Gnarefoucq - - - - - 20=2X10 

Gnare foucq ac bene, &c, &c. - - 21 = 2 X 10 + 1 

Gnete foucq - - - - - 30=3X10 

Gnanette foucq - - - - - 40=4X10 

Gnirome foucq - - - - - 50=5X10 

Gnirome bene foucq - - - - 60 = (5 4- 1) X 10 

Gnirome gnare foucq - - - - 70 = (5 -j- 2) X 10 

Gnirome gnete foucq - - - - €0 = f5 + 3) X 10 

Gnirome gnanette foucq - - - 90 = (5 + 4) X 10 

Temere ------ 100 

Gnare temere ----- 200 

Gnete temere - 300 

Gnanette temere ----- 400 * Sic. in orig. But is appa- 

Gnirome temere ----- 500 rently a mistake for 

Gnirome temere ac gnirome bene* - 600) Gnirome bene temere 

Gnirome temere ac gnirome gnare - 700 > Gnirome gnare temere 

Gnirome temere ac gnirome gnete - 800N Gnirome gnete temere 

Gnirome temere ac gnirome gnanette - 900 Gnirome gnanette temere 

Gunee ------ 1000 

Gnare gunee ----- 2000 

Gnete gunee ----- 3000 

Gnanette gunee - _ - - _ 4000 ] Sic. in orig. Is probably 

Gnirome gunee ----- 5000 a mistake for 

Gnirome gunee ac gnirome benef- - 6000) Gnirome bene gunee 

Gnirome gunee ac gnirome gnare- - 7000 1 Gnirome gnare gunee 

Gnirome gunee ac gnirome gnete - - 8000 C Gnirome gnete gunee 

Gnirome gunee ac gnirome gnanette - 9000' Gnirome gnanette gunee 

Foucq gunee ----- 10000 

Gnare foucq gunee - - - _ 20000 

Gnete foucq gunee - _ _ - 30000 

Gnanette foucq gunee - - - - 40000 + Sic. in orig. Probably a 

Gnirome foucq gunee - 50000 mistake for 

Gnirome foucq gunee ac gnirome bene \ 60000% Gnirome bene foucq gunee 

Gnirome foucq gunee ac gnirome gnare 70000/ Gnirome gnare foucq gunee 

Gnirome foucq gunee ac gnirome gnete 80000 f Gnirome gnete foucq gunee 

Gniromefoucq gunee ac gnirome gnanette 90000.) Gnirome gnanette foucq 
Temere gunee ----- 100000 gunee 

Colonel Thompson, who was one of the earliest governors of 
Sierra Leone, says of the Jolofs : — " They are not a rude race, as 
would be implied, if they could at this day only count five by the 
help of their fingers. Though if they were unable, they would be 
only what the Greeks were in the time of Proteus, if, indeed, any 
body knows when that was. But the Jolofs are the most ad- 
vanced of all the African races, as distinct from mixture with the 
Arabs. Their language is held to be very melodious and compe- 
tent to all purposes. In proof of which, the European ladies who 
find their way to the Senegal and Goree, learn to talk Jolof as in 
India they learn Hindostanee. It is remarkable that the Jolofs, 
though the handsomest race in Africa, are the blackest ; and the 
name Jolof, I understand, means black.''* 

The system of notation employed by the ancient Peruvians, 



170 THE DECIMAL SYSTEM, 

at least as represented by the collection of Quipos, or knot- 
records, as described in the Westminster Review, was ternary, 
or by gradations of threes. " On examining the numerical system 
of knot- writing it is evident that what algebraists call the local 
value is three. For example, one is typified by the simplest 
of all possible knots, as what a sempstress makes on a thread 
previous to taking the first stitch ; two is expressed by putting the 
end through once more, before drawing tight, as a sempstress does 
when it is desired to increase the magnitude of the kncfc ; and 
three is expressed by performing the same operation an additional 
time. Four assumes a new combination, for it is expressed by a 
loop of the simplest kind, such as is made in nautical language, by 
taking a bend in the bight of the rope; and^ye is expressed by 
the same kind of loop, with an additional twist in the clinch or 
part where the whole is drawn tight; and six has another twist still; 
seven is another kind of loop, which is manifestly different from four, 
though it would probably puzzle a forecastle man to define the 
difference in words ; eight is the same with the addition of another 
twist in the clinch, and nine with yet another. Ten is no loop at all, 
but a portentous kind of a knot, such as might be made in a 
cat o' nine tails, when the object was to kill ; eleven is the same 
with an additional twist in the clinch ; and twelve with another. 
Thirteen is the same kind of knot as ten, only with a loop sprouting 
out on one side; and fourteen and fifteen distinguish themselves 
by their twists, as before. In this manner the system goes on to 
a hundred, exhibiting a new knot at every third numeral, and 
expressing the two next by additions at the clinch. The knots 
become exceedingly complicated and artificial, but they invariably 
adhere to the ternary system described."* 

Mr. Gallatin represents, however, "that the arithmetic of the 
Peruvians and of the Araucanians is purely decimal."f Different 
writers give different numerals, many of which appear to be 
rather quinary than decimal. Several of the digits are polysylla- 
bic : 10 is tunca, 100 is pataca (the Spanish for dollar) ; and 
1000, quaranca. 

Yarica says, " The Indians employ threads of cotton which 
they call quippos, and they show the numbers by knots of different 
forms, exhibiting in various distances from units and tens, and so 

* Westminster Rev., vol. xi. 1829, p. 246. 
f American Ethnol. Soc. i. p. 49 (Pott, 73). 



IN NUMBEKS, COINS, AND ACCOUNTS. 171 

upwards ; and they give to the thread the color which is connected 
with the thing they desire to show. In every province there are 
persons who are charged to preserve by these records the memory 
of public events, which are called Quippos Camaios ; and there are 
public edifices filled with these threads, which he who has charge 
of them can readily explain, though they belong to ages antecedent 
to his time." * 

The Guaranies, who are said never to count beyond thirty, 
employ combinations of the first four numbers, and of the words 
for hands and feet to reach that number; 1, petey ; 2, mocoi ; 3, 
mbohapi; 4, irundi; 5, irundi hae nirai, — four and another, or ace 
popetei, one hand ; 6, ace popetei kae petei abe, a hand and one be- 
sides; 9, ace popetei hae irundi abe, a hand and four besides; 10, 
ace pomocoi, two hands ; 20 mbo mbi abe, hands and feet besides ; 
30 mbo mbi hae promocoi abe, hands, feet, and two hands 
besides. 

The Zamucos have the following numerals: — 1, chomara; 2, 
gar; 3, gaddive ; 4, gahagani ; 5, chuena yiminaete, finished hand ; 
6, chomarahi, one of the other; 7,garihi, two of the other; 10, 
chuena yimanadie, finished two hands ; 11, chomara yiritie, one of a 
foot ; 20 chuena yiriddie, finished feet. Beyond 20 the Zamucos 
use the word unaha, many ; if the number greatly exceed twenty, 
they use unahapuz, the superlative of many. But they commu- 
nicate an idea of growing greatness of numbers by elongating the 
sound of the second vowel thus — ana-a-a-a-a-hapuz. But they 
assist their calculations by grains of rice, stones, or seeds ; and 
having placed of these the number required, they point to them 
and say, " choetie" like this.f 

It was in vain, says one of the historians of America, J that the 
Jesuit talked to the negro of angels without number — millions 
upon millions — like stars in the heavens, like leaves on the trees, 
like sands on the shore ; the words made not the slightest impres- 
sion. Inhere was no association between such figures and the 
grains of maize which the negroes employ for counting ; but when 
he said there were more angels than maize-corns in a fanega (a 
large Spanish measure), the negro's attention was awakened into 
wonder, and the preacher's meaning was thoroughly understood. 

La Condamine states, that the American Yancos who inhabit 

* Historia del Peru, vol. iii. pp. 5, 6. 

t Dr. Peacock, p. 479, \ Gilj. vol. iii., p. 305. 



172 THE DECIMAL SYSTEM, 

the banks of the river Amazon, cannot, in consequence of the com- 
plex character of their language, count beyond three, which they 
call poettarrarorincoaroac. Five is a not unfrequent limit to 
numeration among barbarous people. 

The Maipuri, on the Orinoco, call 1 papita ; 5, pdpitaerri capiti 
— i. e., one only hand ; 6 papita yana pauria capiti purena — i. e., 
" one of the other hand we take." But though so cumbrous a mode 
of numeration is employed for counting human beings, other nu- 
merals are used for other animals, and others still for inani- 
mate objects, — a distinction found also among the Japanese. The 
Yaruroes call 5 canniicchimo, "one hand alone;" 10, yoaicchibo, 
"all the hands;" 15, canitaomo, "one foot alone;" 20, canipume, 
" one man." 

The manner of exhibiting the fingers varies among different 
nations. The Ottomacos, to express three, join the thumb, the fore 
and middle finger of the right hand, and close the other two fingers ; 
the Tamanacos, the little, the ring, and the middle finger, and 
close the forefinger and the thumb ; the Maipuros raise the 
fore, the middle, and the ring fingers, and close the thumb and 
the little finger. 

With a vast variety of words, the same mode of employing the 
fingers, hands, and feet, may be traced in the numerals of many 
of the American tribes. Some of the more remarkable charac- 
teristics of the American languages are worthy of note. The Luli 
of Paraguay, while they call 6 four with two, lokep moile tamop, — 
8, four with four, lokep moile lokep, — 9, four with four one, lokep 
moiU lokep alapea; — say for 11, all the fingers of hand with 
one, is yaoum moile alopea; and for 30, all the fingers of hand 
and foot, with all the fingers of hand, is elu yaoum moile is- 
yaoum. For 40, a Luli raises his open hands to his shoulders, 
bends his head to his feet, and says, tamop— two or twice. For 60 
he employs the same action, saying tamlip, three or thrice ; and 
he expresses 100 in a similar way by exclaiming, lokep moile alapea, 
four with one — i. e., five or five times. The Mocobi numerals used 
by a tribe on the Parana river, a branch of the Rio de la Plata, 
use their hands and feet ; but their spoken numerals present no 
higher combinations than 4 : — 1 iniateda ; 2, inabaca; 3, inabocao- 
caini, 2 more : 4, inibacao-cainibao 2 -J- 2, or natolatata; 5, inibacao- 
cainiba iniateda, 2-f-2+ 1, or natolatata iniateda, 4+1; 6, natola- 
tata inabaca, 4+2; 7, natolatata inibacao-caino, 4+2+ more; 8, 
natolatata natolata. The Guaicurus do not go beyond 2 in their 



IN NUMBERS, COINS, AND ACCOUNTS. 173 

numeral combinations: — 1, uninitegui ; 2, iniguata ; 3, iniguata 
dugana, 2+more; 4, iniguata drinignata ; 2+2. For all numbers 
above 4 they employ the oguidi, meaning many. One stage lower 
is presented by the numerals of the Betoi on the Orinoco : — 1, edo- 
jojoi ; 2, edoi, i.e., another ; 3, ibutu, i.e., beyond ; 4, ibutu edojojoi, 
beyond one; 5, rumocoso hand.* From these rude and imper- 
fect fragments to the amazing decimal powers as exhibited in the 
calculations of astronomy, is like a transition from thick darkness 
into infinite light, — from a murky prison into boundless space ; 
and we are actually tempted to inquire, whether a Newton medi- 
tating on the banks of the Thames, and an American wandering by 
the shores of the Orinoco, can be made of the same materials, — can 
be brethren of the same great family ! The interest attached to 
these investigations is far greater than that of a mere inquiry into 
the different modes of notation, — it stretches into the vast ethno- 
logical field of races and their histories — of languages and their 
formation — of civilisation and its multifarious exhibitions — of 
human contrivances and human necessities — of ability to conceive, 
and aptitude to communicate instruction — of climate — of pro- 
duction — of habits — of isolation and of intercourse. How na- 
tions greatly advanced in many of the arts of life have made so 
little progress in those of arithmetic, — how others to whom the 
mysteries of figures have been revealed and developed should have 
remained uninitiated into so many other departments of science 
and philosophy — how instruction and ignorance — how backward- 
ness and movement have been so strangely blended; — these are 
topics for curious speculation and research ! 

As a curious specimen of polysyllabic numerals, I give the 
units of the Timuacana language : — f 

1 minecotamano 5 namaruama 9 napekecheketama 

2 naiuchamima 6 namarecama 10 natumama. 

3 nahapumiraa 7 napikicharaa 

4 nacheketamima 8 napikinahuma 

No doubt the na, which in this language is found in all the 
units except the first, denotes a numeral. It seems as if, to some 
extent, one numeral served as a stepping-stone to the following: — 
In the 7, 8, and 9,napiki, or napeke, are found, as is mima in 2, 3, 

* Hervas, quoted by Dr. Peacock, pp. 479, 480. 
f Balbi Eth., N. 785. (Pott, 06.) 



174 THE DECIMAL SYSTEM, 

and 4 ; nama commences both 5 and 6 ; and ama is the termination 
of 5, 6,7, 9, and 10. 

Of the semi-civilised nations of Mexico, Yucatan, and Central 
America, Gallatin says : — " It is remarkable that these tribes had, 
for the numerals under 20, only four uncompounded names — pil 

1, ajte 2, puguantzam 4, and juyopamany 5. Even the numeral 
3 is ajticpil (2 + 1.) The other numerals are compounded in a 
rariety of ways: — 6 is (2 + 1+2 ;) ajticpilajti; 8 is (4x2 ;) 10 is 
5x2; 11 is 5x2 + 1; 12 is 4x3; 15 is 5x3; and, forAcom- 
pounding the numerals 18 and 19, they have borrowed the 
Mexican word chicnas, 6 : — thus 19 is chicuas ajti c pil co pil, or 
6x(2 + l) + l."* 

In the Ounalaska language, the numerals 1 to 4 and 6 to 9 have 
a remarkable resemblance to one another: — l,atoken; 6,atoon; 

2, arlok ; 7, oolloon ; 3, karikoo ; 8, kancheen ; 4 and 9 are abso- 
lutely identical, seecheen, and can only have been distinguishable 
by referring to the same finger on different hands ; 5 is chaan, 
synonymous with chiaiih (hand).f 

So in the Koljush tribes :\ — 1, tleek ; 2, tech ; 3, neztke ; 4, 
tachwi; 5, ketschtschin ; 6, tletuschu; 7, tachuteuschu.; 8, nes- 
ketuschu ; 9, hisckok; 10, tschinkat. In this and cognate languages, 
the numeral five is the word for hand, and the numeral one re- 
sembles the word for finger. 

In the island of Santa Barbara, the numerals 5, 6, and 7, are 
formed by prefixes to 1, 2, and 3 : — 

1 paca 3 maseja 5 ytipaca 7 ytimasage 9 upax 

2 exco 4 scumu 6 ytixco 8 malahua 10 kerxco§ 

Humboldt gives the numerals of the Eslene tribes, showing 
that the word for 5 is composed of 1 and 4, and that 6, 7, 8, and 9, 
are but compounds or amplifications of 1, 2, 3, and 4 : — 

1 pek 3 julep. 5 pamajala 7 julajualanai 9 jamajusjualanai 

2 ulhai 4 jamajus 6 pegualanai 8 julepjualanai 10 tomoila|| 

And Duponceau shows that similar constructions are found among 



* Transactions of the American Eth. Soc, i., p. 49. (Pott, 69.) 

f See Cook's Voyages, iv., p. 539. (Pott, 61.) 

% Krusenstern, p. 55. (Pott, 66.) 

% Balbi, p. 829. (Pott, 63.) 

II Essai. Pol. sur le Royaume de la Nouvelle Espagne, p. 322. 



IN NUMBERS, COINS, AND ACCOUNTS. 175 

the North American nations.* The Alconquins have — 1, ciutte 
and 6, ciutas ; 2, nissa ; 7, nissas. 

He farther remarks, that though in many of the North 
American languages the numerals have simple words up to 5, 
they frequently present new combinations from 6 upwards — such 
as 5 and 1 for 6, 5 and 2 for 7, 5 and 3 for 8, and 10 less 1 for 9. 
It is observable, that though in the spoken Latin language no 
such association of ideas is traceable, yet it is found in the written 
numerals of Rome, — as vi., vii., viii., and ix., and in no other 
ancient symbols.f 

The Muyscas in New Granada, Humboldt informs us, say 
for 11, quicha ata, foot one; 12, quicha bosa, foot two; 13, 
quicha mica, foot three; and they use the foot for numbering 
when they have exhausted the hands. 20 is foot ten, or 
gueta, meaning a small house or barn — probably with reference to 
the store-house in which the maize is collected, whose grains they 
are in the habit of using for calculation. They say a house and 
ten for 30, two houses or twice twenty for 40, four houses or four 
times twenty for 80. So the Celts ; and some of the Roman- 
derived dialects — as the French, quatre vingt, and even quinze 
vingt,\ for 300 ; six vingt, sept vingt, and huit vingt, are some- 
times employed for 120, 140, and 160. " The poor-house (work- 
house) in Paris is called ' les Quinze Vingt.' " In the Bas Breton 
the words pemzek-ugent, 15 X 20, and tri-chant, 3 x 100, are 
equally employed for 300.§ 

Two forms of numerals are sometimes found even among semi- 
civilised races. " The Otomis expressed the numeral 100 by 
the words Cytta tee, which means 5x20; but they had also a 
distinct, apparently uncompounded word, nthebe, for the same 
numeral; their word for 1,000 was ratta nthebe, 10 x 100, but 
they had also an uncompounded word, mao."\\ 

The Carlbs of Essequibo, according to Biet, for 5 show a 
hand, for ten the two hands, for twenty the feet and hands. The 
word for five is winee etanee, a hand ; for 20, owee catena, or, a 
person. The numerals 6, 7, 8, and 9, are made by adding the 

* Systeme Gramm. des Langues de quelques Nations Indiennes de 
l'Amerique, du Nord. Paris, 1838. 

t Duponceau, p. 59. See also Humboldt in Crelle's Mathematical 
Journal, 1829, p. 211. 

\ Gallatin, p. 53. § Pott, p. 88. || Gallatin, p. 53. 



17b* THE DECIMAL SYSTEM, 

w ord puimapo to the numerals, for 1 oween, 2 oko, 3 oroowa, and 4 
oko baimea. So in the Cavaiban Island they add the word laoyagone, 
5, to dban 1, Mama 2, and eleoua 3, thus making 6, 7, and 8.* 

The Arrawakis add the word timan in the same manner to the 
four first units, and so convert them into the four last.f It is 
remarkable, however, that puimapo among the Caribs, and timan 
among the Arrawakis, do not represent 5, which number is 
wineetanee and abbatohabbe in these languages ; — so strange are 
the caprices and irregularities which have led to the formation of 
the words in most ordinary use. 

It has been observed, that the tribes of South America possess 
much more perfect systems of numeration than those of the 
north. Few of the nations of Northern America have a decimal 
system, — and without this, or some other means of grouping 
numbers, the powers of language fail, and the higher numerals 
are represented by a phraseology so lengthy and entangled, as to 
embarrass and overcome the means of utterance. Humboldt 
gives the system of the ancient Peruvians, which exceeds in extent 
and simplicity anything to be found in the Greek or Roman 
vocabulary :— 

10 chunca. 10,000 chunca huaranca. 10x100. 

100 pachac. 100,000 pacha huaranca. 100x1000. 

1,000 huaranca. 1,000,000 hunu.J 

The numerals of the Cayababi, a tribe on the banks of the 
Mamore river, exhibit some remarkable forms of quinary and 
decimal combinations. Arue is the word for hand, and, being 
appended to 1,2, 3, and 4, make 6, 7, 8, and 9 ; 10 is hand hand ; 
100, hand four times repeated— a multiplication of 10 by itself; 
and 1,000, a multiplication of 100 by 10. 

1 carata 10 bururuche 

2 mitia 11 bururuche-caratorogicne. 10+1 

3 curapa 12 bururuche-mitiarogicne 

4 chadda 19 bururuche-chaddarirobogicne 
6 maidaru 20 mitiaburuche. 2x10 

6 caratarirobo 30 curapabururuche. 3x10 

7 mitiarirobo 100 buruche-buruche. 10x10. 

8 curaparirobo 1,000 buruche-pene bururuche. 10 X 100§ 

9 chaddarirobo. 

* Rudiger, p. 129. f Balbi, No. 685. 

" Vues des Cordilleres," p. 252. Peacock, p. 379. § Ibid, p. 478.' 



IN NUMBERS, COINS, AND ACCOUNTS. 



177 



Dr. Peacock quotes from Hervas the following numerals from 
the ancient languages of Peru and Chili :— 



Quichtia. 


Araucana. 


Aimarra. 


Sapibocona. 


