434 
up this discovery, and by employing i, half the 
figure used for 100, he expresses 50. At length 
the rude man procured a better knife, with which 
he was enabled to give a more graceful form to his 
C, by rounding it into C; then two such, turned 
different ways, with a distinguishing cut between 
them, made (D, to express a thousand; and as, 
by that time, the alphabet was introduced, they 
recognised the similarity of the form at which they 
had thus.arrived to the first letter of Mille, and 
called it M, or 1000. The half of this #1) was 
adopted by a ready analogy for 500. With that 
discovery the invention of the Romans stopped, 
though they had recourse to various awkward ex- 
pedients for making these forms express somewhat 
higher numbers. On the other hand, the Hebrews 
seem to have been provided with an alphabet as 
soon as they were to constitute a nation; and they 
were taught to use the successive letters of that 
alphabet to express the first ten numerals. In 
this way b and c might denote 2 and 3 just as 
well as those figures; and numbers might thus be 
expressed by single letters to the end of the alpha- 
bet, but no further. They were taught, however, 
and the Greeks learnt from them, to use the letters 
which follow the ninth as indications of so many 
tens; and those which follow the eighteenth as 
indicative of hundreds. ‘This process was exceed- 
ingly superior to the Roman; but at the end of 
the alphabet it required supplementary signs. In 
this way bdecba might have expressed 245321 as 
concisely as our figures; but if 320 were to be 
taken from this sum, the removal of the equivalent 
letters cb would leave bdea, or apparently no more 
than 2451. The invention of a cipher at once 
beautifully simplified the notation, and facilitated 
its indefinite extension. It was then no longer 
necessary to have one character for units and 
another for as many tens. The substitution of 00 
for cb, so as to write bdeooa, kept the d in its 
place, and therefore still indicating 40,000. It 
was thus that 27, 207, and 270 were made distin- 
guishable at once, without needing separate letters 
for tens and hundreds; and new signs to express 
millions and their multiples became unnecessary. 
Thave been induced to trespass on your columns 
with this extended notice of the difficulty which 
was never solved by either the Hebrews or Greeks, 
from understanding your correspondent “T.S. D.” 
p. 367, to say that “ the mode of obviating it would 
suggest itself at once,” As to the original query,— 
whence came the invention of the cipher, which 
was felt to be so valuable as to be entitled to give 
its name toall the process of arithmetic? —“T.S.D.” 
has given the querist his best clue in sending him 
to Mr. Strachey’s Bija Ganita, and to Sir E. Cole- 
brooke’s Algebra of the Hindus, from the Sanscrit 
of Brahmegupta. Perhaps a few sentences may 
sufficiently point out where the difficulty lies. In 
the beginning of the sixth century, the celebrated 
NOTES AND QUERIES. 
[No. 27. 
Boethius described the present system as an in- 
vention of the Pythagoreans, meaning, probably, 
to express some indistinct notion of its coming 
from the east. The figures in MS. copies of Boe- 
thius are the same as our own for 1, 8, and 9; the 
same, but inverted, for 2 and 5; and are not with- 
out vestiges of resemblance in the remaining 
figures. In the ninth century we come to the 
Arabian Al Sephadi, and derive some information 
from him; but his figures have attracted most no- 
tice, because though nearly all of them are different 
from those found in Boethius, they are the same as 
occur in Planudes, a Greek monk of the fourteenth 
century, who says of his own units, “These nine 
characters are Indian,” and adds, “they have a 
tenth character called téippa, which they express 
by an 0, and which denotes the absence of any 
number.” The date of Boethius is obviously too 
early for the supposition of an Arabic origin; but 
it is doubted whether the figures are of his time, 
as the copyists of a work in MS. were wont to use 
the characters of their own age in letters, and 
might do so in the case of figures also. H.W. 
ROMAN NUMERALS. 
There are several points connected with the 
subject of numerals that are important in the 
history of practical arithmetic, to which neither 
scientific men nor antiquaries have paid much 
attention. Yet, if the principal questions were 
brought in a definite form before the contributors 
to the “ Norrs anp Quertss,” I feel quite sure 
that a not inconsiderable number of them will be 
able to contribute each his portion to the solution 
of what may till now be considered as almost a 
mystery. With your permission, I will propose a 
few queries relating to the subject, 
1. When did the abacus, or the “tabel” re- 
ferred to in my former letters, cease to be used as 
calculating instruments ? 
The latest printed work in which the abacal 
practice was given for the purposes of tuition that 
I have been able to discover, is a 12mo. edition, by 
Andrew Mellis, of Dee's Robert Recorde, 1682. 
2. When did the method of recording results in 
Roman numerals cease to be used in mercantile 
account-books? Do any ledgers or other account- 
books, of ancient dates, exist in the