1 hue 


kine 


mai 


pebbi 


2 iscai 


epu 


paya 


bbeta 


3 kimsa 


kula 


kimsa 


kimisa 


4 tahua 


meli 


pusi 


pusi 


5 pichca 


kechu 


pisca 


pissica 


6 socta 


kayu 


sogta 


succuta 


7 canchis 


reighi 


pacalco 


pacalucu 


8 passae 


pur a 


kimsacalco 

3+5 


kimisacalucu 


9 iscon 


ailla 


pusicalco 

4+5 


pusucalucu 


10 chunca 


mari 


tunca 


tunca 


11 chunca hue niyoc 


marikine 


tunca mayani 


tunca peapebbi 


10+1 


10+1 


10+1 


10+1 


12 chunca iscai niyoc mari epu 


tunca payani 


tunca peabbeta 


10+2 


10+2 


10+2 


10+2 


20 iscai chunca 


epu mari 


paya tunca 


bbeta tunca 


2X10 


2x10 


2x10 


2X10 


30 kimsa chunca 


kula mari 


kimsa tunca 


kimisa tunca 


3X10 


3X10 


3X10 


3X10 


40 tahua chunca 


meli mari 


pusi tunca 


pusi tunca 


4x10 


4X10 


5X10 


4x10 


100 pachac 


pataca 


pataca 


tunca tunca 
10X10 


1,000 huaranea 


huaranea 


huaranea 


tunca tunca tunca 
10X10X10* 


1,000,000 hunu 









All these represent decimal notation; the resemblances and the 
differences are equally remarkable. In the three last, the terms 
for 100 and 1,000 are the same, exhibiting a similarity in the 
higher numbers which is not traceable in the lower. 

Another group of numerals is furnished by Hervas, viz. : — 
the Aztec, or ancient Mexican, the Yucatan, and Coran' (Nueva 
Galicia). 



• Peacock, p, 478, from Hervas. 



178 



THE DECIMAL SYSTEM, 



Aztec. 


Yucatan. 


Coran. 


] ce 


hunppel or yax 


ceaut 


2 ome 


cappel „ ca 


hualpoa 


3 yei 


oxppel „ yox 


huaeia 


4 nahui 


camppel „ cantzel 


moacoa 


5 macuili (maitl, hand) 


hoppel „ ho 


amxuoi 


6 chicuace 5+2 


uacppel „ uac 


aceri 


7 chicome 5+2 


uncppel „ uuc 


ahuapoa 


8 chicuei 5+3 


uaxacppel „ uaxac 


ahuaeica 


9 chicunahui 5+4 


bolonppel „ bolon 


amoacua 


10 matlactli 


lahunppel „ lahun 


tamoamata (moamati, hand) 


11 matlactli- oce 10+1 


huncahunppel 1 + 10 


tamoamataapon ceaut- 10+1 


12 matlactli omome 10+2 lahca 2+10 


tamoamata aponhualpal0+2 


15 chaxtoli 


holhunte 5+10 




16 chaxtoli-occe 15+1 






20 cempohuali 


kal or hunkal 


ceitevi, i. c, one man 


30 cempohuali-i-pan 




ceitevi poan tamoamata 


matlactli 20 + 10 




20x10 


40 ompohuali 


cakal 2x20 


huahcatevi 2 x 20 


60 epohuali 


oxkal 3x20 


huaeicatevi 3 x 20 


100 macuilpohuali 5x20 


hokal 5 x 20 


anxiitevi 5x20 


200 matlacpohuali 10x20 


lahunkal 10x20 


tamoamatatevi 10 x 20 


400 cen-tzontli 




ceite vitevi, 20 men 


800 ontzontli (hairs of the 






head) 






8000 ce-xikipili 


hunpic, or pic 





A fanciful spirit seems to have possessed some of the Indian 
nations in the formation of their numerals. The tribe which oc- 
cupied Bogota, for 1 used ata, meaning water, . . . 

afield 
changeable 



2 bosa 

3 mica 

4 muyhica 

5 hisca 

6 ta 

7 cahupqua 

8 sahuzu 

9 aca 

10 tibchica 



tempest clouds 

repose 

harvest 

deaf 

a tail 

(unknown) 

bright moon* 



In this there has been an attempt to associate the numerals 
either with changes of the heavenly bodies, or the labours of the 
field, and the objects of worship, but little light has been thrown 
on the matter. After the number 10 the quicha is introduced, 
meaning foot. Quicha ata, or foot +1, meaning 11 ; 20 has two 



terms — quicha ubchica, 10-f-lO, or gueta, meaning hours. 
bosa, 2 hours. 



40, gue- 



* Peacock, 388, 478. 



FRENCH COINS, 





FRENCH GOLD COINS. 






rKKHCB SILVER COINS. 






KHENCU COPPER COINS. 



IN NUMBERS, COINS, AND ACCOUNTS. 179 



CHAPTER IX. 

DECIMAL CURRENCY AS ESTABLISHED IN OTHER COUNTRIES. 

The nations which have adopted the decimal system are, France, 
Holland, Sardinia, Naples, Rome, Modena, Greece, Belgium, 
Switzerland (in part), Lombardy, Tuscany, Spain, Poland, Japan, 
China, Russia, Zollverein (metrical in weights and measures), 
Portugal, Brazil, New Granada, Chili, Mexico, Columbia. 

The foundations of the French system of weig-hts and measures 
and of coinage as dependent upon them, are purely scientific, and 
not subject to arbitrary change. The standard of measures was the 
dimension of the earth — i.e. the distance from the equator to the 
pole, which, being divided into 10,000,000 parts, gave the metre = 
39*371 inches; which, being subjected to decimal multiplications 
and divisions, establish all the legal measures of length of France. 
For the standard of weights, a cube of pure water, at the tem- 
perature of melting ice, measuring in each direction the hundredth 
part of this metre (called a centimeter), gave a weight which was 
named a gramme, whose decimal subdivisions and multiplications 
are the standard of all authorised weights. The gramme is equal 
to 15*435 troy grains. By a decree of the 28 Thermidor, an in. 
(Aug. 19, 1795), the five-franc piece and its divisions were intro- 
duced at the rate of 200 francs to the kilogramme — 9-10ths fine ; 
and in 1803 the deviations of permitted fineness were limited to 
Yo^o above or below the standard, — so that a coin is not allowed 
to exceed 903 in fineness, or 897 in alloy. 

The object of the various regulations which have determined 
the coinage in France, was to make every species of coin harmonise 
with a decimal system, not only as regarded money, but every 
calculation of weights and measures. 

The law of the 7 Germinal, year xi. (28th March. 1803), decided 
that the currency should consist of — 

In gold — Pieces of 40 francs and 20 francs. 
„ silver — „ of of., 2f., If., |f. = 75c, £f. = 50c, £f. = 25. 
„ copper — „ of 10c, 5c, 3c, 2c 

m2 



180 THE DECIMAL SYSTEM, 

It will be seen, however, that many of these coins were rather 
introduced to facilitate transactions than to represent decimal divi- 
sions. In process of time the non-decimal coins have almost wholly 
disappeared, and the only pieces now issued are — 

Gold, of 20 and 10 francs. 

Silver, of 5, 2, 1 francs, and 50 and 20 centimes. 

Copper and bronze, of 10c, 5c., 2c, and lc 

The standard in France has a decimal foundation — namely, l-10th, 
or 9 parts of pure gold and silver, and 1 of alloy. 

In gold, the proportions of pieces of 20 francs to those of 10 
francs is 9 to 1. 

In silver, the proportions are l-40th part in the following 
coins :— 

50 in pieces of 2 franca. 
120 „ 1 franc 

65 „ 50 cents. 

15 „ 20 „ 

250 
The rest in pieces of 5 francs. 

TLe mint' is dependent upon the Ministry of Finance. 

The Belgian coins and modes of account generally agree with 
those of France, though, in some parts, the Dutch currency is main- 
tained. 

In Holland, the guilder or florin is the money of account, and 
is divided into 100 cents — the value of the florin being about 
twenty pence. 

In Geneva the French currency prevails. In Bale, the Swiss 
franc, whose value is about 13£d., is divided into 100 raps or 
cents. 

In Lombardy and Vienna, the Austrian lira = 8*13d., is divided 
into 100 centesimi. 

The Neapolitan ducat = 3s. 4d., is divided into 100 grani. 

Rome divides the scudo romano = 505d., into 100 bajocchi. 

The lira nuova of Genoa and Sardinia is equal to the French 
franc, and is divided into 100 centesimi. 

In Tuscany, the lira toscana, = 7'82d. ; is divided into 100 cen- 
tesimi. 

The dollar of Spain, divided into 100 cents, now established by 
law, is gradually superseding the ancient forms of villon rials, and 
maravedis. 



GREEK COIXS, 




GREEK SILVER COINS. 




GREEK. COWER COINS. 



IN NUMBERS, COINS, AND ACCOUNTS. 181 

In Portugal and Brazil the milrei is the money of account, and 
is divided into 1,000 reis. 

A project for decimalising* the currency of Sweden and Norway 
has now been prepared by the authorities of these countries ; and 
Austria and Prussia have under consideration a plan for deci- 
malising 1 the currency of Germany. 

The decimal coinage and accountancy of Greece are established 
by a law of the 8th Feb. (O.S.) 1833. The unit is the drachma, 
which is divided into 100 lepta; and in these two denominations 
all accounts are kept. The sterling value of the drachma is about 
8|d. Six are equal to a Spanish dollar. 

The gold coins are of 40 and 20 drachmas ; 
The silver 5, 1, \ y and \ drachmas ; 
The copper 10, 5, 2, and 1 lepta ; 

Ten coins in all ; which are abundantly adequate to all purposes of 
currency. As these coins represent the latest application of a 
decimal system, fac similes are here given. 

The Canadas have proposed to adopt the American dollar as the 
integer of accounts, to be divided into 100 cents, according to 
the now universal usage of the United States of America, and 
which has been adopted by all the Central and South American 
States which were formerly the colonies of Spain. 

In China and Japan, an integer of account is the tael, or ounce 
of pure silver. It is divided into 1,000 cash == 100 candereens = 10 
mace. The sterling value of the tael is about 78d. 



182 THE DECIMAL SYSTEM, 



CHAPTER X. 

COLONIAL CURRENCY. 

In the British colonies, an arbitrary system has been introduced, of 
keeping all the public accounts in pounds, shillings, and pence 
sterling". No matter in what coins or currency the transactions of 
commerce really take place — no matter what may be the usages 
of merchants, or the habits of the people ; in utter disregard to the 
loss of revenue, to the difficulties of adjusting contracts, and to 
the innumerable inconveniences which are connected with two 
systems of accountancy in the same locality, English coins and 
English denominations have been adopted for all receipts and 
payments in the public departments. In countries where the 
pound sterling is unknown to commercial book-keeping, and where 
its value is subject to perpetual fluctuations, an unchangeable value 
has been affixed to it by royal proclamation. The errors of legis- 
lation may to a great extent be traced to ignorance or miscalculation 
of the powers of legislation, — and no error is more common than 
the supposition, that the exchangeable value of coins and currency 
can to any considerable extent be regulated by law. In Hong 
Kong, for example, her Majesty's orders in Council have pro- 
claimed that a Spanish pillar dollar and a dollar of Mexico 
shall have the same current value, — in the face of a notorious fact, 
that the Spanish dollar is habitually received at a premium of 
from 2 to 10 per cent, above the Mexican. A sovereign is 
ordered to pass for 4 dollars and 80 cents, though it sometimes 
(gold not being current in China) will not produce within 8 to 10 
per cent, of that value, and, in the ports of China, has been known 
to be at a discount of more than 20 per cent. The fluctuations of 
exchange are a necessary result of the fluctuations of supply 
and demand, and can no more be controlled by laws or ordinances 
than can the flux or reflux of the tides. A memorable instance of 
the blindness and impotency of legislation may be found in the 
resolution of Mr. Vansittart, affirmed by Parliament, that a bank- 
note and a shilling were equal in value to a guinea. This was but 
one form of averring that 21 shillings were equal in value to 28 ! 



IN NUMBERS, COINS, AND ACCOUNTS. 

In legislating- with reference to coinage and currency, n u^ 
never to be forgotten that the intrinsic value of a coin by no 
means establishes its exchangeable value. The relative values of 
different metals is notoriously subject to many fluctuations ; but, 
as regards coins of the same metal, habit often gives to coins of a 
particular mintage an unreal and almost capricious value. The 
Chinese are accustomed to make their larger payments in Sycee 
silver, a metal of great purity ; and the art of assaying metals is 
pretty extensively known. Hence the shroffs and money-dealers 
are quite aware of the fact, that the dollars of the different 
American States are intrinsically of nearly the same value as the 
Carolus or pillar dollar of Spain. Yet, in every one of the trading 
ports of China, the Spanish dollar invariably passes at a consider- 
able premium, sometimes as high as 10 per cent, upon the dollars 
of other countries ; and frequently, though the dollar of Spain has 
only 910 parts of 1,000 of pure metal, it is of equal value in weight 
to the Sycee silver, which averages 980 parts of pure metal to 
the 1,000. 

In 1825, the British Government determined to introduce 
British currency into all the colonies. The effects have been thus 
described : — 

" On the introduction of British silver coins into the colonies, 
instructions were given to the officers of the commissariat to grant 
bills upon her Majesty's treasury, at the rate of £100 for £103 (after- 
wards reduced to £101 10s.) of British silver. This measure, it was 
expected, would secure to the silver the same extrinsic value which it 
possessed in the mother country, and render it a more useful and 
convenient instrument of circulation than the degraded coins, or bits 
of coins, then circulating in the colonies. 

" These expectations were not realised. Not only was the con- 
current circulation of the Spanish dollar, and the British silver, 
rendered impossible by the erroneous adaptation to each other of 
the rates respectively assigned to them, but the free circulation of 
both was impeded by the high proportionate rate at which the gold 
coins of Spain were a legal tender." * 

* " Currency of British Colonies," pp. 54-5. The simple fact is, 
that there can be no adaptation of different currencies to one another, 
which will not be disturbed and overthrown by circumstances wholly 
beyond the control of legislation ; and it would be quite as reasonable 
to declare by Act of Parliament that so many cwts. of sugar should 



184 THE DECIMAL SYSTEM, 

In 1838, the arrangements of 1828 were superseded as regards 
the West India colonies. The 16 dollar piece (Spanish onza), 
generally known as the doubloon, was to be received for 64s., the 
dollar at 4s. 2d. This was deemed a " correct adjustment " of 
what can never be adjusted. In Jamaica, the legislature adapted 
the royal proclamation to the currency of their island by declar- 
ing that £166 13s. 4d. (Jamaica currency) should represent £100 
sterling, or, in other words, that the island currency should be- 
come sterling by a deduction of 40 per cent., and the gold* and 
silver coinage of Spain was regulated accordingly. 

In Guiana a decimal system was introduced in 1839, the 
accounts being kept in dollars and cents, which superseded the 
more ancient Dutch form of guilders, (= 20) stivers, (=16) pen- 
nings, and it was ordered that 3 guilders should represent 1 dollar 
currency. But whatever be the real value of the dollar, the public 
accounts reckon it at 4s. 2d., as in the other colonies. 

In the British provinces of North America, though accounts 
were kept and bargains made in pounds, shillings, and pence, the 
Spanish dollar was considered the principal measure of exchange, 
and the basis of money contracts, and it was rated at 4s. 6d., cor- 
responding with the value given to it by Sir Isaac Newton in 1717. 
But as, in common language, the dollar was divided into five 
shillings, the nominal par of exchange with England was com- 
puted by adding one-ninth to the valuation of the dollar ; so that 
£111$, or £111 2s. 2fd. (Halifax money), represented £100 ster- 
ling. The division of the dollar into shillings — no doubt to ac- 
commodate new moneys to old names — has prevailed in many parts 
of the world which have been colonised by Englishmen. In New 
England the dollar is six shillings ; in New York, eight shillings ; 
in Pennsylvania, seven shillings and sixpence; in Nova Scotia, 
five shillings ; in Upper Canada the shilling was valued at fourteen 
pence, and fifteen since 1836; in Lower Canada, it was thirteen 
pence; in Nova Scotia, fifteen pence. It would seem far more 
easy to introduce a new value into accounts than a new name into 
popular language. The sterling value of a dollar being estimated 
at 4s. 2d., the par of exchange should now be £120 Halifax cur- 
be received in exchange for so many pounds of wool, as to fix the 
relative values of different coins. The law says that the dollar in 
Hong Kong shall be 4s. 2d. ; at the time when I write (October 1853), 
5s. 7d. must be given for a dollar. 



IN NUMBERS, COINS, AND ACCOUNTS. 185 

rency for £100 sterling-, or 480 dollars at 4s. 2d. In Lower 
Canada the guinea had the official value of £l 3s. 4d. ; the 
British crown, 5s. 6d. ; the Spanish dollar, 5s. In Upper Canada 
the British crown was, by an act of 1827, rated at 5s. 9d. ; the 
Spanish and American dollar, at 5s. ; and the sovereign, in 1836, 
was made a legal tender at £1 4s. 4d., and the crown at 6s. ; but 
the dollar was made equal to 4s. 2d. sterling, and to 4s. sterling 
in English shillings. The effect of this arrangement was of 
course to drive out the coins to which a high value was given, and 
replace them by those of a low value. Twenty shillings were 
worth '£l 5s. currency, while the sovereign was represented by 
8d. less, or £1 4s. 4d., the par of exchange between Canada 
and Great Britain. Gold against gold is, in Canada currency, 
£121 13s. 4d. for £100 sterling: but, for silver against gold, 
£122 5s. 6d. 

The Nova Scotia currency was arranged in 1836 and 1842, by 
adding one-fourth to the pound sterling, and thus making £125 
currency to represent £100 sterling. The dollar was estimated at 
5s. 2£d., the crown at 6s. 3d., the doubloon at £4, agreeing with 
the proclamation of 1838. 

In New Brunswick the currency is, in sovereigns, at £1 4s. ; 
United States eagle, £2 10s. ; dollars at 5s. ; crowns at 6s., and 
the aliquot parts in proportion. Excepting that the eagle is 
overvalued — (with reference to the sovereign, it should represent 
£2 9s. 3d.) — the currency would be convertible into sterling by 
deducting one-sixth from any given amount. 

The Newfoundland currency is not regulated by enactment. 
The dollar passes for 5s., and as its supposed value is 4s. 4d., the 
par of exchange is called £115 7s. 8d. per £100 sterling ; but as 
the sterling value of the dollar is over-estimated, bills on England 
generally bear a premium of 4 to 6 per cent. The shilling fluc- 
tuates from Is. 2d. to Is. 3d. ; but the shifting value of the cur- 
rency often creates confusion and inconvenience. 

The currency in Bermuda previously to the proclamation of 
1838, which fixed the value of the doubloon at 64s., and the dollar 
at 4s. 2d. sterling, was most irregularly provided for. The Legis- 
lature decreed that £150 currency should represent £100 sterling; 
but the colonial treasury, requiring three dollars at 4s. 4d. for every 
pound sterling, exacted £153 16s. 7d. currency for every £100 
sterling ; while, among individuals, the shilling was paid at the 
rate of four to the dollar, so that £100 sterling was represented by 



186 THE DECIMAL SYSTEM, 

£166 13s. 4d. currency. In 1842, the English currency was es- 
tablished in all accounts, and all existing 1 contracts in the currency 
of the island were directed to be settled at the rate of £l§ cur- 
rency = £1 13s. 4d. per pound sterling. 

It will be seen that strange contradictions, anomalies, and 
absurdities are to be found in the systems of currency of the 
various British colonies, which must be all attributed to the desire 
of giving fixity to that which is in its very nature shifting. The 
perpetual fluctuations of foreign exchanges show that no laV can 
make them stationary. In fact it would be as reasonable to 
require by legislation that quicksilver should be made into solid 
bars for the everyday purposes of life, as to decree that the re- 
lative values of different objects shall be inexorably maintained. 

In the colony of Gibraltar, it has been directed, by an order in 
Council, dated 23rd March, 1845, that Spanish, Mexican, and 
South American dollars, shall be legal tenders at 4s. 2d. sterling 
each ; and that the gold doubloons, or 16 dollar pieces, of the same 
countries, shall pass for £3 6s. 8d. Commercial accounts are kept, 
and trading operations are carried on, in dollars and cents. The 
exchange value of the dollar is not, and cannot be fixed by autho- 
rity, except in the cases of public servants and others, who are not 
in a position to object to the conditions imposed by the Govern- 
ment. Complaints are frequently and naturally made by soldiers 
and others of the operation of the currency regulations, which 
subject a nominally fixed and certain pay to all the fluctuations of 
a varying exchange. 

In Malta, accounts are kept in scudi, tair, and grani — 

1 scudi = 12 tair = 240 grani. 

But the nominal currency is in pounds, shillings, and pence ster- 
ling, the pound being (by proclamation) 12 scudi, the shilling 
7 tair and 4 grani, the penny 12 grani. As, however, doubloons 
and dollars form the principal circulating medium in Malta, it 
was ordered, in 1845, that the Spanish or South American dollar 
should pass for 4s. 2d., or 30 tair, and the dollar of Sicily for 
4s., or 28 tair and 16 grani. The proclamations which regulate 
the currency are founded on the " intrinsic value " of the coins 
which are made a legal tender, in forgetfulness or inattention to 
the fact, that the intrinsic and exchangeable or commercial value 
are by no means identical, and cannot be made identical by the 
powers of legislation. The introduction of a decimal system into 



IN NUMBERS, COINS, AND ACCOUNTS. 187 

our currency and accounts will greatly assist the establishment of 
sound principles of exchange between the mother country and her 
dependencies. Where there is no currency but British coins, and 
while all accounts are kept in pounds sterling-, there is no difficulty 
in matters of exchange ; but wherever accounts are kept, and com- 
mercial transactions carried on, in other than British currency, that 
currency must fluctuate in exchangeable value, and there ought 
to be no attempt to give it a false and fictitious import. 

Were it only that the relative value of silver and gold is sub- 
ject to perpetual change, it would be obviously impossible for any 
country adopting a gold standard to fix an invariable rate of ex- 
change with a country having a silver standard ; but there can 
be no such invariable rate even between countries which have 
the same standard, inasmuch as the demand for money in a parti- 
cular place, or at a particular time, may increase or diminish its 
commercial value, without reference to its intrinsic value. 

On the western coast of Africa, accounts in the British posses- 
sions are generally kept in pounds, shillings, and pence ; but in 
consequence of a nominal value of 80s. per ounce given to gold 
dust, which is the principal article used for receipt and payment — 
which gold dust, when remitted to England, nets only about 
£3 12s. per ounce — the pound sterling is generally at a premium 
of about 11} per cent. — in other words, £100 currency, or 25 ounces 
of gold dust, are given for a bill upon London of £90 sterling. 
In the Gambia settlement, accounts are kept in current pounds, 
sterling pounds, or dollars and cents, according to the caprice 
of the merchant. 

In the island of St. Helena, the principal circulation is in 
doubloons, which are made legal tenders at 64s. sterling, and 
dollars of Spain, Mexico, and South America, at 4s. 2d. In the 
year 1843, when these rates were established, the commissariat 
called in all such money as had previously been current, and paid 
for them at the established rate. 

The currency of the Cape of Good Hope, from the period of 
its conquest by the British down to 1835, was an inconvertible 
paper, in which the rix-dollar, whose metallic value is. about 4s. 
sterling, was represented by an exchangeable value of Is. 6d. 
This was about the depreciation inherited from the time of the 
Dutch occupation, when the premium of bills on Holland was 
160 per cent. The public accounts are now kept in pounds, 
shillings, and pence sterling. Some private persons retain the 



Mauritius 
dollars. 



188 THE DECIMAL SYSTEM, 

ancient usage of reckoning in rix-dollars, skiUings, and stivers, 
whose values, reduced to British currency, are — 

1 Stiver Os. Ogd. 

6 Stivers = 1 Skilling . . Os. 2^d. 

1 Rix-Dollar = 8 Skillings . . Is. 6d. 

Fixed property is sold at auction in guilders, each equal to 6d. 
sterling. 

An order in Council of 1843 established the pound sterling as 
the money in which the public accounts are to be kept in the 
Mauritius, and gave to the coins ordinarily circulating in the 
colony the following values : — 

The E. I. C. Gold Mohur . . . 29s. 2d. 7"29J \ 

Napoleon of 20 francs . . .15s. lOd. 3'95| 

Dollars of Spain, Mexico, and South ) . „, - .. I ,„ . 
. . ^ ' * 4s. 2d. l-4i ) »* — *■ 

America ) 

E. I. Rupees Is. lOd. *45£ 

5 Francs 3s. lOd. -96|J 

But the inconvenience of these fractions has led the population to 
receive the rupees at the rate of two to the Mauritius dollar, so 
that its sterling value, in spite of the order in Council, is really 
3s. 8f d. instead of 4s. Thus British coins have been practically 
excluded, and rupees have become the main currency of the 
island. British coins bear a premium of from 4 to 6 per cent., 
and are used only in transactions with the British Government. 

Down to 1825 the island of Ceylon had a currency of its own, 
consisting principally of silver rix-dollars, and inconvertible 
Government paper rix-dollars, which usually circulated at a depre- 
ciation of about 10 per cent. Since 1825, the public accounts, by 
order in Council, are kept in sterling moneys, at 4s. 2d. the Spanish 
dollar, 2s. the Sicca rupee, and Is. lOd. the rupee of Madras and 
Bombay ; but in commercial transactions and accounts, the Sicca 
rupee supersedes the sterling currency, whose value is determined, 
not by the order in Council, but the more influential laws of supply 
and demand. Government paper circulates, which is convertible 
into such coins as have a legal value ; but the exchangeable value, 
which after all is the only real value, as far as receipts and pay- 
ments are concerned, seldom or never agrees with the proportions 
fixed by the ordinance, either as regards the proportions which one 
coin should bear to another, or any coin to the standard pound 
sterling. 



IN NUMBERS, COINS, AND ACCOUNTS. 189 

I have referred to Hong* Kong" as being an example of bad 
legislation in currency questions. No case more clearly, and, as 
far as the public service is concerned, more injuriously exhibits the 
absurdity of attempting to maintain, and the impossibility of 
maintaining, various coins at a fixed and invariable value, than is 
displayed in the legislation of the youngest of our colonial pos- 
sessions — the island of Hong Kong. The order in Council now in 
operation directs that the public accounts shall be kept in sterling 
money, but that all money contracts may be legally in gold 
mohurs, at the rate of 29s. 2d. ; in the dollars of Spain, Mexico, 
and South America, at 4s. 2d. ; and in rupees, at the rate of 2s. 
sterling ; and that the currency of England shall circulate in the 
island at its standard value. 

But as the monetary transactions of Hong Kong are small 
and those of the adjacent continent of China enormous, all the 
accounts, except those of public functionaries, are kept in Spanish 
dollars alone. 

Neither is gold as a metal, nor the sovereign as a coin, known 
or negotiable in China, except for the fluctuating value of the 
gold itself ; and in the ports of Spain, at Shanghai for example, 
the sovereign is sometimes at a discount of 22 per cent. 

Though the order in Council declares that the dollars of Spain, 
Mexico, and South America, shall represent the same value of 
4s. 2d. each, there is such a preference given to the Spanish 
dollar, which is the only coin by which the transactions of foreign 
commerce are regulated, that it bears a premium varying from 
2 to 15 per cent. The exchangeable value of rupees also fluctuates 
in a similar manner. As English coins are thus depreciated, there 
would be a loss either to the public service or to public servants to 
the extent of that depreciation, except that, where money is 
wanted for transmission to England, the exchange, which is 
almost invariably higher than the ordinance value, gives to the 
remitter the difference between the 4s. 2d. and the real rate of 
the exchange. But the Government loses all the benefits of the 
greater exchange value of the dollar. It has been stated, that the 
motive for giving the same legal value to the dollars of different 
nations, was the expectation that such assimilation of value in 
coins of the same intrinsic worth would lead to the removal of 
prejudices from the Chinese mind in favour of a particular coin. 
The result has proved the utter impotence of such legislation, as 
the difference between the exchangeable value of the dollars of 



190 THE DECIMAL SYSTEM, 

Spain and America has never been so great as since the existence 
of the order in Council which declared their values to be equal. 
Changes in language are slowly introduced. In the United States 
of America, we are told, "People are extremely reluctant to 
change their pounds and bushels, by which they are accustomed 
not only to measure, but to speak and think. Before our own 
revolution, we had the cumbrous nomenclature of pounds, shil- 
lings, and pence, brought from the mother country ; and although 
advantage was taken of our new political condition to inttoduce 
a decimal system of money, it required many years to accustom 
the people to the alteration. It was common to reduce dollars 
and cents to shillings and pence before they could be well appre- 
hended."* 

But a decimal system of book-keeping has gradually pene- 
trated into most of the British colonies, which the colonial 
ordinances have been made to subserve. Canada has lately 
emancipated herself from ancient trammels by adopting the deci- 
malised accountancy of the United States ; and there can be no 
doubt that the example of the mother country, in adopting a 
decimal system in coins, weights, and measures, would be speedily 
followed by all her dependent colonies. 

• Eckfeld and Dubois, p. 53. 



IN NUMBERS, COINS, AND ACCOUNTS. 191 



CHAPTER XL 

CHINESE NUMERALS AND THE ABACUS. 



The Chinese notation is thus given by Morrison (Diet. p. 466) ; 

jit 1 

+ 1 shit 10 

i5 2 pih 100 

4 3 tseen 1,000 

% 4 wan 10,000 

Ik 5 yih 100,000 

ijli 6 chaon 1,000,000 

& 7 king 10,000,000 

f & 8 kai 100,000,000 

£$ 9 tsze 1,000,000,000 

i% lOjang 10,000,000,000 

,yjt 11 kow 100,000,000,000 

tftfi 12 keen 1,000,000,000,000 

jp t 13 ching 10,000,000,000,000 

^ 14 toai 100,000,000,000,000 

<$^? 15 keit 1,000,000,000,000,000 

i#n# 16 hang ho sa, sands of the Hang river, 10,000,000,000,000,000 

ffili&k 17 o-sang-te, 100,000,000,000,000,000 

$$i& 18 na y ew ta " where is it ?" 1,000,000,000,000,000,000 

5H8&JL 19 put ko sze e, "inconceivable," 10,000,000,000,000,000,000 

<&§t:\ 20 wooleangso, "infinite number," 100,000,000,000,000,000,000 

He adds, that 321,987,654,321,987,654,321, in European nota- 
tion, carried, as above, to twenty-one places of figures, would 
amount to three hundred and twenty-one trillions, nine hundred 
and eighty-seven thousand six hundred and fifty-four billions, 
three hundred and twenty-one thousand nine hundred and 
eighty-seven millions, six hundred and fifty-four thousand three 
hundred and twenty-one. , 

Besides the notation )$$&% , advancing decimally as above, 



192 THE DECIMAL SYSTEM, 

some J3(3£\{f, advance by tens of thousands, as $ $ tz>)Ml 
ten thousand times ten thousand are called yih, ten yih are called 
chaon; and others, J"A kS if^fe advance by multiplying every 

number into itself, or squaring it, as S ^ q 1% ^ j§. E) ^ • 

Wan wan yue yih, yih yih yue chaon, — ten thousand times ten 
thousand are called yih, or million ; a million times a million 
are called chaon, or a billion. 

The Chinese have a complicated character to represent a 

cipher ^ , ling, all whose purposes are quite as efficiently 

answered by the dot or small circle of the Arabs. 

There is a form of digital decimals among the Chinese, by 
which they express from the left hand any number up to 100,000. 
The little finger exhibits the 9 digits, the second finger the tens, 
the hundreds are shown on the third, thousands on the fourth, and 
tens of thousands on the thumb. Every joint is reckoned three 
times, first by passing up the external side, then down the internal 
middle, and 'then down on the other side. And Dr. Peacock 
remarks, that the employment of the other hand might be used 
to extend much farther this system of numeration, by continuing 
the progression of decimal figures. This process will be easily 
understood by making the first joint of the little finger, reckoned 
from the outside, to represent 1, the second joint 2, the third 
joint 3 ; then taking the inside of the finger, the first joint 
represents 4, the second 5, the third 6 ; then, beginning again with 
the third joint outside, it counts for 7, the second joint for 8, and 
the first joint for 9,— exactly the same process being carried on 
for the tens with the joints of the ring finger, for the hundreds 
those of the middle finger, the thousands those of the fore finger, 
and the ten thousands those of the thumb. 

Like most other nations, the Chinese took their standard of 
measurement from the human body. They have a proverb which 
says, " The rule for pun, che, chih, tsin, chang, and jin,* is, 
taken from the human body." The foundation of the land 
measure is the kiver, or one step. A decimal system is found in 

* -A* &*&■$) f>§ These are various measures of length. 



IN NUMBERS, COINS, AND ACCOUNTS. 193 

the long measure, each of which is a decuple of the adjacent 
number. From the chang downwards, the measures descend in 
simple monosyllables to the 14th gradation, after which compound 
terms are used; at the 22nd gradation, the measure is called 
vacancy, — at the 23rd, absolute purity. Weights descend also 
from the leang, or ounce, — exactly the same signs being used as 

the measures, excepting that from the chan £ to the fun^y^ 
there are three grades— ^^^N c hih, tsin,fun,—m the measures, 
while in the weights there are only two from the f^|» leang, 
to the fun, j$g> , tseen, and fiy ,fun. The dry measure is also 
decimal, descending in eight gradations, from the shih /£J , or stone. 
The foundation of weights and measures in China is the 
musical reed called -gg/;|l§» , hwang chung, which was supposed 
to hold a certain number of grains. 100 grains placed cross- 
wise made the fcj{ , koo chih, the ancient cubit, equal to about 
10 inches; a hundred grains placed lengthways make the >%«^ , 
kin chih, or modern cubit. 

The abacus, or swan pan, « ilS" , which is sometimes called 
Jr nr>n 

the soo pan, 3^. jjj^ , is the instrument universally employed for 

account keeping throughout the Chinese dominions and their depen- 
dencies. Its value consists in the facilities it affords for decimal 
calculations. It is a table across which are fastened a succession 
of equidistant wires, upon which wires move balls, — the balls on 
every wire representing ten times the amount of the balls upon 
the wires beneath it, — that is to say, the balls on the lowest wires 
represent units ; those on the next above, tens ; the next hundreds, 
then thousands, then tens of thousands, and so on. The table is 
divided into two parts, upon one side of which are five balls, 
each representing one ; and on the other side are two balls, each 
representing 5. The number 1 is exhibited by moving one ball 
from the five towards the centre of the tables, 2 by moving 2, 
3 by moving 3, and 4 by moving 4, while 5 may be represented 

v 



CHINESE ABACUS WITH SUMS WORKED. 



a-*— am 
d— «— am 
b— *— am 
ih*=- am 
b-+— am 



b=*— aaxd 
b-«— am 
b=*— am 
d- —am 
b— = am 
b- —am 
B— =-axaa 

B OOXD 

d— —am 

b- am 

b- —one 

b — -am: 

rB— — am 

EHl-mii 



J<« g Mt WNM 



s.ttnce iJu'pmpM^wnw, « 



Hh 



J — Q 



u- 






am- 



-ill 



-imj 






-JUJ 
-33 



■0133 



J3> 



-ama 



-312] 



9 9,000/50 

2 2P0,0flP 

5" 54M0 

¥ 4JDM 



700 

to 



ysymv 



u- 



j — a 



3 — Q 



H — I 

n- 



n- 



3 — j 
3 — 4 



J> 



ao- 



j> 



-axm 

—003 

— a 



-am 
—cm 



D> 






3 — 



-am 



H2> 



7 loqm 

t 40,090 

S SfiOO 

2 260 

1 It 

S 3 



3 

n 



W52/53W 



THE DECIMAL 8YSTEM. 195 

either by moving the whole 5 balls from one side, or one Lull 
from the other. To work a sum in addition, whenever the 
amount reached is 10, a ball is added to the wire above ; — so, 
when the addition exceeds 100, one is added to the next wire, — 
so for 1000 to the next; and so onwards, a multiplication by 10 
being always represented. 

The word swan pan is composed of W (chuh), bamboo, 

whose abbreviation is «fc*« an ^ ^ r or li *«-, or -fe , being 

to play. 

There is a sentence in Chinese which everybody learns, as we 
learn the multiplication table : — 



+ 



Shit shit wei pih, 
. Shit pih wei trien, 

^ Shit trien wei wan, 

§ Shit wan wei yih, 

Shit yih wei chaon. 
That is :— 

Ten tens are a hundred, 
Ten hundreds a thousand, 
Ten thousands a wan = 10,000 

i Ten wans a yih = 100,000 

j& Ten yihs a chaon = 1,000,000 



4, 

ft 



At early morn, one of the first sounds heard in the shops of 
all the towns and cities of China, is the shaking and cleaning the 
swan pans preparatory to the business of the day. As, in Christian 
lands, the sound of the bells calls the worshippers to church — as, in 

n2 



196 THE DECIMAL SYSTEM, 

Mahomedan countries, the voice of the Muezzin from the mina- 
rets bidding the devout Mussulmans to prayers — so, in "the middle 
kingdom," the rattling of the abacus announces that another 
morning's labours are begun. 

With that instrument the Chinese youth has been as familiar 
as with his hemetrical classic, the first and most popular of his 
school-books. From it he has received the most correct impres- 
sions of the relations of numbers to one another ; and he^ has 
acquired the habit of moving the balls on the wires of his swan 
pan with considerable dexterity and rapidity. Wonderful are the 
ease and accuracy with which all calculations are made and 
recorded. In my own person I have had to settle a great variety 
of accounts with various classes of people in China, and I never 
remember to have detected an error ; and in cases where 
my reckoning has disagreed with that of the Chinese, I have 
invariably found that their amount was correct, and my own 
erroneous. In China it might almost be laid down as an axiom, 
that a mistake in an account is in itself strong evidence 
of fraudulent intention. I have compared my observations 
with those of persons of the longest and most extensive expe- 
rience as to the general correctness of Chinese accountancy, 
and my opinion has been fully confirmed, that among China- 
men intending to be honest, an error in reckoning is almost 
unknown. 

In the Chinese mind, the proportions and distances between 
units, tens, hundreds, thousands, tens of thousands, hundreds of 
thousands, and millions, as well as the decimal division of the 
unit into a thousand parts, are as clearly presented as to our 
minds the differences between one unit and another. The decimal 
scale is like the steps of a ladder, which the Chinese youth is 
taught to ascend and descend with inconceivable agility. His 
fingers play with the balls representing the various values of 
decimal notation, as a practised musician with the keys of a piano. 
The higher numbers being subjected to exactly the same process 
as the lower, present equally clear conceptions to his thoughts. 
According to our system of addition or subtraction, it is absolutely 
necessary that the work should begin with the units on the right 
hand, and so proceed through the higher denominations towards 
the left ; but with the abacus the process is carried on merely by 
adding or subtracting each denomination to or from its own, it 



IN NUMBERS, COINS, AND ACCOUNTS. 197 

being indifferent whether the operation is commenced from the 
higher or the lower denomination. 

The recommendations of the abacus are found in its simplicity, 
and the rapidity and ease with which calculations are made, and 
the security it gives to the accuracy of results. Where, as in most 
cases, two persons are interested in a calculation, there are three 
ways in which the operation may be performed — either by a 
simple abacus, where one party moves the balls along the 
wires, the operation being watched by the eye of the other ; 
or where a double abacus is used, by which the calculations 
can be simultaneously and separately carried on at the two 
ends ; or where each of the parties has a distinct abacus of his 
own. 

There is generally confidence enough in the person making 
the calculation, so that a second reckoning is scarcely ever deemed 
necessary as a check upon the first. The Chinese are trained 
from their infancy to the greatest agility in the use of their 
fingers. They are taught to use the chop-sticks, kmai tsze, to 
convey their food to their mouths ; and the beautiful specimens 
of carving in wood and ivory are remarkable evidence of their 
dexterity, to which the employment of the abacus in the ele- 
mentary schools essentially contributes. 

Whenever a servant in China comes to settle accounts with 
his master, he brings his swan pan with him; and I have invariably 
found, that as rapidly as I had noted down the items of an 
account, my servant had correctly added up all the amounts. 
My habit was fortnightly to settle my household accounts ; they 
comprised a great variety of matters, and I never recollect having 
detected an error in the calculations of my servants. Very 
frequently, in the multitudinous trifles which formed the items of 
account, there were differences between my reckonings and those 
of the Chinese ; but I do not recollect any instances in which re- 
examination did not prove me to have been in error ; and I always 
found the additions made quite as fast as I could run over the 
figures — in fact, so rapid is the motion of the balls upon the wires 
in the hands of a dexterous calculator, that the eye cannot follow 
the movements, and the operations appear rather like triumphs 
and tricks of legerdemain, than the exercise of a universally 
acquired habit — so universal, that it would be an opprobium not 
to possess it. 

The Abacus is frequently referred to by ancient authors. 



198 



THE DECIMAL SYSTEM, 



Horace speaks of boys going to school with the table and counters 
suspended on their left arm.* 



ROMAN ABACUS. 



(Ill 



9 9 9 



u 



cd». oo. d. x: i. Q 





There is an imperfect abacus sometimes used in our schools 
for teaching the multiplication table. It consists of 12 rods, on 
each of which are twelve moveable balls. A still simpler abacus 
is employed to teach the numeration table, which has only 6 wires, 
upon which a number of balls circulate. 

An abacus, but much less simple and efficient than the Chinese, 
is described by Dr. Peacock.f Counters were used for the pur- 



Quo pueri magnis e centurionibus orti, 
Laevo suspensi loculos tabulamque lacerto. 



t Pp. 409-10. 



Sat. 1 vi., p. 75. 



IN NUMBERS, COINS, AND ACCOUNTS. 



199 



Jiose of carrying on this process ; and as the whole partakes of a 
decimal character, the explanatory extract is here given at length. 

" They commenced by drawing seven lines with a piece of chalk, 
or other substance, on a table, board, or slate, or by a pen on paper ; the 
counters (which were usually of brass) on the lowest line represented 
units, on the next tens, and so on as far as a million on the last and 
uppermost line ; a counter placed between two lines was equivalent 
to five counters on the lower line of the two. Thus the disposition 

NOTATION. 



a — • 

• 

• — • — ■ 

• — •» 

• — • 



of counters in the annexed example represents the number 3,629,638 ; 
and it is clearly very easy to increase the number of lines, so as to 
comprehend any number that might be required to be expressed. 
"Addition. — Suppose it was required to add together 788 and 383, 



r~ r~" 

• ■••• ' • — 



express the numbers to be added in the two first columns. The sum 
of the counters on the lowest line is 6 ; write, therefore, 1 on that 
line in the third column ; carry one to the first space, which, added 
to the 1 already there, is equal to 1 on the second line ; place a 
counter there, and add all the counters on that line together, the sum 
is 7; leave, therefore, two counters on that line together, and pass 
one to the next space ; add the counters on that space together, 
which are three ; leave one there, and place one also on the next 
line j add all the counters on that line together, the sum is 6. Leave 



200 



THE DECIMAL SYSTEM, 



one counter, and pass another to the next space ; add all the counters 
on that space together, which are 2 ; leave no counter in the space, 
but pass one to the next, or fourth line ; we thus represent the sum, 
which is 1,171. 

"The principle of this operation is extremely simple; and the pro- 
cess itself, after a little practice, would clearly admit of being per- 
formed with great rapidity. In giving a scheme of this operation, 
we have made use of three columns ; but in practice no more would 
be required than are sufficient to represent the sums to be added, the 
counters on each line being removed as the addition proceeds,*and 
being replaced by the counters which are requisite to denote the sum. 

" Subtraction — We shall now proceed to a second example — 
namely, to subtract 682 from 1,375. Write the numbers in the first 



• 1 . 

• • 
• ■ ■ . • • 

• I ; . • 

l ■ ■ 1 m m • 



and second columns. The two counters on the last line have none to 
correspond to them in the minuend ; bring down the counter in the 
first space, and suppose it replaced by 5 counters ; take away two, 
and three remain on the lowest line of the remainder. Again the 
three counters on the second line must be subtracted from 7, (bringing 
down 5) ; and therefore leaving 4 on the second line of the remainder. 

" The counter on the second space has now no counter correspond- 
ing with it in the minuend ; remove one counter from the next line, 
and replace it by two counters in the next inferior space ; there will 
remain, therefore, one counter for that space in the remainder. 

" There is now one counter on the third line to subtract from two in 
the minuend, and there remains one for the remainder. The counter 
in the next space has nothing corresponding to it ; and we must, 
therefore, bring down the counter on the highest line and replace it by 
two counters in the space below it ; if one counter be subtracted 
from them, there will remain one, and the whole remainder will be 
693. 

" Recorde writes the smaller number in the first column, and com- 
mences the subtraction with the highest counters ; and very little 
consideration will show in what manner the operation must be per- 
formed, with such a change in the process. 

"Multiplication.— We shall now give an example of multiplica- 
tion ; and let it be proposed to multiply 2,457 by 43. 



IN NUMBERS, COINS, AND ACCOUNTS. 



201 



" Write the multiplicand in the first column, and the multiplier in 
the second ; multiply first by three, and write the product in the third 
column, and then by 4 in a superior place, and write the result in the 
fourth column ; add the numbers in these two columns together, and 
the sum is the product required. 



— ~\~ 11 i • — r 

j-i a — — e — 

• • • 

a — ■ 1 1 1 m l—a— » — 0- 

• 

0—0 — — 0-J ll m 0—0 

a • • • 

• — •— • — •— - L -L-«— ■ • — • — • 

• 

• — • L- ■ — • — • !■■_ • 1 1— • 



" Division. — We shall conclude with an example of division ; and let 
it be required to divide 12,832 by 608. 

" Write the dividend in the first column, and the divisor in the 
second, reserving the third for the quotient ; then, since 6 is con- 
tained twice in 12, in the line above that in which 6 is written, we 



~_i i i ~r— 

• ■ 

-0—0 — ■— 1— « 1 1—* 

-0— 0— 0— I L I I 



may put down 2, in the last line but one- in the column for the quo- 
tient; multiply 6 by 2, and subtract; there is no remainder; mul- 
tiply 8 by 2, and subtract 16 from the number expressed by the 
countersremaining in the dividend in the line above the last; first take 
one counter from the three in the third line, and two remain; next take 
6, which is done by taking 1 from the second line from the bottom, and 
bringing 1 from the third line, replacing it by 2 in the space below, 
and then subtracting one of them, thus leaving 67 in the remainder, 
to be denoted in the second and third lines and the spaces above 
them; the remaining two counters in the dividend are transferred to 
the corresponding line in the column for the first remainder; the 
operation is now repeated, the next figure in the quotient, as 1, being 



202 THE DECIMAL SYSTEM, 

written on the lowest line; it is now merely necessary to subtract the 
divisor from the first remainder, and we get 64 to the second and last 
remainder. It is evident that the same process may be repeated to any 
extent that may be required; and that the complication of the pro- 
cess as exhibited in'a scheme is much greater than in practice, when the 
dividend is replaced by the first remainder, and so on successively 
until the remainder is zero, or less than the divisor." 

There is an instrument frequently seen in the houses and 
buildings of China, called the Lines of Fohi, to which mysterious 
virtues are attached. The broken lines represent zero, entire line 



r^^l 



units ; and it will be seen, that taking the top line to represent 
digits, the second line ten, and the third hundreds, the result will 
be that the following numbers will be represented : — 

12 3 4 5 6 7 8_ 

— — — — 10 10 — — — — 10 10 

— — 100 100 100 100 

The Jesuits lauded this instrument as containing the elements 
nf all knowledge, and as a part of revelation from the greatest of 
sovereigns and philosophers, by which all the revolutions of the 
celestial orbs were to be calculated, and all the mysteries of nature 
developed and explained. But they do not give us the key to the 
mystery, or interpret the teachings of the oracle. 



IN NUMBERS, COINS, AND ACCOUNTS. 203 



CHAPTER XII. 



COINS, MEDALS, ETC. 



In sending forth a book connected with decimal coinage, it is 
scarcely fitting to pass over unnoticed that portion of the field of 
history which is associated with numismatic progress, — a topic 
in itself of remarkable interest, and boundless variety. 

The following are Larcher's observations in his notes to 
Herodotus, on the moneys of the ancients : — 

"'A<T0ev6«e Xpj7/ta<ri — were not rich in money. At the time 
of the siege of Troy, the use of money was unknown to the Greeks. 
Neither Homer nor Hesiod speak of gold or silver money ; they 
express the value of things by a certain number of sheep or oxen; 
they indicate the wealth of a man by the number of his flocks, and 
that of the country by the abundance of its pastures, and the 
quantity of its metals. In the camp before Troy, trade was car- 
ried on in kind, and not in money ; the wines of Lemnos were 
bought with copper, iron, skins, oxen, slaves, &c. — See the Iliad, 
book vii. verses 473 — 475. 

" Lucan (Pharsal., lib. vi. verse 402) attributes the invention 
of money to Itonus, king of Thessaly, and son of Deucalion ; 
whilst others ascribe it to Erichthonius, king of Athens, who was 
said to be the son of Vulcan, and who was brought up by the 
daughters of Cecrops. Aglaosthenes (in Jul. Pollux, lib. xi. 
cap. vi., segm. lxxxiii. pp. 1063, 1064) attributes the glory of 
this invention to the inhabitants of the island of Naxos. The most 
common opinion is, that Phidon, king of Argos, contemporary with 
Lycurgus and Iphitus, first brought money into use in the island 
of JEgina, to afford to the JEginetae the facility of subsisting by 
commerce, their island being remarkably barren. — See Strabo, 
book viii., p. 577. We have at the present day some coins oi 
this prince, (Sperling, de Nummis non cusis,) which represent 
on one side the species of buckler called by the Latins ' ancile,' 
and on the other a small pitcher of grapes, with the word *IAO 
Plutarch (in Lycurgo) informs us, that Lycurgus, with a totally 



204 THE DECIMAL SYSTEM, 

opposite design, and to alienate the Lacedaemonians from any com- 
merce with strangers, caused to be manufactured a coarse heavy 
coin, of iron, steeped in vinegar whilst red-hot, in order to render it 
unfit for any other use. l He wished,' says Justin, (lib. iii., cap. ii. 
p. 124,) ' that traffic should be carried on, not with money ,but by 
an exchange of merchandise ; Emi singula non pecunia, sed com- 
pensatione mercium jussit.' 

" According to Athenaeus (lib. vi., cap. iv.) neither gold nor 
silver was suffered at Lacedaemon. A certain number o# oxen 
was given to the widow of King Polydorus, who reigned about 130 
years after Lycurgus, for the purchase of her house. From the 
time that Lysander pillaged Athens, the Lacedaemonians began 
to have money, both of gold and silver ; but this was limited to 
the public transactions, the use of it being forbidden to private 
individuals, on pain of death. The form of the small money of the 
Greeks was very remarkable. According to Plutarch (in Lysan- 
dro, p. 442) they were small rods or pieces of iron, or copper, 
called * obeli,' (spits,) whence the word ' obolus ; ' and the name of 
1 dragma' (handful) was given to a piece of money of the value of 
six oboli, because six of these little rods or bars made a handful. 
— See Eustathius, in Iliad, p. 102. 

" Herodotus (lib. i., § 94) says, that the Lydians were the 
first who struck coins of gold and silver, and used them in com- 
merce. Zenophanes (in Julius Pollux, lib. ix., cap. vi.) says the 
same thing. But neither the one nor the other mentions at what 
precise period this occurred. 

" It does not appear that in the time of Croesus, the Lydians had 
any regular stamped coin. The treasures of that prince con- 
tained only gold and silver in the mass, either dust or ingots ; * for 
Herodotus (lib. vi., § 125) says that Alcmaeon, in his ample 
dress, large shoes, and even in his hair» carried away from the 
treasury of Crcesus, by permission of that prince, a complete load 
of gold dust. 

" Neither does it appear that, before the time of Darius, the son 
of Hystaspes, money was in use amongst the Persians. Darius 
regulated the tribute which he required of his subjects, and the 



* This does not amount to any proof, because these princes struck 
money only as it was needed, and kept their stock of gold bullion. 
Witness what he says, a few lines lower down, of Darius. 



IN NUMBERS, COINS, AND ACCOUNTS. 205 

weight in gold and silver was separately melted in earthen pots ; 
the pots were broken afterwards, and the metal cut from the mass 
as it was wanted." 

"Darius caused coins to be struck of the purest gold, which 
were called Darics. We do not learn that any king had done so 
before him. — See Herodotus, lib. iv. § 166. Polycritus (in 
Strabo, book xv., towards the end) and Diodorus Siculus (book 
xviii.) also assert, that the kings of Persia kept in their palace the 
produce of the tribute in ingots, coining but very little of it. 
Xerxes, according to Herodotus (bookix. § 40), left a considerable 
quantity of gold and silver, both in bars and money, with Mar- 
donius, whom he had commissioned to carry on the war in Greece ; 
so that, from the time of Darius, a vast number of Darics, pieces 
of money which bore the figure of an archer on the reverse, were 
seen in that country, as we find from Plutarch, in his Apoph- 
thegmata Laconica. 

" No ancient coins, either of the Lydians or the Persians, are 
now extant. The most ancient medals found in the cabinets of the 
collectors are Greek, and amongst the Greek coins the oldest are 
of the time of Alexander the Great. We must not, therefore, be 
surprised that Herodotus should say (book viii., § 137) that 
neither the people nor even the kings were rich in money in those 
ancient times ; but that their riches consisted in herds, &c. Gold 
and silver were formerly exceedingly scarce, both in Greece and 
the adjacent countries. Athenaeus (lib. vi. cap. v.) cites Anaxi- 
menes of Lampsacus, who says it was only on account of the 
scarcity of gold that the golden necklace of Eriphyle became so 
famous in Greece ; and that, at that time, a silver cup excited 
much admiration, as being a remarkable novelty. The same 
Athenaeus informs us, that Philip, king of Macedonia, whenever 
he retired to rest, put under his pillow a small gold cup that he 
had, and which he highly esteemed on account of the scarcity of 
that metal."* 

" Before the time of Gyges, king of Lydia, no other metal was 
seen in the temple of Delphi but copper ; and this not in the form 
of statues or other ornaments, but only in tripods. The Lacedae- 
monians were obliged to have recourse to Croesus for the gold 
of which they made their statue of Apollo on Mount Thornax, 
as we learn from Herodotus (book i. § 69.) Hiero, king of 

* Larcher's Notes on Herodotus, vol. ii. pp. 520-3. 



206 THE DECIMAL SYSTEM, 

Syracuse, diligently sought for gold to make a statue of Victory, 
and a tripod for the temple of Delphi : he at length found some 
at Corinth, in the house of a certain Architeles, who had accumu- 
lated it by purchasing it in small quantities, and who, beyond the 
weight required of him, made the king a present of a handful, 
in return for which Hiero sent him a vessel laden with corn."* 

There is no reason to suppose that the most ancient moneys 
referred to in the Old Testament were coins. As in China to this 
hour, so probably in the patriarchal times, pieces of gold and 
silver were weighed. Thus, when Abraham buys the field of 
Machpelah, we are informed of the proceedings in the bargain. 
Abraham says to Ephron, " I will give thee money for the field : 
— take it of me — and I will bury my dead there ;" and Ephron 
answers, " The land is worth four hundred shekels of silver 
— what is that between us? — take the place, and bury thy 
dead. So Abraham weighed to Ephron the silver — four hundred 
shekels of silver, as current among merchants."! Though there 
are among the Nineveh sculptures many representations of tribute 
bearers, and there can be no doubt that gold and silver almost 
invariably formed part of the spoils collected by ancient con- 
querors, there is no record of coined money in the remotest times 
of authentic history. 

There can be little doubt that payments in money by counting, 
or tale, would soon follow, or even be associated with the met- 
ing or weighing the precious metals, whose portableness and value 
made them the convenient instruments of barter or exchange. 
The natural process would be the employment of pieces of a 
similar weight to represent the same value ; but if such pieces 
had no stamped evidence of their being really of the value they 
represented, no payments would take place without the employ- 
ment of scales, or some other instruments to be used as a security 
against fraud or error. It was quite natural that for the public 
benefit the stamping of the coin should be a function of the 
highest authorities ; hence the right of coining would be assumed 
by sovereigns, by corporate bodies, or by influential persons, 
whose effigies, symbol, cipher, name, or other designation or de- 
vice, would obtain for the coin public appreciation and currency. 
Long after money ceases to circulate by weight, the name of the 

* Bellanger, cited in Larcher's Notes on Herodotus, vol. ii. p. 523. 
f Gen. xxiii. 13—16. 



IN NUMBERS, COINS, AND ACCOUNTS. 207 

weight will be retained, and the divisions of the weight will be- 
come the ordinary instruments of exchange. Thus in England 
the pound weight of sterling silver, which is the base and integer 
of our accountancy from the Anglo-Saxon times, was divided 
into 240 pennies, — no larger coin than a penny being in general 
circulation. 

Herodotus speaks of the Lydians as the first people who coined 
gold and silver — (see Larcher i., 94, 143). Other authorities ascribe 
the invention of coined money to the inhabitants of iEgina, under 
Pheidon, king of Argos, 895 years before the Christian era, and 
give to the Lydians the second rank. Then comes the coins of 
the Persian kings, beginning with Darius the First, about five cen- 
turies before Christ. It has been truly remarked that the coins of 
ancient nations are among the most interesting and the most valu- 
able of historical records ; and it is a matter of regret that metallic 
and enduring memorials are now confined to medals struck to com- 
memorate some particular event, whose number is very limited, 
and which obtained little circulation among the multitude. 
There is no reason why a metallic currency should not be the 
vehicle, as in times called classical, of much historical instruction. 
Why should not coins be made the recorders of interesting events ? 
Why should we not preserve, as of old, specimens of beautiful 
architecture, the originals of which time has not spared? Why not 
exhibit the progress of scientific discovery — the march of geographi- 
cal knowledge — the conquests of commerce and civilisation ? The 
Mint of the Augustan Age, has been well called the seat of 
Roman genius; and why should not the genius of Britain be 
installed where its works would assuredly be imperishable ?* 

The Jewish skekel was undoubtedly a weight, and not a coin. 
For the Medo-Persian coins, called Darics, the highest antiquity 
is claimed, as traceable to a period antecedent to the Macedonian 
conquest. It has been suggested that they were stamped upon 
pieces of metal current as money, inasmuch as the standard 
weight and value are strictly Grecian, though the devices are 
clearly Persian, and they are traceable to the middle of the fifth 
century before Christ, say b. c. 560.f 

The earliest coins are almost certainly those whicn have an 

* Consult Addison's Dialogues on the usefulness of ancient medals. 
t The perfect reverse is found in the coins of Gelo of Syracuse, b.c 
490. 



208 THE DECIMAL SYSTEM, 

impression on only one side. " The coins of the first four or five 
centuries of the art, so far as Greece and her immediate depen- 
dencies were concerned, hence present us with various stages from 
the one or more irregular hollows in place of the reverse, which 
may have been produced in the process of applying the die to a 
piece of metal fixed on a pointed surface (and, in some instances, 
by subsequent deterioration), until these hollows become gradu- 
ally replaced by the square, which is itself often found sub- di- 
vided, and taking a radiated or star-like appearance, (a circum- 
stance which could not have resulted from the mere process of 
striking, and which was therefore a step towards the purposes of 
the reverse)."* 

" The Roman imperial coins, on the other hand, in addition to 
their individual characters and interest, possess a general historical 
interest, in consequence of being, for the most part, struck to 
commemorate remarkable events. The difficulties of history are, 
consequently, cleared up by these contemporary records, which 
are so complete until the time of Constantine, that histories have 
been compiled from them. 

"They form the most authentic data in the Roman annals ; — the 
years of the consular and tribunitian offices held by the emperors, 
appearing in the front ; and, on the reverse, representations of the 
events whose dates are expressed on the other side. 

"The coins of Trajan, Hadrian, and the Antonines, are remark- 
able for this, and for the accurate data which are thereby supplied 
to history, by which the mistakes of chroniclers are often corrected. 
Among the description of events commemorated, are the departure 
of the emperors on expeditions ; their successes and returns ; their 
munificence to provinces wasted by famine; visits to the pro- 
vinces, and benefits conferred during such visits, &c, as in the case 
of Hadrian's visit to Britain, a.d. 121. 

" Conquered provinces are represented in a pleasing, and often 
poetical manner, as in the weeping * Judaea capta ' of the coins 
of Vespasian and Titus ; and universal peace is symbolised by the 
closed temple of Janus, on medals of Nero, with the legend, 'Pace 
Populo Romano terra, marique parta, Janum clusit.' "f 

* Cullismore's Proceedings of Numismatic Society, 1836-7, p. 11. 
f See a Commentary on the amphibious and universal character 
of Janus, as god of the land and sea, maintained by Sir W. Betham ; 









8 









IN NUMBERS, COINS, AND ACCOUNTS. 209 

The deaths and consecrations of emperors and empresses are 
depicted, and their virtues and other attributes beautifully per- 
sonified. Happiness, hope, abundance, security, piety, modesty, 
are poetically represented, together with the different countries of 
the world, and the provinces of the empire. 

Even naturalists may derive advantage from the study of these 
coins — those struck on the occasion of the secular games, as the 
coins of Philip, representing various animals, some of which ap- 
pear to be now unknown. 

Accurate portraits of persons of historical eminence are re- 
presented, so that busts may be referred to their owners by the 
agency of medals, together with representations of buildings now 
in ruins, as they originally stood — as triumphal arches, temples, 
&c. ; so that the poet, the painter, the sculptor, and the architect, 
derive no less advantage from the study than the historian.* 

It is remarkable that no reference to coined money is found 
in Egypt anterior to the times of the Ptolomies, notwithstanding 
the recorded riches of the Pharaohs and the great cities on the 
banks of the Nile. The hieroglyphic character for money is a 
loop. 

In earliest times gold had only a decuple value of silver, 
both among the Romans and the Greeks.f It was stamped gene- 
rally with the same devices as the silver; and in the coins 
struck by C. Claudius, Nero, and M. Livius Salinator, it bore the 
proportion of 12^ to 1. 

" The earliest representatives of value," says Mr. John 
Williams, "appear to have been pieces of the precious metals 
taken by weight, as bullion at the present day, and circulating as 
a medium of exchange. After a time an obvious improvement 
upon this system seems to have been made, as there is evidence 
to show that the pieces so circulating were of a certain definite 
weight, and also of an agreed degree of purity. This is evidently 
hinted at in the accounts of some early transactions, in which we 

or a complete description of these inestimable illustrations of history, 
chronologically arranged, in Captain Smyth's " Descriptive Catalogue 
of a Cabinet of Roman Imperial large Brass Medals," and in Mr. 
Akermann's "Descriptive Catalogue of Rare and Inedited Roman 
Coins." 

* Mr. Williams, in Proceedings of Numismatic Society, 1836-37, 
pp. 25, 41-42. f Evelyn, p. 7. 

o 



210 THE DECIMAL SYSTEM, 

read of ■ pieces of silver, such as are current with the merchant,' 
being employed as the medium of exchange. We also find that 
all the primary denominations of money, such as the shekel, 
drachma, as libralis, &c, were the names of weights employed by 
the several people who struck the money known by those appel- 
lations. Still, however, much inconvenience must ha?e been felt 
in the circulation of mere pieces of metal, in consequence of there 
being no guarantee that the weight and purity of the metal were 
such as had been thus generally agreed upon ; and this necessary 
security was obtained by the happy expedient of several states or 
cities issuing pieces of gold or silver, stamped with the known 
symbols of such states or cities, thus impressing them with their 
common seal, as it were, and affording the necessary public 
guarantee that the pieces thus stamped were precisely such as 
they professed to be. 

" This stamping of money appears to have first taken place 
in Greece, about the sixth or seventh century before the Christian 
era. The earliest coins are of an irregular globular form, having 
on one side one or more irregular cavities or indentations. These 
appear to have been produced by rude projections rising above 
the surface upon which the piece of metal was laid ; and these 
appear to have been the means by which it was firmly fixed, so as 
to enable the workman to stamp the upper side with the required 
symbol, which was evidently done by means of a hollow punch 
and a heavy hammer. After a time it was found that the desired 
impression might be produced without the metal being so firmly 
fixed; and thus we find the indentations gradually getting 
shallower, until at length a slightly indented square, is all that 
remains. This, in its turn, gradually gives place to the perfect 
reverse. At first this consists merely of a small figure, or figures' 
placed either in the centre of the square (as in an early coin of 
Syracuse), or in one or more of the divisions of the square as in 
some of the coins of ^Egina. A coin of Gnossus, in Crete, pre- 
sents us with four deep indentations, placed at a considerable 
distance from each other, alternating with which are portions of 
the Cretan Labyrinth, and in the centre is the minotaur, figured 
as a human figure with the head of a bull. This filling up of the 
indentations, and substitution of the square, appears to have 
taken place between the time of the invention of coinage and the 
reign of Alexander I. of Macedon, b.c 497 to 454, as we have 
coins of this monarch having the shallow square, with the name 



GO 

i— i 

© 

o 

« 
H 
W 

O 







ANCIENT ROMAN COINS.— Plate III. 





Fig. a-SKMis. 




k 




Fig. 9.— Tiiiexs. 





Fig. 13.— Thtess. 



IN NUMBERS, COINS, AND ACCOUNTS. 211 

'Alexander' surrounding it. The square finally disappears in 
the reign of Amyntas II., b.c. 397 to 371. From this period the 
Greek coinage gradually improves in workmanship, until at length 
they present those beautiful specimens of workmanship which, 
although they may have been equalled, have certainly never been 
surpassed, even in modern times. 

"The figures 1, 2, 3, 4, represent Greek coins of the earliest 
kind ; 5 is a Persian daric, which has also the irregular hollow, 
but appears from the workmanship to be of later date ; 6 is a coin 
of iEgina, also of much later date, shewing the indented square, 
with letters and figures in the divisions of the square. 

" The Roman coinage," continues Mr. Williams, " appears to 
have originated in the as, a copper piece weighing twelve ounces. 
The pieces of the most common occurrence have on their obverse 
the double head of Janus, and on the reverse the prow of a ship. 
Others, as in the specimen represented in Fig. 7, have on 
them the head of Rome and a Bull, with the word Roma. The 
divisions of the as, were the semis, or half of six ounces, marked 
S. ; the quincunx, or piece of five ounces ; the triens, of four ; 
the quadrans, of three ; the sextans, of two ; and the uncia, of one 
ounce. These have on them dots or pellets expressing the num- 
ber of ounces contained in them individually. There were also 
multiples of the as, as high as the dicussis, or piece of ten ases. 
The as and its parts originally weighed as much as was expressed 
upon them ; but they gradually decreased in weight, until, at the time 
of the second Punic war, the as was reduced to only half an ounce. 
This depreciation in value, and consequently in size, may be ex- 
emplified by a comparison of Figs. 9 and 13, representing the 
triens or piece of four ounces, at different periods. Figs. 1 1 and 
14 show the sextans, and Figs. 12 and 15 the uncia of ancient and 
more modern times, and thus the as and its parts became of a 
merely nominal value. 

As these heavy pieces must have been very inconvenient in their 
use before their reduction in weight, silver appears to have been 
soon substituted for them, and the denarius, or silver piece origi- 
nally of the value of 10 ases, and afterwards of 16, became the 
most common representative of value ; this piece is frequently 
marked X. The quinarius, or victoriatus, which was the half of 
the denarius, and marked V, to show it was of the value of five 
ases, also occurs. These are represented in Figs. 17 and 18. The 
sestertius, or fourth of a denarius, equal in value to two and a 



212 THE DECIMAL SYSTEM, 

half ases, was also a silver coin in common use, and formed the 
general unit of value in speaking of money. Thus a person was 
said to have died worth so many sesterces, &c. These, perhaps, are 
the nearest approach to the decimal division among the ancient 
coins, — there being nothing like it in the valuations of the 
Greek coins. The former of these, with the exception of the 
lepton and the tetrobolon, were halves of the next higher 
denomination ; of the latter of these, seven made a chalcos, and 
one and a-half tetroboloi made a drachma; all the others, 
to the tetradrachma, increased by doubling. In like manner, the 
later Roman coins, from the teruncius to the denarius, were in- 
creased by doubling the preceding denomination, with the excep- 
tion of the sestertius, which was of the value of two and a-half 
ases. In reckoning Hebrew money, 50 shekels made a maneh, and 
'50 manehs a talent. These last, however, were only nominal coins, 
and I cannot now refer to the values of the divisions of the shekel 
(which formed the general currency of the Jewish nation), and 
consequently am unable to say whether they conform to the de- 
cimal system or not." 

I shall conclude this chapter by some amusing examples of 
the manner in Which coins and medals have been employed, and 
in which they serve as curious mirrors of public feeling, and as 
permanent records of transitory passions. 

There is a medal coined in the time of Joseph of Austria, bear- 
ing the inscription 

" Josephus Imperator regnat amore et timore, facit mdccv. 
(The Emperor Joseph reigns by love and fear— which makes mdccv.) 

On the reverse is a curious cabalistic interpretation, thus 
given : — 







CABBAL-fi 


CLAVIS. 




A 1 




G 7 


N 40 


T 100 


B 2 




H 8 


O 50 


V 200 


C 3 




I 9 


P 60 


W300 


D 4 




K10 


Q 70 


X 400 


E 5 




L20 


R 80 


Y 500 


F 6 




M30 


S 90 


Z 600 


The exergue 


has— 









ANCIENT ROMAN COINS.— Plate IT. 





Fig. 10 — QlJADRANS. 




Fig. 11— Sextans. 




Fig. 14— Sextans. 



IN NUMBERS, COINS, AND ACCOUNTS. 213 

" Sit ineffabilis, sit innumerabilis Austria) gloria." 
(Ineffable and innumerable be Austria's glory.) 



1 


9 


I 


9 


R 80 


A 1 


T 100 


() 


50 


M 


30 


E 5 


M 30 


I 9 


s 


90 


P 


60 


G 7 


O 60 


M 30 


E 


5 


E 


5 


N 40 


R 80 


U 60 


E 


60 


R 


80 


A 1 


E 5 


R 80 


H 


8 


A 


1 


T 100 


E 5 


E 6 


11 


200 


T 


100 


. 


T 100 




B 


90 


O 


50- 


233 





274 







R 


80 




271 


271 




612 




415 






233 
415 
512 



1705 

The date of the reform of the calendar in 1700, is curiously 
and variously recorded in many medals of the time. 
One has — 

"GereChtes Lobopfer Denk MahL." 
(The record of merited gratitude.) mdcll. 

Another — 

" GeenDerten CaLenDers DenkzahL." dddcll. 
(In remembrance of the reformation of the Calendar.) 
One has — 

" Hoert doch, wunder ! im Jahr mdcc. wusten de leuthe nicbt 
wie alt sie waren." 

(Listen to a wonder ! In the year 1700 people did not know how 
old they were.) 

One medal portrays a boy asking an old man his age ; and the 
answer is Nescio. 
Another has — 

* Wo sind wir f" 

(Where are we?) 
Another — 

" Ey was wunder! 
mdcc sind de noch nicht herunter • 
Wers nicht glaubet lieber herr 
Bleibt ein 99 er."' 



214 • THE DECIMAL SYSTEM. 

What a wonder ! 
mdcc. has not knock'd under! 
Who won't believe it, my dear sir, 
Is a 99-er. (Is a nine and ninetyer.) 

There is a medal struck at Ostend, one side of which exhibits 
a map of the neighbourhood of Helvoetsluys, and the other a battle 
between the Spaniards and the Flemings at the taking of Ostend, 
with a Greek inscription — 

XPY2EA XAAKEIQN. 

"Gold for copper;" * and in Latin this chronogram — 

* Itane fLanDbIaM LIbebas Ibeb ?" f 

The large letters exhibiting the date MDLLHII. 
Another has, to celebrate the peace of 1678: — 

"A DoMlNO VeNIENS POPVLIs PAX L.ETA BEFVLgET.J" 

Where, as is generally sought to be accomplished, all the numeral 
letters are fixed, on to exhibit the date. 

There is a medal of William III. containing the names of all 
British sovereigns, with the date of their succession to the throne, 
and that of their deaths, from Egbert a.d. 801, with this inscrip- 
tion in Dutch : — 

" These clomb to the throne 
With sceptre and crown 
But none were more glorious, 
And none more victorious, 
That ever we heard, 
Than William the Third." 

At the rupture of the treaty of Ryswyk— 

" Auwey ! der fried hat shon en loch 1702." 
(Alas! there is already a hole in the peace.) 

Reverse : — 

"Auwey! auwey! auwey! auwey! . 
Ryswikscher Fried is gar entzwei." 
(O woe! O woe! O woe! O woe! 
The Ryswyk peace is torn in two.") 

* Iliad vi., 236. 

t Is it thus, Spaniard! thou freest Flanders? 

X Peace, which is the gift of heaven, brings gladness to the people. 



APPENDIX. 



APPENDIX. 



The immense majority of intelligent and thoughtful opinions have heen 
expressed in favour of the decimal system as proposed by the parliamentary 
committee, which leaves the pound sterling unchanged, as the integer and basis 
of our currency and accountancy, and divides it simply into one thousand 
parts. A plan supported by Mr. Theodore Rathbone has, however, found some 
favour. He would reduce the value of the shilling to tenpence, and make 
the said new shilling to consist of ten pennies — the groundwork of a new 
decimal coinage. I have been favoured with a paper by a gentleman who 
has given much attention to the subject, and which so completely demolishes 
Mr. Rathbone's scheme, that I venture to insert it entire. 

Observations on Mr. Theodore Rathbone's Pamphlet on 
"Decimal Coinage." 

Mr. Rathbone and the committee of the House of Commons are agreed in 
giving a preference to the decimal system over cur present denominations of 
account. They are agreed also in their estimate of the nature of the problem 
that has to be solved, in order to introduce that system into our currency; for 
they both consider it a matter of primary importance to effect the change in 
such a manner as to create the least possible disturbance in the transition 
from one system to the other ; but they differ as to the means by which 
this object should be effected. 

The committee, adopting the opinion of the witnesses of greatest weight 
and reputation examined before them, recommend that the unit of account 
which represents our standard of value, and governs all existing contracts, 
should be preserved, and that the decimal system should be applied to the 
subdivisions of the pound sterling. In recommending this course, they have 
followed the example of the two greatest countries, France and the United 
States, in which a decimal coinage has been established. In France, owing 
to an over- valuation of silver by the Mint regulations of the country, the 
,franc superseded the gold coins, and became the standard of value. The 
currency of France was, therefore, decimalised by dividing the franc into 
one hundred parts. In the United States, when they were yet colonies 
of Great Britain, the dollar had been over-valued for circulation, and had 
superseded all other coins, though the denominations of pounds, shillings, 



218 APPENDIX. 

and pence were long retained. In settling the currency of the country, 
therefore, the dollar, as the practical standard to which all contracts re- 
ferred, was adopted as the unit of account, and the decimal system was 
established by subdividing that coin into cents. In Great Britain, after the 
standard had long oscillated, as in other countries, between gold and silver, 
the former gained the preference, and the sovereign has been established as 
the unit. It is proposed, therefore, to decimalise our currency, by subdi- 
viding the sovereign into a thousand parts, by a gradation of tenths, 
viz., sovereigns, florins, cents, and mils. * 

Mr. Rathbone considers that the system proposed would be "clumsy, 
inconvenient, and unsound." He objects to the names of the new coins pro- 
posed to be introduced, and he dwells upon, and, to some extent, exaggerates 
the difficulties of issuing money of the new denominations in exchange for 
that which now circulates. When we bear in mind the ease with which an 
entirely new silver coinage was put into circulation after the Act of 1816, the 
partial change which is now contemplated cannot be considered a very formid- 
able operation ; and it should be borne in mind that the withdrawal of none 
of the existing coins would be absolutely necessary, because, previously to 
the introduction of the proposed decimal system, the silver coins now in 
circulation could be adjusted to the system by giving them new denomi- 
nations, and a new value could be given to the copper coins now current, as 
was done in the case of the pence of Ireland, when the currency of that 
country was changed. Mr. Rathbone's greatest objection, however, to the 
proposed scheme is, that it would operate with " extreme injury and in- 
justice to the poorer classes," by sacrificing " our copper coin — that useful, 
precious penny" which, in his imagination, " happily coincides so accu- 
rately and harmonises so well with the great features of the foreign decimal 
systems." 

The scheme which he proposes to substitute for that suggested by the 
committee is based on the penny, and he thinks to accomplish his object 
without " the sacrifice or alteration of any one existing money of account, 
but our duodecimal shilling," without actually requiring "the issue of one 
single new coin," until quite convenient. He characterises his plan as one 
which " would rapidly and insensibly conduct and initiate all classes into 
the current ready use, not only of a decimal system, but of the only pure 
and perfect decimal system of numeration." 

The system which he adopts as his model is the French system, which he 
prefers " because it is thoroughly decimal," and his plan is simply to sub- 
stitute for the shilling a coin of ten pence, which he proposes to call a franc, 
and to divide the halfpenny into five parts, each, of course, the cent of 
the franc. 

We might ask, whether it is conceivable that the many able, practical 
men, who have long laboured for the establishment of a decimal system of 
currency, would not have thrown pence tables, and all legal definitions to 



APPENDIX. 219 

the winds, in the management of their own accounts, if so simple an < x- 
pedient as that proposed by Mr. Rathbone would have worked ? But let 
that pass. 

Let us examine his project under its several recommendations. 

lstly. That it will preserve to the poor man his penny, as " his landmark 
and integer." 

2ndly. That it is not only thoroughly decimal, but the only pure and 
perfect decimal system of numeration. 

3rdly. That it will establish entire harmony, and instant, easy converti- 
bility as regards all foreign coinage and accounts whatever. 

I. — Is it a fact that the penny is the poor man's integer and standard 
of value ? The penny is known to him as the subdivision of the shilling. 
If it were not so, if his notions of value were confined to pence and half- 
pence, there would be no advantage to him in attempting to facilitate his 
computations by giving him a decimal system. It would, under such a 
supposition, be the same to him whether the penny represented the decimal, 
duodecimal, or any other fraction of a higher coin. Leave him his integer, 
and he will be contented. But the poorest labourer has a higher conception 
of value. His wages or earnings are usually so many shillings a day or 
week. His rent, likewise, is computed in weekly payments of shillings. 
His deposits in the savings'-bank are accumulations of shillings. And he 
knows full well that twenty of those shillings make a pound, though he 
may not be much used to reckon by pounds. His pence are the change of 
his shilling. The shilling is in his eyes much what the pound is to the man 
of wealth ; pounds are to him what fifties and hundreds of pounds are to 
the latter. 

It is easy to raise a cry by the confident assumption of a proposition, 
especially when it is brought forward under the amiable guise of protecting 
the poor. But the shilling has as many claims, from associations of olden 
time and from positive utility, as the penny. As it is the greater value to 
which the lesser must be referred, even by the poor man, it has more preten- 
sions to be considered " his landmark and integer ; " and it may be asserted, 
with at least as much claim to acceptance as the confident assumption in 
this pamphlet in favour of the penny, that the sacrifice of that " useful, 
precious " shilling, for the purpose of preserving the pence unchanged, 
would operate as no boon to the poor man. The subdivision of the shilling 
may be altered, as it has been altered before, without entailing more than a 
temporary inconvenience; but take away the shilling, and you- deprive the 
poor man of his practical standard of value. More serious alterations of 
the value of the penny than that now proposed have been carried out, 
without much difficulty, in Ireland and the Isle of Man, amongst a people 
more rude and uninformed than the English. Why should we apprehend 
such serious difficulty here ? 



220 APPENDIX. 

And it may be urged, that an alteration which increases the number of 
pieces into which a coin is subdivided, will generally operate favourably, 
rather than otherwise, to the purchaser in retail dealings. In the rude ad- 
justment of prices which must to a certain extent attend the division of 
commodities into small quantities, the portion sold for a coin of a low de- 
nomination must often be overpriced: ordinary weights and measures of 
value cannot accommodate themselves with exactness to such minute 
divisions; the seller will take care to be on the safe side, and some 
articles, not admitting of subdivision, must be sold for the smallest 
coin in ordinary use, whatever its value may be. A man who buys 
a halfp'orth of tobacco now, will probably get as much (or so nearly 
the same quantity as to make the difference hardly perceptible) when 
there are twenty-five instead of twenty-four halfpence to the shilling, and 
he will have twelve pence (or forty-eight mils) remaining in his pocket. 
If eggs are now sold at a halfpenny each, they must still be sold for a half- 
penny (or two mills) when the value of the coin is altered, and the pur- 
chaser will get twenty-five instead of twenty-four for a shilling. These 
matters will soon adjust themselves in the huckstering of the market. 

II. — But allowing, for the sake of argument, that the one great object is 
to preserve the penny at its present value for the poor man's benefit, let us see 
how this great boon is to be accomplished, and how, at the same time, all 
classes are to obtain the benefit of a pure and perfect decimal system of 
numeration, " without the sacrifice or alteration of any one existing 
money of account, except our duodecimal shilling." 

It is not easy to understand in what light the French system can 
be considered more thoroughly decimal than that proposed by the com- 
mittee. It is the beauty of decimals that they admit of being carried to 
any amount, in either direction, without a break in the calculation. Decimals 
of pounds are as thoroughly decimal as decimals of francs. It is a question 
of convenience where the decimal point should be put to mark the termi- 
nation of the decimal fractions and the commencement of the unit. The 
French wisely adopted the franc as their integer, because it accorded with 
the practical standard of value already in use. The sous, into which the 
franc or livre was subdivided, were convertible into decimals by extension 
of their terms, without any alteration of their current value. Circumstances 
thus afforded the framers of the French system the opportunity, which Mr. 
Rathbone imagines he has found in our case, of establishing a decimal 
system of computation without an alteration* of the coins. But, apart from 
the considerations of practical convenience which presented themselves, there 
is nothing in the scheme which subdivides the smallest copper coin into five 
nominal parts, and thereby multiplies the ciphers by which small values 

• The trifling alteration which was made in the silver coin was immaterial to the 
introduction of the system. 



APPENDIX. 221 

are expressed, that in point of principle gives it any special claim f I r 
imitation. On the other hand, it is an objection felt by many to the French 
system, that in large sums it involves an inconvenient number of cipher-. 
and there can be little doubt that to English apprehensions the expression of 
sums in pounds sterling, to which we are used, gives a clearer notion of 
value than the multiplicity of francs. We shall act wisely if, instead of 
imitating the details of the French system, which is inapplicable to our 
existing coins, we adopt the principles upon which they acted, and adhere 
to what we have, so far as it can be made subservient to a thoroughly 
decimal scale. Examples may be found in which the nominal unit or 
integer of account has been altered, as in the case of the United States, and 
in that of our Irish Currency, for the purpose of fitting it to the practical 
standard of value to which contracts referred. Examples may also be found 
of alterations of coins, as in the case of the abolition of our guinea, in order 
to fit them to existing denominations of account. But it would be a new 
thing to set at nought all existing tests, whether of money or account, by 
which value has been habitually ascertained, in order to substitute a fancied 
system of perfection, in regard to which it would be difficult to find agree- 
ment among any body of men. A change of that character would create 
such an utter derangement of all existing accounts, and such confusion in 
adjusting pecuniary engagements, that, great as are the advantages of a 
decimal system of numeration, the ultimate convenience would be too dearly 
purchased, if it could only be acquired by a revolution so subversive. 

The pound sterling, represented by the gold sovereign, is the measure of 
value by which every contract in this country, from the highest to the 
lowest sum, is ascertained. It is incumbent on those who advocate a theo- 
retical change, to show a reason for it. The pound is as susceptible of a 
thoroughly decimal subdivision as any smaller coin. The subdivision into 
florins, cents, and mils is not essential to the proposed system : it was sug- 
gested with the view of adjusting the scheme to current coins and facilitating 
its use to persons who are inapt in the decimal mode of computation ; but, 
for calculations, pounds, and their thousandths, would be all that would be 
required; and, if it were desirable, the decimal scale could be carried to a 
lower fraction without inconvenience. 

But we must bear in mind that Mr. Rathbone promises to effect his 
object without the alteration of a single coin. Our coins are numerous, but 
we find at the extremes the penny and the pound, to one or other of which 
all the intermediate coins refer. If, therefore, we are to obtain a thorough 
decimal scale without alteration of a single coin, it can only be effected by 
some scheme which would convert the pound into a decimal multiple of the 
existing penny, or the penny into a decimal divisor of the pound. Our 
existing penny is a fractional coin, which represents one-twelfth of a 
shilling or one-two-hundred-and-fortieth of a pound. Any one acquaint .1 
with the common rules of arithmetic can satisfy himself that these fractions 



222 APPENDIX. 

cannot be converted into finite decimals, and of course it follows that no 
process of subdivision or combination can bring out a different result. The 
problem of converting a recurring into a finite decimal is startling to 
ordinary apprehensions, yet this is the problem which, if his proposition 
means anything, Mr. Rathbone undertakes to solve. 

Let us look then a little closer into his scheme, and, allowing again for 
the sake of argument that the French system is the best, let us examine the 
process by which Mr. Rathbone proposes to adapt it to our existing coins. 

When he states, that " the course of proceeding would be simply, as the 
first great step, to make pounds, francs, and pence, instead of pounds, 
shillings, and pence," it would appear that the pound is to be retained in 
this system ; but when he proceeds to explain that " in all sums whatever 
vp to the pound sterling, the dot dividing, or the column in account 
separating the two first items— pence and ten pences, tens and hundreds — 
would present the ordinary figures of account, and at the same time the 
amount decimally stated in the most pure and perfect form of decimals," 
a doubt arises as to his treatment of our great " land-mark and integer," 
the pound. How is it to be brought into the system of account ? Is its 
value to be altered ? No. The sovereign is to be excluded from the decimal 
scale, but retained as the standard of value. "The old pound sterling," 
Mr. Rathbone says, "would retain its time-honoured useful place in all 
such large amounts as the national debt and the public accounts, and would 
be ever at hand and most easily accessible to state all large amounts of 
figures, &c." But what of smaller amounts of figures? "What of rents, 
salaries, and other innumerable contracts expressed in pounds ? How is a 
system to be worked which goes up to the pound, but does not include it, 
and yet retains it as a standard of value? But it is to be "at hand," though 
unseen, behind the scenes. This is verily the play of Hamlet, omitting the 
character of the Prince of Denmark. 

If Mr. Rathbone had not said that he intended his scheme for all classes, 
it might have been supposed that he contemplated two systems— a decimal 
one for the poor, who do not want it ; a more complicated one for the mer- 
cantile classes and accountants, to whom the decimal scale would be more 
especially beneficial. But no ; it is clear that he proposes to substitute, for 
our present denominations of pounds, shillings, and pence, a scale by which 
the pound will be divided into twenty-four francs, which latter coins will 
alone be decimalised. He is even conscious of the defect of his system, for 
he admits his treatment of the pound, his omission of the Prince of Den- 
mark, to be an " imperfection and irregularity ; " and yet, notwithstanding 
this admission, he has the hardihood to maintain that his plan gives " a 
pure and perfect decimal system of numeration," and he sets at scorn the 
scheme of the committee — which is really decimal— and characterises it as 
" clumsy, inconvenient, and unsound." 

III.— But we have yet another promised benefit to consider. We are told 



APPENDIX. 223 

that "a vast and overwhelming portion of the civilised world would he at once 
financially united, as it were," by the adoption of the scheme which i.s to har- 
monise with "all foreign coinage and accounts whatever." Let us see. An«l let 
us again, for the sake of argument, assume that Mr. Rathbone's qua-i <1. ( imal 
scale could be worked in accounts, and, consequently, in calculations re- 
lating to the foreign exchanges. First, he conceives that the franc of ten 
pence would exactly correspond with the French franc, and the half- 
penny with the French sou of five centimes. He takes the vulgar ap- 
proximate computation of the franc at ten pence, and adopts it without 
inquiry or investigation. The weekly quotations of the French exchanges 
in the City article of The Times, which can hardly have escaped the notice 
of a man so prompt to dissect, might have taught him a better lesson as to 
the real comparative value of the French franc in relation to our money. 

The florin piece of twenty pence will, according to Mr. Rathbone, exactly 
correspond with the Dutch florin. It cannot be supposed that a man so 
conversant with the names of coins, and who writes so confidently on the 
subject, can be ignorant of the laws which regulate their value in exchange. 
If he had given himself time to reflect, he must have been aware that there 
can be no real par of exchange between two countries, one of which has a gold 
and the other a silver standard of value ; and that the relative price of the 
two descriptions of coins will fluctuate according to the production of one 
or other of the precious metals, and the demand for them, either for coinage 
or other purposes. Three years ago twenty pence might have been taken 
fairly as the average and approximate value of the Dutch florin. Now it 
is much higher. 

The same observation applies to the silver dollar. Mr. Rathbone adopts 
some crude statements from the evidence of General Pasley before the 
Decimal Coinage Committee, and fixes the value of the dollar immutably 
at fifty pence. Mexican dollars were sold readily in London the other day 
at the rate of sixty-one pence the ounce, which gives a value of more than 
fifty-two pence to each dollar. 

He talks of the dollar of the United States, evidently in ignorance of the 
change which was made in the Mint law of that country in 1834, and which 
based its currency practically on a gold standard. The gold eagle, or ten 
dollar piece of the United States, is worth about two pounds one shilling of 
our money, which gives forty-nine pence and a small fraction to the gold 
dollar. 

There cannot, in truth, be a greater mistake than to suppose that a mere 
similarity in denominations of account can have the slightest effect upon 
the calculations of foreign exchanges. "Without identity of standards of 
value the use of common denominations creates confusion instead of afford- 
ing facility for computations. We have an example of this in our North 
American Colonies, in all of which our denominations of pounds, shillings, 
and pence prevail, but in which the pound currency differs from the pound 



224 APPENDIX. 

sterling, and differs in each colony from its neighbour. When a sum is 
mentioned in any colonial account, it is always a matter of calculation to 
ascertain what value the pound represents. 

There are many descriptions of dollars current in the world. The old 
Spanish pillar dollar, which has a peculiar value in China, and the gold 
dollar of Spain ; the dollar of Mexico, and the South American States, which 
vary slightly from each other ; the gold dollar of the United States, and the 
silver dollar of those States, which differs from the Spanish and Mexican 
dollars. There are, besides, the Maria Theresa dollar, the Sicilian dojjar, 
and at least nine dollars of German States, differing from each other in 
weight and contents, of pure silver. None of the coins above enumerated 
are identical in value, and confusion is always created when they come 
into concurrent circulation at the same place. Not one of them coincides 
at this time in value with that of 50 English pence. What, then, it may be 
asked, is the dollar with which this vaunted scheme is to harmonise ? 

Mr. Rathbone has formed high notions of the effect of the example of 
Great Britain in the proposed regulation of the currency. Other nations, 
however, have their own ways and their own prejudices. We cannot even 
effectually control our own Colonies in these matters. Our great dependency 
of India has established a system of currency of its own, differing entirely 
from ours. Last year, after the discovery of gold in Australia, the question 
was raised at the India House, whether or not they should adhere rigidly 
to their silver standard. It was decided, probably on good grounds, as 
regards Indian interests, but questionably as regards Imperial interests, 
to exclude gold from their circulation. 

But there is a difficulty to be overcome, independent of national laws, 
before such an universal system of concord as Mr. Rathbone contemplates could 
be effectually established— the difficulty of overcoming mercantile habits and 
prejudices. The tenacity with which merchants will adhere to old formula in 
calculations of the exchanges, rather than incur the trouble of altering them, 
is remarkable. The calculations of the exchanges between England and the 
United States afford a pregnant example of the force of such habits. The 
two countries have gold standards of well-defined quality. The comparative 
value of the coins of each is, therefore, easily ascertained, and the par of 
exchange could be readily fixed on that simple basis; but the Spanish dollar, 
which was the origin of the North American currency, was valued in the 
reign of Queen Anne at 4.?. 6d., and that rate is still adhered to in the cal- 
culation of the exchanges. A fictitious valuation is first given to the 
silver dollar, which is then converted into the gold dollar; and this 
circuitous operation brings out the par of exchange at the nominal amount 
of 109 23-40ths per cent. In international transactions it is easier to adhere 
to an intricate process once learnt, than to adopt a change for the sake of 
simplicity. 

Such is the result of an examination into the propositions contained in 



APPENDIX. 



225 



this pamphlet, and some surprise may he entertained at the countenan -■•■ 
which it has received among the mercantile community of Liverpool. Hut 
it has often been observed, that those who take the trouble of thinking for 
themselves are a very small minority of mankind ; and a dashing and spark- 
ling style of writing, which sweeps away, in a summary manner, the opinions 
of those who have been considered to have claims to respect, is wonderfully 
captivating. The reader enjoys the work of destruction, without reflecting 
on the merits of the structure proposed to be substituted. The pamphlet 
may be considered able, if fluency and vivacity of style can alone constitute 
force ; but fluency is easy, if facts and principles do not stand in the way of 
the writer, and vivacity is a quality which is commendable only when an 
author's confidence in his own judgment proves to be well-founded. 



226 APPENDIX. 



(II.) 



Mr. F. Bennoch's experience exhibits so satisfactorily the advantages of a 
decimal system, as contrasted with the present usages, that I have much 
pleasure in presenting a considerable portion of his evidence before the 
committee. 

Extracts from the Examination of Mr. Francis Bennoch. 

What is your opinion of the evils of the present system ?— It is, in my 
judgment, a mass of evils and inconsistencies. It necessitates several pro- 
cesses of different calculations, where one might serve : for instance, here is 
the cost of a manufactured article, requiring four different calculations, and 
four different values, before we can arrive at the simple cost of 3*. 2fd. ; and 
it is next to impossible, in our present coinage, to give an accurate result ; we 
must have a small fraction on each item left over, which would not be the 
case with the decimal coinage. 

Does the present coinage involve a consumption of more time than if it 
were arranged decimally ?— Infinitely : this cost would occupy five minutes, 
while in a decimal system it might be done in the fraction of a minute. 

How do you propose to effect this, and what alterations in our present 
coinage woidd you suggest?— In the first instance we require very few 
changes. Gold being fixed in price, and circulating at what is considered its 
intrinsic value, expresses its market price ; but silver and copper, being cir- 
culated above their value, are in reality merely tokens. There is, in fact, so 
far as I can understand, no alteration in the relative value of gold and silver 
contemplated. There would be the same quantity of copper given in ex- 
change for a florin, and the same quantity of silver given for a sovereign, 
that there is now. The alteration desired is only one of arrangement, to 
facilitate calculations and exchanges. 

"What are the real and nominal values of silver and copper ? — The value 
of copper is, I find, to-day, Is. -\d. per pound, while it circulates at 1*. Ad. 
to Is. 6d. per pound ; silver is 5*. to 5s. Id. per ounce, while it circulates at 
5s. 6d. per ounce ; there is no fear, therefore, of the copper or silver coin 
being used for manufacturing purposes, while gold coin is being continually 
broken up ; in fact, watchmakers and others prefer new sovereigns to 
bullion ; they are sure of the purity ; they can buy a quarter of an ounce, 
or sovereign, with 20s., without the trouble of assaying it , and I have been 



APPENDIX. 82? 

informed, that several thousands are consumed weekly in the district of 
Clerkenwell. 

What are the changes that would be required to make a decimal system 
work properly?— They are very few. One of the difficulties is, in having 
our unit of account fixed so high that it requires more coins than under 
other circumstances might he required. Still there are many reasons for 
retaining our unit of value or pound as it is now ; and with the farthing 
coined into the 1,000th part of a pound, instead of the 960th, leaving the 
sovereign and florin as they are, we should only require another coin to 
render the system nearly perfect. 

What do you mean by another coin?— I mean a coin of the value of 10 
mils, or tenth of a florin ; we should then have the pound, florin, cent, and 
mil. These four standard coins of account would, I think, be sufficient ; to 
facilitate exchanges, it would be indispensable to have these divided into 
parts. 

How would you divide them ? — I would divide, first, the gold into three 
coins ; i. e., the sovereign or 1,000 mils, the half-sovereign or 500 mils, and 
quarter sovereign or 250 mils ; the silver coins I would divide into the florin 
or 100 mils, half-florin or 50 mils, and quarter-florin or 25 mils ; and the 
cent, or whatever name you adopt, of 10 mils ; in copper, I would have a 
two-mil piece and a one-mil piece ; giving nine coins in all. 

Is there any great advantage in having so small a number of coins ? — I 
think there are many advantages ; in the first place, fewer dies would be 
required, and consequently there would be less expense ; a smaller quantity 
of metal would be required ; and it would be more easily counted, there 
being less labour in division. 

What would be the size of the smallest gold coin ?— About the size of a 
silver fourpenny-piece ; and a small gold coin would be very advisable, for 
several reasons. The recent discoveries of gold are likely to disturb the 
relative value of gold and silver ; and the more you can displace, or rather 
replace, silver by the introduction of gold, the less inconvenience will be 
felt ; besides, if with one coin of light weight, say 1-1 6th of an ounce of gold, 
you can supply the place of five coins of silver, weighing in the aggregate 
nearly an ounce, the advantage would be immediately felt. 

Would there not be an objection on the part of the public to being obliged 
to carry so small a gold coin in their pockets ?— I think there might be some 
objection at first, but the prejudice would soon be overcome, and the quarter- 
sovereign would become a favourite ; a similar coin is now current in 
America. They have a gold dollar which is nearly one-fifth' less than our 
250-mil piece would be ; it would weigh nearly 31 grains ; and I find that 
so long ago as the time of Henry the Third, in the year 1257, we had a gold 
penny, which weighed 45 grains. 

Might it not be objected to on the ground that it might be mistaken for 
a silver coin of a small size, in giving change ? — That is one of the evils of 

p2 



228 APPENDIX. 

any metallic system, and it might as reasonably be assigned as an objection 
to our present coinage, that the sovereign is sometimes passed for a shilling, 
and the half-sovereign for sixpence. 

Are you of opinion that our gold coinage requires no amendment, beyond 
the introduction of 250-mil pieces?— None, with the exception that I would 
advise that every gold coin should have stamped upon it the number of mils 
it represents, so as to familiarise the public with the two most important 
parts of our system, and ultimately lead them to look upon mils as the prin- 
ciple of our currency, while pounds should remain as our unit ; and it would* 
be a vast improvement could it be arranged to make our sovereign 120 
grains instead of 123 grains ; it would then be a quarter of an ounce, which 
would render bullion calculations very easy. 

Would you not adopt the mil as the unit ? — There are several objections 
to that ; first, the sovereign or pound is our standard measure of value, and 
now that gold is abundant, it ought not to be changed ; secondly, all our debt 
is reckoned in pounds sterling ; and, thirdly, all the salaries and estimates of 
income are based upon that unit, which has one advantage, it expresses a 
great sum in few figures. 

What would you recommend as regards the silver coinage? — First, I 
would recommend that an abundance of 10-mil or cent pieces and florin 
pieces should be circulated, and that all half-crowns and crowns should be 
withdrawn as speedily as possible, and that no more threepenny and four- 
penny pieces should be issued, nor indeed sixpences or shillings. 

How would you deal with sixpences and shillings?— Sixpences and 
shillings I prefer to the crowns and half-crowns ; they are of very little 
inconvenience, because they express fractional and even decimal parts of a 
pound, and therefore would easily harmonise with any system that might 
be introduced. 

You do not see any objection merely because they are not divisible by 
10 ? — Not at all ; and instead of being called shillings and sixpences, I 
should hope they would be called half florins and quarter florins. 

You suggest 1-mil pieces and 2-mil pieces only, would not that be 
attended with very considerable inconvenience in the payment of tolls and 
of penny stamps, inasmuch as you would have to carry about so many 
single mil-pieces?— The penny is an unfortunate coin ; it is neither the one 
thing nor the other, because you cannot make it harmonise with any 
system that has convenience for its object, and is one of the chief difficulties 
in the change proposed. If the penny were only thought of as the 240th 
part of a pound, all difficulty would vanish. During the last three months 
I have paid considerable attention to this matter, and have taken pains to 
ascertain, from all classes of people, what their opinions are with regard 
to a copper coinage, and 1 am satisfied that in 99 cases out of 100 two 
halfpence would be preferred to a penny piece. People prefer a single 
coin when it saves weight or trouble ; but if neither object is attained, 



APPENDIX. 229 

they prefer the smaller coin, because a halfpenny will often serve the purpose 
of a penny. 

How would you like a 5-mil piece ? — I think 5-mil pieces would be very 
objectionable, as they would be very clumsy ; and as they would be the 
same weight as two 2-mil pieces and one 1-mil piece, there is therefore no 
advantage gained. 

When you speak of economising labour in the small coins, do you mean 
in the counting of them ? — I do ; thus, to the merchant, and all others en- 
gaged in trade and commerce where book-keeping is necessary, a decimal 
system is of high utility, for a simple process of multiplication and addition 
produces the result desired, while fewer figures are used. 

Have you any calculations to show to the committee explanatory of your 
views ? — I have taken two or three easy calculations ; for instance, if I wish 
to enter and carry out 799 yards, at one farthing or one mil per yard, the 
figures 799 embrace the fact decimally without calculation ; but if I have 
to reduce it into pence and shillings, I have first to divide by four, and then 
by twelve, making fifteen figures and five lines to produce the result, 
16*. 7%d. If I am quick in mental arithmetic, and do not require to put 
my pen to paper, I have still the same mental working, which is so much 
time wasted. I may also refer to another fact, that if I wish to express 
196". life?., or to enter it in columns of my book, I use six figures and three 
lines, where three figures, 999, are enough ; and instead of three columns in 
our ledgers and day books, we need only two, — a simple bne to divide the 
pound sterling from its decimal parts ; or we may have three columns, as 
now, one for pounds, one for florins, and one for mils, which would have this 
important advantage, all our present account-books would be ruled 
correctly. 

In either paying or receiving accounts, do you consider the decimal 
system the most convenient ?— Decidedly, and for this reason : if I have to 
pay 999 mils, I might pay it in one half sovereign, one quarter sovereign, 
two florin pieces, one quarter florin piece, two cent pieces, and two 2-mil 
pieces, making nine coins in all. In our present coinage it would require, to 
pay the same amount, one half-sovereign, one crown, one half-crown, one 
florin, one fourpenny piece, one penny, one halfpenny, and one farthing, also 
making nine coins ; but that arises from the fact of our having in circulation 
a florin. In an ordinary case, instead of paying the whole money, we should 
probably pay a sovereign and receive back one mil or a farthing in ex- 
change. 

Have you considered any plan by which the objection to the small silver 
and gold coins might be overcome ?— I have ; one by having a perforated 
coin like the Chinese, where they can be strung like beads and suspended 
round the body. There is, indeed, some reason for believing that among the 
earliest coins of the world the perforated system prevailed ; pockets not 
being used, the money or property so carried gave distinction to the owner, 



230 APPENDIX. 

and this was doubtless the origin of bracelets and neck ornaments of precious 
stones, and also of chains of gold. 

As a means of carrying money ? — As a means of carrying money. As a 
sort of support of the theory I have just mentioned, I may state that there 
is abundance of inferential proof of the probability that such was the case ; 
and the fact will be found very interesting. It is recorded that one of our 
Ambassadors or Ministers of State, on visiting Antwerp, wrote that he had 
purchased a painting by Rubens, with so many links of his gold chain, from 
which we may reasonably conclude that the links were of a certain weight 
and fineness, and perhaps stamped by the goldsmiths, who at any time might 
be called to lend their notes on the deposit of the chain ; and the stamp 
would save the trouble of re-assaying, self-protection being the cause of the 
introduction of the hall-mark of the goldsmiths. 

Have you any objection to the perforated coin ? — I have, especially of 
the more valuable metals ; it would give a tempting facility to the dishonest 
to scrape metal from the inner edge, and thus the coin might get rapidly 
reduced in weight, and of course decreased in value. 

How would you overcome the objection ? — I should prefer a solid coin, 
and when I know that the dollar gold coin is becoming popular in America, 
where the people are quite as alive to a true system as we are, and when I 
remember that a coin of similar character was common in England 600 years 
ago, when hands were as hard and horny as they are now-a-days, the ad- 
vantages weighed against the disadvantages are vastly superior. The small 
silver coin might have more alloy than the other coins, as in the case of the 
3-cent piece in the United States, where the alloy is, I believe, seven per 
cent, more than in the other silver coins. 

What are the advantages and disadvantages of the large and small coins ? 
— The advantages of the large coins, or coins of considerable amount, are, that 
a large sum is more easily counted ; the disadvantage is to the poorer classes, 
who frequently have some difficulty to get them changed. The advantage 
of the small coin is to all who have to pay wages, the result of piece-work, 
where fractional payments are to be made, and to all the poor, who have to 
buy their articles in small quantities. 

Can you show what are the evils resulting from an abundance of large 
coins, whilst there is a scarcity of coins of smaller value ?— Every manufac- 
turer in the kingdom is cognisant of the mischief, inconvenience, and even 
vice, resulting from the difficulty of obtaining an abundance of small coins. 

How is that ? — I have known, when silver was scarce, several workpeople 
collect together in the pay-office of a manufactory, each person received a 
slip of paper, with the amount due, and one of them (nominated by them- 
selves) received a round sum in gold, and as little silver as possible, and 
were then dismissed to divide it among them. They might not all deal 
with the same grocer, or baker, or butcher, but there was one with whom 
they all dealt — I mean the publican, — where change could be obtained; and 



APPENDIX. 231 

I need hardly add, that frequently the division of their wages hy this method 
led to the diminution of their wages and the debasement of their minds. 

Have any other inconveniences resulted from it ? — Where goods are ma- 
nufactured at the homes of the workpeople, the manufacturer finds it easier 
to treat with one person than with a number of persons, and this has led to 
the introduction of a class called undertakers or middlemen, who come 
between the master and the workpeople ; they undertake all the responsi- 
bility, and receive and pay all the money. 

Might not the well-being and convenience of the working-classes be pro- 
moted by the middlemen? — Undoubtedly; one man could perform the 
details for 20, so that 20 might be kept at work while one was doing a duty 
which otherwise each must do for himself; nevertheless, I consider our 
clumsy coinage to have been the primary cause of the system. 

Do you apprehend any difficulties in carrying out a system of decimal 
coinage ?— Of course there are great difficulties, and doubtless there will be 
objections innumerable, but a little firmness will overcome all obstacles. A 
little enlightened despotism, or the mild exercise of arbitrary power, would, 
in such cases, be a national good. We are so much the slaves of custom, 
that we cling with tenacity to acknowledged evil, because we are either too 
timid or too idle to adopt a wiser course. 

Who, in your judgment, would be the chief objectors; merchants and 
traders, or the general public ? — I cannot conceive it possible for any one 
pretending to the character of a banker or a merchant objecting to a system 
which would save him 20 per cent in clerks, whose aim is to do the largest 
possible amount of business with the least possible amount of labour. 
I should naturally expect that great prejudice would exist among the 
ignorant, and all that extensive class who still sell butter at seventeen and 
a half ounces instead of sixteen ounces to the pound, corn by the 
old instead of by the imperial bushel, and reckon by bolls instead of 
quarters. Government, however, is to blame here for levying the duty on 
the cwt. of 112 lbs. instead of by the pound ; sometimes by shillings and 
pence, instead of on some principle which should be a certain part of a pound 
sterling. From this defect nearly £5,000 per annum is lost by the Income 
Tax, being the difference 3 per cent and 7d. in the pound. In the silk trade, 
a contract for so many cwt. means so many 100 lbs. net. 

Would not the quantity sold very much adjust itself to the amount 
received, after a little experience ? — No doubt it would. 

Do you think a half farthing would be of any use?— I think they would 
be of no use whatever. I think it would be given in, the same way as people 
now give the farthings. There is one point I should like to name to the 
committee in regard to the name of our new coins. I have said I consider 
there need be only four ; the pound, the florin, the cent, and the mil as coins 
of account. I think it is very important also that we should establish the 
principle of heading our ledger columns with the initial letters of our simple 



232 APPENDIX. 

English terms, and it is very important that, whatever names you adopt, 
they should be as far as possible removed from those we now have in use, in 
order to prevent confusion ; more especially where a new value might be 
given to a coin with an old and familiar name. 

As you have dealings in French goods, you may probably be able to 
inform us whether it would be any convenience if we were to accept a 
decimal system of weights and measures, as well as a decimal system of 
coinage ?— There can be no doubt whatever that it would greatly facilitate 
commercial transactions. . 

Do you think it would be attended with more public difficulty than the 
adoption of a decimal system of coinage ? — I think it would, because the 
chances are you would have a greater variety of articles to measure than 
merely in money. 

If both systems were adopted, do you think it should be done at the 
same time? — I think it would be well if we could manage it, but it is not 
essential ; our present weights and measures could be calculated in decimal 
money very easily; but I think it would be very convenient that they 
should bear a relationship to the money calculations, and be regulated by 
the same principle, and the sooner the better. Every year increases the evil, 
and makes the change more difficult. 



APPENDIX. 



233 



(III.) 



Table for Converting the various existing Subdivisions of the 
Pound Sterling into Decimal Coins, supposing the Plan of 
the Committee is adopted. 





Decimals 




Decimals 




Decimals 




Decimals 




of £1 




of £1 




of £1 




of £1 


t. d. 


in Mils. 


s. d. 


in Mils. 


s. d. 


in Mils. 


*. d. 


in Mils. 






10 


•041 


1 8 


•083 


2 6 


•125 


o 01- 


•001 


10i 
10i 
10f 


•042 


1 s\ 


•084 


2 64 
2 6j 


•126 


O.i 


•002 


•043 


1 8k 
1 8| 


•085 


•127 


Of 


•003 


•044 


•086 


2 6| 


•128 


1 


•004 


11 


•045 


1 9 


•087 


2 7 


•129 


o ii 


•005 


o n* 

11* 

ll| 


•046 


1 9* 


•088 


2 74, 


•130 


o n 

if 


•006 


•047 


i n 

1 9| 


•089 


2 n 


•131 


007 


•048 


•090 


2 7| 


•132 


2 


•008 


1 


•050 


1 10 


•091 


2 8 


•133 


2i 


•009 


1 0£ 


•051 


1 10i 


•092 


2 81 


•134 


2A 


•010 


1 0i 


•052 


1 10£ 


•093 


2 8£ 


•135 


o n 


•011 


1 0* 


•053 


1 lof 


•094 


2 8| 


•136 


3 


•012 


i l 


•054 


1 11 


•095 


2 9 


•137 


3£ 


•013 


i i\ 

1 H 

i if 


•055 


1 Hi 


•096 


2 9J 


•138 


3i 
3f 


•014 


•056 


1 11^ 

i in 


•097 


2 9£ 
2 9f 


•139 


•015 


•057 


•098 


•140 


4 


•016 


1 2 


•058 


2 


•100 


2 10 


•141 


4£ 


•017 


1 2* 

1 2| 


•059 


2 0i 


•101 


2 10J 
2 10£ 


•142 


4£ 
4| 


' -018 


•060 


2 01 


•102 


•143 


•019 


•061 


2 Of 


•103 


2 10J 


•144 


5 


•020 


1 3 


•062 


2 1 


•104 


2 11 


•145 


5^ 


•021 


1 H 

l H 

1 3| 


•063 


2 ii 


•105 


2 Hi 


•146 


5± 
5f 


•022 


•064 


2 lj 


•106 


2 111 


•147 


•023 


•065 


2 If 


•107 


2 11* 


•148 


6 


•025 


1 4 


•066 


2 2 


•108 


3 


•150 


6i 


•026 


1 ±\ 


•067 


2 2i 


•109 


3 01 


•151 


6| 


•027 


i 4 


•068 


2 2| 


•110 


3 Of 


•152 


6| 


•028 


1 41 


•069 


2 2| 


•111 


3 Of 


•153 


7 


•029 


1 5 


•070 


2 3 


•112 


3 1 


•154 


n 

1\ 


•030 


1 5^ 
1 5| 


•071 


2 3i 


•113 


3 ii 
3 l| 


•155 


•031 


•072 


2 3'- 


•114 


•156 


7| 


•032 


•073 


2 3f 


•115 


3 If 


•157 


8 


•033 


1 6 


•075 


2 4 


•116 


3 2 


•158 


8i 


•034 


1 6i 


•076 


2 4£ 
2 4£ 


•117 


3 24. 
3 2.^ 
3 2| 


•159 


8^ 

8f 


•035 


1 H 


•077 


•118 


•160 


•036 


1 6| 


•078 


2 4| 


•119 


•161 


9 


•037 


1 7 


•079 


2 5 


•120 


3 3 


•162 


9i 


•038 


l u 


•080 


2 6} 


•121 


3 3i 


•163 


9£ 
9| 


039 


1 7A 


•081 


2 5* 


•122 


3 3h 


•164 


•040 


1 7| 


•082 


2 5f 


•123 


3 3| 


•165 



234 



APPENDIX. 




•308 
•309 
•310 
•311 
•312 
•313 
•314 
•315 



4 

1 

5 

H 

6 

i 

7 

7', 
7l 



6 8 

6 8J 

6 S] 

6 8^ 

6 9 

6 91 

6 9] 

6 9^ 

6 10 
6 101 
6 101 
6 lOf 
6 11 
6 11* 
6 111 
6 ll| 



ArPEXDIX. 



235 



7 10 
7 10J 
7 10i 
7 lOf 
7 11 
7 11* 
7 114 

7 llf 

8 
8 0} 
8 0£ 
8* OJ 
8 1 
8 If 
8 1* 
8 1| 

8 2 

8 2J 

8 2| 

8 2| 



8 3j 
8 31 
8 3! 



Decimals 

of £1 
iii Mils. 



•366 
•367 
•368 
•369 
•370 
•371 
•372 
•373 

•375 
•376 
•377 
•378 
•379 
•380 
•381 
•382 

•383 
•384 
•385 
•386 
•387 



•390 

•391 
•392 
•393 
•394 
•395 
•396 
•397 



•400 
•401 
•402 
•403 
•404 
•405 
•406 
•407 

•408 
•409 
•410 
•411 
•412 
•413 
•414 
•415 



s. d. 



8 

8 5" 
8 6i 



8 



8 6i 

8 6 
8 6i 



8 



8 8 

8 8i 

8 8i 

8 8$ 

8 9 

8 9J 

8 9i 

8 9| 

8 10 
8 101 
8 10i 
8 10| 
8 11 
8 11J 
8 Hi 

8 llf 

9 
9 Oi 



9 
9 

9 2f 

9 3" 

9 3i 

9 31 

9 3| 



Decimals 

of £1 
in Mils. 



•416 
•417 
•418 
•419 
•420 
•421 
•422 
•423 

•425 
•426 
•427 
•428 
•429 
•430 
•431 
•432 

•433 
•434 
•435 
•436 
•437 
•438 
•439 
•440 

•441 

•442 
•443 
•444 
•445 
•446 
•447 
•448 

•450 
•451 
•452 
•453 
•454 
•455 
•456 
•457 

•458 
•459 
•460 
•461 
•462 
•463 
•464 
•465 



10 Of 



10 3i 
10 31 
10 3# 



Decimals 

of £1 
in Mils. 



•466 
•467 
•468 
•469 
•470 
•471 
•472 
•473 

•475 
•476 

•477 
•478 
•479 
•480 
•481 
•482 

•483 
•484 
•485 
•486 
•487 
•488 
•489 
•490 

•491 
•492 
•493 
•494 
•495 
•496 
•497 
•498 

•500 
•501 
•502 
•503 
•504 
•505 
•506 
•507 

•508 
•509 
•510 
•511 
•512 
•513 
•514 
•51$ 



«. d. 



10 4 
10 4i 
" 4i 
H 
B 



10 
10 

10 
10 5i 
10 5i 
10 5$ 



10 6 

10 6£ 

10 6i 

10 6f 

10 7 



10 7i 
10 7i 
10 7i 



10 8 

10 8i 

10 8i 

10 8| 

10 9 

10 91 
10 91 

10 9| 

10 10 
10 101 
10 101 
10 10| 
10 11 
10 Hi 
10 11* 
10 llf 



11 01 
11 Oi 



11 8| 



Decimals 

of £1 
in Mils. 



•516 

•517 
•518 
•519 
•520 
•521 
•522 
•523 

•525 
•526 
•527 
•528 
•529 
•530 
•531 
•532 

•533 

•534 
•535 
•536 
•537 
'538 
•539 
•540 

•541 

•542 
•543 
•544 
•545 
.546 
•547 
•548 

•550 
•551 
•552 
•553 
•554 
•555 
•556 
•557 

•558 
•559 
•560 
•561 
•562 
•563 
•564 
•565 



236 



APPENDIX. 





Decimals 




Decimals 




Decimals 




Decimals 




of £1 




of £1 




of £1 




of £1 


?. d. 


in Mils. 


*. d. 


in Mils. 

* 


t. d. 


in Mils. 


t. d. 


in Mils. 


11 4 


•566 


12 4 


•616 


13 4 


•666 


14 4 


•716 


li 4* 


•567 


12 4* 
12 4* 
12 4§ 


•617 


13 4i 

1 13 H 
13 4f 


•667 


14 4* 


•717 


ii H 

11 4| 


•568 


•618 


•668 


14 4* 


•718 


•569 


•619 


•669 


14 4| 


•719 


11 5 


•570 


12 5 


•620 


13 5 


•670 


14 5 


:$ 


11 5*. 


•571 


12 5*. 


•621 


13 51 


•671 


14 5*. 


11 5*, 


•572 


12 5* 


•622 


13 5*. 


•672 


14 5* 


•722 


ii si- 


•573 


12 6j 


•623 


13 5| 


•673 


14 5| 


•723 


ll 6 


•575 


12 6 


•625 


13 6 


•675 


14 6 


•725 


ii H 

11 6± 
11 6| 


•576 


12 6*. 
12 64 
12 6| 


•626 


13 6i 


•676 


14 6i 


•726 


•577 


•627 


13 6* 


•677 


14 61 
14 6| 


•727 


•578 


•628 


13 6| 


•678 


•728 


11 7 


•579 


12 7 


•629 


13 7 


•r.T'.i 


14 7 


•729 


11 7\ 


•580 


12 7*, 


•630 


13 7*, 


•680 


14 71 


•730 


11 7* 


•581 


12 71 
12 7| 


•631 


13 7* 
13 7$ 


•681 


14 7*. 


•731 


11 7-f 


•582 


•632 


•682 


14 7| 


•732 


11 8 


•583 


12 8 


•633 


13 8 


•683 


14 8 


•733 


11 8i 


•584 


12 8*. 


•634 


13 8* 


•684 


14 8i 


•791 


11 8? 


•585 


Lfl 8j 


•635 


13 81 


•685 


14 8* 


•735 


11 8-f 


•586 


12 8| 


•636 


13 8$ 


•686 


14 8| 


•736 


11 9 


•587 


12 9 


•637 


13 9 


•687 


14 9 


•737 


ii 9* 


•588 


12 9* 


638 


13 9* 


•688 


14 9* 


•738 


11 9* 


•589 


12 9* 


•639 


13 9* 


•689 


14 9j 


•739 


11 9f 


•590 


12 9| 


•640 


13 9f 


•690 


14 9| 


•740 


11 10 


•591 


12 10 


•641 


13 10 


•691 


' 14 10 


•741 


11 10* 


•592 


12 10i 


•642 


13 10*. 


•692 


14 10* 


•742 


11 10* 


•593 


12 10* 


•643 


13 10* 


•698 


14 10* 


•743 


11 io| 


•594 


12 10} 


•644 


13 10} 


•694 


14 10| 


•744 


11 11 


•595 


12 11 


•645 


13 11 


•695 


14 11 


•745 


11 IH 


•596 


12 11* 


•646 


13 11* 


•696 


14 11* 


•746 


11 111 


•597 


12 11* 


•647 


13 11* 


•697 


14 11} 


•747 


11 ll| 


•598 


12 ll| 


•648 


13 ll| 


•698 


14 ll| 


•748 


12 


•600 


13 


•650 


14 


•700 


15 


•750 


12 0* 
12 0} 
12 Of 


•601 


13 01 


•651 


14 0* 


•701 


15 0i 


•751 


•602 


13 0* 


•652 


14 0>- 


•702 


15 01 


•752 


•603 


13 Of 


•653 


14 Of 


•703 


15 Of 


•753 


12 1 


•604 


13 1 


•654 


14 1 


•704 


15 1 


•754 


12 h 


•605 


13 1* 


•655 


14 li 


•705 


15 1} 


•755 


12 11 


•606 


13 1* 


•656 


14 1* 


•706 


15 h 


•756 


12 If 


•607 


13 If 


•657 


14 if 


•707 


15 l| 


•757 


12 2 


•608 


13 2 


•658 


14 2 


•708 


15 2 


•758 


12 2*. 


•609 


13 2i 
13 2* 
13 2$ 


•659 


14 2i 


•709 


15 2} 
15 24 
15 2f 


•759 


12 2* 


•610 


•660 


14 2*. 


•710 


•760 


12 2| 


•611 


•661 


14 2f 


•711 


•761 


12 3 


•612 


13 3 


•662 


14 3 


■ -712 


15 3 


•762 


12 3* 


•613 


13 3$ 


•663 


14 3* 


•713 


15 3* 
15 3| 


•768 


12 8* 


•614 


13 3*. 


•664 


14 3* 


•714 


•764 


12 3f 


•615 


13 3| 


•665 


14 3| 


•715 


15 3J 


•765 









APPENDIX. 






237 




Decimals 




Decimals 




Decimals 




Decimals 




of £1 




of £1 




of £1 




of £1 


ft (I. 


in Mils. 


«. d. 


in Mils. 


t. a. 


in Mils. 


«. d. 


in Mil*. 


15 4 


•766 


16 4 


•816 


17 4 


•866 


18 4 


•916 


15 4i 


•767 


16 4£ 


•817 


17 44 


•867 


18 4i 


•917 


15 n 


•768 


16 44 


•818 


17 4j 


•868 


18 44 


•918 


15 4| 


•769 


16 4§ 


•819 


17 4| 


•869 


18 4f 


•919 


15 6 


•770 


16 5 


•820 


17 5 


•870 


18 5 


•920 


15 5£ 


•771 


16 51 


•821 


17 54. 


•871 


18 54. 


•921 


15 6} 


•772 


16 64 


•822 


17 54. 
17 5| 


•872 


18 54 


•922 


15 5§ 


•773 


16 5| 


•823 


•873 


18 5| 


•923 


15 6 


•775 


16 6 


•825 


17 6 


•875 


18 6 


•925 


15 6* 
15 64 


•776 


16 6* 


•826 


17 64. 


•876 


18 6i 
18 64. 


•926 


•777 


16 64. 


•827 


17 64. 


•877 


•927 


15 6-1 


•778 


16 6| 


•828 


17 6| 


•878 


18 6| 


•928 


15 7 


•779 


16 7 


•829 


17 7 


•879 


18 7 


•929 


15 7* 


•780 


16 7^ 


•830 


17 7i 


•880 


18 7i 


•930 


15 n 


•781 


16 74 
16 7f 


•831 


17 74. 

17 7| 


•881 


18 74. 


•931 


15 7§ 


•782 


•832 


•882 


18 7| 


•932 


15 8 


•783 


16 8 


•833 


17 8 


•883 


18 8 


•933 


15 Si 


•784 


16 8i 


•834 


17 8i 


•884 


18 8i 


•934 


15 84 
15 8| 


•785 


16 84 
16 8| 


•835 


17 84 


•885 


18 84. 
18 8| 


•935 


•786 


•836 


17 8| 


•8S6 


•936 


15 9 


•787 


16 9 


•837 


17 9 


•887 


18 9 


•937 


15 9J 


•788 


16 9i 


•538 


17 9i 


•888 


18 9i 
18 94 
18 9| 


•938 


15 94 
15 gf 


•789 


16 94 


•839 


17 94 
17 9| 


•839 


•939 


•790 


16 9| 


•840 


•890 


•940 


15 10 


•791 


16 10 


•841 


17 10 


•891 


18 10 


•941 


15 10J 
15 104 


•792 


16 10i 


•842 


17 10i 


•892 


18 101 


•942 


•793 


16 104 


•843 


17 104 
17 10| 


•893 


18 104 


•943 


15 10} 


•794 


16 lOf 


•844 


•894 


18 lOf 


•944 


15 11 


•795 


16 11 


•845 


17 11 


•895 


18 11 


•945 


15 Hi 


•796 


16 IH 


•846 


17 ni 


•896 


18 Hi 


•946 


15 11| 


•797 


16 11| 


•847 


17 114 


•897 


18 114 


•947 


15 llf 


•798 


16 llf 


•848 


17 llf 


•898 


18 llf 


•948 


16 


•800 


17 


•850 


18 


•900 


19 


•950 


16 Oi 


•801 


! 17 °i 


•851 


18 0i 


•901 


19 01 


•951 


16 04 
16 .Of 


•802 


1 17 04. 


•852 


18 04 


•902 


19 04 


•952 


•803 


17 Of 


•853 


18 Of 


•903 


19 0| 


•953 


16 1 


•804 


17 1 


•854 


18 1 


•904 


19 1 


•954 


16 li 


•805 


17 14 


•855 


18 li 


•905 


19 li 


•955 


16 14 


•806 


17 14 


•856 


18 n 


•906 


19 14 


•956 


16 if 


•807 


17 If 


•857 


18 If 


•907 


19' l| 


•957 


16 2 


•808 


17 2 


•858 


18 2 


•908 


19 2 


•958 


16 2i 


•809 


17 2i 


•859 


18 2i 


•909 


19 2i 


•959 


16 24. 
16 2| 


•810 


17 24 
17 2| 


•860 


18 2£ 


•910 


19 24 


•960 


•811 


•861 


18 2t 


•911 


19 2| 


•961 


16 3 


•812 


17 3 


•862 


18 3 


•912 


19 3 


•962 


16 34, 


•813 


17 3* 
17 34 


•863 


18 3i 
18 34 


•913 


19 3i 


•963 


16 34 


•814 


•864 


•914 


19 34 


•964 


16 3| 


•815 


17 3| 


•865 


18 


| -915 


19 3| 


•965 



238 



APPENDIX. 





Decimals 
of £1 






Decimals 
of £1 






Decimals 
of £1 




Decimals 
of £1 


*. a. 


in Mils. 


«. 


d. 


in Mils. 


«. 


d. 


in Mils. 


». d. 


in Mils. 


19 4 


•966 


19 


6 


•975 


19 


8 


•983 


19 10 


•991 


19 44 


•967 


19 


4 


•976 


19 


% 


•984 


19 10* 


•992 


19 U 


•968 


19 


•977 


19 


•985 


19 lOi 
19 10| 


•993 


19 4| 


•969 


19 


•978 


19 


H 


•986 


•994 


19 5 


•970 


19 


7 


•979 


19 


9 


•987 


19 11 


•995 
•91)6 


19 5J 


•971 


19 


7| 


•980 


19 


8 


•988 


19 Hi 
19 1U 
19 llf 


19 5i 


•972 


19 


7 7 


•981 


19 


•989 


•997 


19 5f 


•973 


19 


7| 


•982 


19 


9f 


•990 


•998 



shillings equal to 1*000 mils. 



APPENDIX. 



239 



(IV.) 

Table No. 2. — Showing Value of Decimal Coinage in Present 
Coinage, with Fractional parts. 

FROM 1 MIL TO 176 MILS. 



Florins. 




Florins. 




Florins. 




Florins. 




Cents. 




Cents. 




Cents. 




Cents. 




Mils. 


s. d. 


Mils. | 


s. d. 


Mils. 


s. d. 


Mils. 


s. d. 


.001 


Oft 


.045 


10i j 


.089 


1 9& 


.133 


2 71 


.002 


o og 


.046 


1U 


.090 


1 9§ 


.134 


2 &ft 


.003 


o W 


.047 


nX 


.091 


1 98 


.135 


2 8f 


.004 


0| 


.048 


llS ! 


.092 


1 io.f 5 


.136 


2 8& 


.005 


o i| 


.049 


lijg 


.093 


1 N>ft 


.137 


2 m 


.006 


lfl 


.050 


1 


.094 


1 io| 


.138 


2 9& 


.007 


lg 


.051 


1 o<i 


.095 


HO! 


.139 


2 9ft 


.008 


1|3 


.052 


1 m 


.096 


1 14 


.140 


2 9§ 


.009 


o 24 


.053 


1 0^ 


.097 


1 11* 


.141 


2 9f£ 


.010 


2f 


.054 


1 o| 


.098 


1 11S 


.142 


2 10ft 


.011 


2>§ 


.055 


1 H 


.099 


1 ii$ 


.143 


2 10ft 


.012 


2|f 


.056 


1 4 


.100 


2 


.144 


2 10& 


.013 


H 


.057 


1 ! 


.101 


2 04 


.145 


2 10! 


.014 


3it 


.058 


1 ll 


.102 


2 on 


.146 


2 lift 


.015 


3| 


.059 


1 2 S 


.103 


2 Og 


.147 


2 lift 


.016 


3g 


.060 


1 22 


.104 


2 Ojf 


.148 


2 11$ 


.017 


4l 


.061 


1 2g 


.105 


2 1£ 


.149 


2 1U§ 


.018 


3 


.062 


1 m 


.106 


2 xy 


.150 


3 


.019 


4g 


.063 


1 3 h 


.107 


2 i§ 


.151 


3 Oft 


.020 


3 


.064 


1 4 

1 3# 


.108 


2 1 i 


.152 


3 OB 


.021 


&A 


.065 


.109 


2 2J 


.153 


3 Oil 


.022 


4 


.066 


1 3|l 


.110 


2 2| 


.154 


3 OS 


.023 


5 M 


.067 


1 H 


.111 


2 2J« 


.155 


3 ll 


.024 


4 


.068 


1 4 

1 4i 


.112 


2 2§ 


.156 


3 1& 


.025 


6 


.069 


.113 


2 3| 


.157 


3 lfi 


.026 


6ft 


.070 


.114 


2 3| 


.158 


3 m 


.027 


6i| 


.071 


1 4 


.115 


2 3| 


.159 


3 2ft 


.028 


6^ 


.072 


1 5 S 


.116 


2 % 


.160 


3 2§ 


.029 


6| 


.073 


1 5J1 . 


.117 


2 4 


.161 


3 2^ 


.030 


7\ 


.074 


1 m 


.118 


2 4 


.162 


3 2$ 


.031 


° 7fi 


.075 


1 6'° 


i .119 


2 4g 


.163 


3 3ft 


.032 


m 


.076 


1 6a 


! .120 


2 4f 


.164 


3 3ft 


.033 


7| 


.077 


1 Si 


.121 


2 4 


.165 


3 3§ 


.034 
.035 


8 S 
81° 


.078 
.079 


1 6ii 

1 7? 


! .122 

.123 


2 5* 

2 &8 


.166 
.167 


3 3M 
3 44 


.036 


8g 


080 


.124 


2 5 


.168 


3 4ft 


.037 
.038 


8l 
9 X 


.081 
.082 


1 $ 
1 ffl 


.125 
; .126 


2 6 
2 6A 


.169 
.170 


3 m 
3 4! 


.039 


»l 


.083 


1 s 


.127 


2 i 


.171 


3 5ft 


.040 


9a 


.084 


1 8a 


.128 


2 6>| 
2 4 


.172 


3 5ft 
3 5$ 


.041 


9ii 


.085 


1 8f 


.129 


.173 


.042 


log 


.086 


1 1 

1 4 


.130 


2 74 
2 7 S 


.174 


3 5^ 
3 6 


.043 


10? 

oiog 


.087 


.131 


.175 


.044 


.088 


.132 


2 4 


j .176 


3 6ft 



240 



APPENDIX. 



No. 2 Table — Continued. 







FROM 177 MILS TO 250 MILS. 






Florins. 




riorins. 




Florins. 


' 


Florins. 




Cents. 




Cents. 




Cent*. 




Cents. 




Mils. 


s. d. 


Mils. 


s. d. 


Mils. 


s. d. 


Mils. 


8. d. 


.177 


3 ey 


.196 


3 HA 


.215 


4 3f 


.234 


4 8,1 


.178 


3 6S 


.197 


3 H& 


.216 


4 m 


.235 


4 jjf 


.179 


3 6g 


.198 


3 11J3 


! .217 


4 4* 


.236 




.180 


3 71 


.199 


3 ll| 


.218 


4 4* 


.237 


4 8| 


.181 


3 m 


.200 


4 


.219 


4 4.H 


.238 


4 <$ 


.182 


3 m 


.201 


4 Oft 


! .220 


4 4J 


.239 




.183 


3 m 


.202 


4 Qfi 


.221 


4 4 


.240 


4 9? 


.184 


3 8^5 


.203 


4 Oil 


.222 


4 & 


.241 


4 9U 


.185 


3 8| 


.204 


4 0$ 


.223 


4 5M 


.242 


4 10^ 


.186 


3 8£i 


.205 


4 11 


.224 


4 5g 


.243 


410 A 


.187 


3 m 


.206 


4 m 


.225 


4 6 


.244 


4 Wfc 


.188 


3 9£ 


.207 


4 l| 


.226 


4 6.?, 


.245 


4 10? 


.189 


3 9& 


.208 


4 If 


.227 


4 m 


.246 


4 llg 

5 


.190 


3 9J 


.209 


4 2g 


.228 


4 6fi 


.247 


.191 


s m 


.210 


4 2| 


.229 


4 6|4 


.248 


.192 


3 10f 5 


.211 


4 2ft 


.230 


4 n 


.249 


.193 


3 10A - 


.212 


1 2 


.231 


4 7» 


.250 


.194 


3 10.1* 


.213 


4 3fc 


.232 


4 :. : 






.195 


3 10| 


.214 


4 $ 


.233 


4 7$ 







(V-) 



Mr. Robert Mears has rendered good public service by his little 
pamphlet called " Decimal Coinage Tables." The decimal calcula- 
tion shows the facility with which one system of weights and mea- 
sures may be decimally reformed. In order to exhibit the saving of 
figures which decimals would accomplish in calculations of interest, I 
have here given extracts from Mr. Mears' calculations: — 



APPENDIX. 



241 



DECIMALS OF A YEAR. 

1 DAY TO 182£ BATS (OB HALF-YEAR). 





Decimal 




Decimal 




Decimal 




Decimal 


Days 


of 


Days. 


of 


Days. 


of 


Days. 


of 




a Year 




a Year. 




a Year. 




a Year. 


1 


.0027 


47 


.1287 


92 


.252 


138 


.378 


2 


.0054 


48 


.1315 


93 


.2547 


139 


.3808 


3 


.0082 


49 


.1342 


94 


.2575 


140 


.3835 


4 


.0109 


50 


.1369 


95 


.2602 


141 


.3863 


5 


.0136 


51 


.1397 


96 


.263 


142 


.389 


6 


.0164 


52 


.1424 


97 


.2657 


143 


.3917 


7 


.0191 


53 


.1452 


98 


.2684 


144 


.3945 


8 


.0219 


54 


.1479 


99 


.2712 


145 


.3972 


9 


.0246 


55 


.1506 


100 


.2739 


146 


.4 


10 


.0273 


56 


.1534 


101 


.2767 


147 


.4027 


11 


.0301 


57 


.1561 


102 


.2794 


148 


.4054 


12 


.0328 


58 


.1589 


103 


.2821 


149 


.4082 


13 


.0356 


59 


.1616 


104 


.2849 


150 


.4109 


14 


.0383 


60 


.1643 


105 


.2876 


151 


.4136 


15 


.041 


61 


.1671 


106 


.2904 


152 


.4164 


16 


.0438 


62 


.1698 


107 


.2931 


153 


.4191 


17 


.0465 


63 


.1726 


108 


.2958 


154 


.4219 


18 


.0493 


64 


.1753 


109 


.2986 


155 


.4246 


19 


.052 


65 


.178 


110 


.3013 


156 


.4273 


20 


.0547 


66 


.1808 


111 


.3041 


157 


.4301 


21 


.0575 


67 


.1835 


112 


.3068 


158 


.4328 


22 


.0602 


68 


.1863 


113 


.3095 


159 


.4356 


23 


.063 


69 


.189 


114 


.3123 


160 


.4383 


24 


.0657 


70 


.1917 


115 


.315 


161 


.441 


25 


.0684 


71 


.1945 


116 


.3178 


162 


.4438 


26 


.0712 


72 


.1972 


117 


.3205 


163 


.4465 


27 


.0739 


73 


.2 


118 


.3232 


164 


.4493 


28 


.0767 


74 


.2027 


119 


.326 


165 


.452 


29 


.0794 


75 


.2054 


120 


.3287 


166 


.4547 


30 


.0821 


76 


.2082 


121 


.3315 


167 


.4575 


31 


.0849 


77 


.2109 


122 


.3342 


168 


.4602 


32 


.0876 


78 


.2136 


123 


.3369 


169 


.463 


33 


.0904 


79 


.2164 


124 


.3397 


170 


.4657 


34 


.0931 


80 


.2191 


125 


.3424 


171 


.4684 


► 35 


.0958 


81 


.2219 


126 


.3452 


172 


.4712 


36 


.0986 


82 


.2246 


127 


.3479 


173 


.4739 


37 


.1013 


83 


.2273 


128 


.3506 


174 


.4767 


38 


.1041 


84 


.2301 


129 


.3534 


175 


.4794 


39 


.1068 


85 


.2328 


130 


.3561 


176 


.4821 


40 


.1095 


86 


.2356 


131 


.3589 


177 


.4849 


41 


.1123 


87 


.2383 


132 


.3616 


178 


.4876 


42 


.115 


88 


.241 


133 


.3643 


179 


.4904 


43 


.1178 


89 


.2438 


134 


.3671 


180 


.4931 


44 


.1205 


90 


.2465 


135 


.3698 


181 


.4958 


45 


.1232 


91 


.2493 


136 


.3726 


182 


.4986 


46 


.126 


91* 


.25 


137 


.3753 


182£ 


.5 



242 



APPENDIX. 



DECIMALS OF A YEAR.— (Continued). 

183 DAYS TO 1 TEAB. 





Decimal 




Decimal 




Decimal 




Decimal 


Days. 


of 


Days. 


of 


Days. 


of 


Days. 


of 




a Year. 




a Year. 




a Year. 




a Year. 


183 


.5013 


229 


.6273 


274 


.7506 


320 


.8767 


184 


.5041 


230 


.6301 


275 


.7534 


321 


.8794 


185 


.5068 


231 


.6328 


276 


.7561 


322 


.8821 


186 


.5095 


232 


.6356 


277 


.7589 


323 


.8849 


187 


.5123 


233 


.6383 


278 


.7616 


324 


.8876 


188 


.515 


234 


.641 


! 279 


.7643 


325 


.8904 


189 


.5178 


235 


.6438 


280 


.7671 


326 


.8931 


190 


.5205 


236 


.6465 


281 


.7698 


327 


.8958 


191 


.5232 


237 


.6493 


282 


.7726 


328 


.8986 


192 


.526 


238 


.652 


283 


.7753 


329 


.9013 


193 


.6287 


239 


.6547 


284 


.778 


330 


.9041 


194 


.5315 


240 


.6575 


285 


.7808 


331 


.9068 


195 


.5342 


241 


.6602 


286 


.7835 


332 


.9095 


196 


.5369 


242 


.663 


287 


.7863 


333 


.9123 


197 


.5397 


243 


.6657 


288 


.789 


334 


.915 


198 


.6424 


244 


.6684 


289 


.7917 


335 


.9178 


199 


.5442 


245 


.6712 


290 


.7945 


336 


.9205 


200 


.5479 


246 


.6739 


291 


.7972 


337 


.9232 


201 


.5506 


247 


.6767 


292 


.8 


338 


.926 


202 


.5534 


248 


.6794 


293 


.8027 


339 


.9287 


203 


.5561 


249 


.6821 


294 


.8054 


340 


.9315 


204 


.5589 


250 


.6849 


295 


.8082 


341 


.9342 


205 


.5616 


251 


.6876 


296 


.8109 


342 


.9369 


206 


.5643 


252 


.6904 


297 


.8136 


343 


.9397 


207 


.5671 


253 


.6931 


298 


.8164 


344 


.9424 


208 


.5698 


254 


.6958 


299 


.8191 


345 


.9452 


209 


.5726 


255 


.6986 


300 


.8219 


346 


.9479 


210 


.5753 


256 


.7013 


301 


.8246 


347 


.9506 


211 


.578 


257 


.7041 


302 


.8273 


348 


.9534 


212 


.5808 


258 


.7068 


303 


.8301 


349 


.9561 


213 


.5835 


259 


.7095 


304 


.8328 


350 


.9589 


214 


.5863 


260 


.7123 


305 


.8356 


351 


.9616 


215 


.589 


261 


.715 


306 


.8383 


352 


.9643 


216 


.5917 


262 


.7178 


307 


.841 


353 


.9671 


217 


.5945 


263 


.7205 


308 


.8438 


354 


.9698 


218 


.5972 


264 


.7232 


309 


.8465 


355 


.9726 


219 


.6 


265 


.726 


310 


.8493 


356 


.9753 


220 


.6027 


266 


.7287 


311 


.852 


357 


.978 


221 


.6054 


267 


.7315 


312 


.8547 


358 


.9808 


222 


.6082 


268 


.7342 


313 


.8575 


359 


.9835 


223 


.6109 


269 


.7369 


314 


.8602 


360 


.9863 


224 


.6136 


270 


.7397 


315 


.863 


361 


.989 


225 


.6164 


271 


.7424 


316 


.8657 


362 


.9917 


226 


.6191 


272 


.7452 


317 


.8684 


363 


.9945 


227 


.6219 


273 


.7479 


318 


.8712 


364 


.9972 


228 


.6246 


273| 


.75 


319 


.8739 


365 


1.0 



APPENDIX. 



24^ 



Example— £240 for 120 days at 4 
per cent. 

Decimal Method. — 34 Figures. 
240 Principal 
4 Rate per Cent. 

960 
3287 Decimal for Time. 

6720 

7680 
1920 
2880 

3155520— which, divided by 
100, gives 3 Pounds, 1 Florin, 5 



Cents, 5 Mils; 
£3 3s. IJd. 



or, reconverted, 



Another Example— £118 12s. 6d. 
for 73 days at 4 per cent. 

Decimal Method. — 20 Figures. 

1 1 q aoK Decimal for Money, from 
11SW5 Coinage Tables. 

4 Rate per Cent. 

474-500 

2 Decimal for Time. 



949000— which, divided by 100, 
gives 9 Florins, 4 Cents, 9 Mils; 
or, reconverted, 18s. 11 |d. as the 
Interest. 



Pbesent Method. — 80 Figures. 
£240 
120 

4800 
240 



28800 

4 Rate per Cent. 



365)1152/00(£3 3s.ljd. 
1095 

"~67 
20 

365)1140(3 
. 1095 

~45 
12 

365)540(1 
365 

175 

4 

365)700(1 
365 

335 
Present Method. — 88 Figures. 
£118 12 6 Principal. 
20 

2372 
12 

28470 

4 Rate per Cent. 



113880 

73 Time. 



341640 
797160 



365)83132/40(12)227§jg 

730 

18s. ll^d. 

1013 
730 

"2832 
2555 

"277 



APPENDIX. 



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APPENDIX. 



245 





•SJ0}}91 -* 




< 


W 




i 


W 




w < ^ 

« 3 * 


tween the Directors and the Engraver-General j. 
Deliberation of the Commission of 10th Jan., 1851. 
k. Ordonnance of Francis I. of 14th Jan. , 1539. 

* This fabrication has been directed by a law 
of 6th May, 1852. 

t The composition of the alloy of bronie money is 
fixed at 95 parts of copper, 4 of tin, and 1 of zinc = 
100. 


g 







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ber,1849. /. Law of 7 Germinal, year XI., and 15th 
September, 1849. g. Deliberation of the Commis- 
sion of 13th April, 1848. h. Deliberation of the 
Commission of 10th March, 1832. t. Delibera- 
tion of 10th March, 1832. The price of the broken 
mould has been placed against the account of 
the Directors by Deliberation of 30th December, 
1834. That of damaged moulds is regulated be- 


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a. Tarifs annexed to the Loi of 17 Prairial, year XI., 
and the Decree of 15th September, 1849. b. Law 
of 7 Germinal, year XI. Decree of 3rd May, 
1848. Addition to the programme of the compe- 
tition of 18th April, 1848. c Law of 7 Germinal, 
year XI. Decree of 3rd May, 1848. d. Law of 7 
Germinal, year XI. Decree of 22nd May, 1849. 
«. Instruction of the Commission of 31st Decern- 


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The allowance of" 
weight above and 
below the standard, 
is 1 per cent, for 
pieces of 5 and 10 
cents., and 1J per 
cent for pieces of 1 
and 2 cents. 


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FETTER AND GALPIN, PLAYHOUSE TARD, ADJOINING THE "TIMES" OFFICE. 









\ 













<& 



BINDING SECT. MAY 2 71983 



/'■ 



PLEASE DO NOT REMOVE 
CARDS OR SLIPS FROM THIS POCKET 

UNIVERSITY OF TORONTO LIBRARY 



(Of) 



HG 
939 
B65 
1854 



Bowring, John 

The decimal system in 
numbers, coins, and accounts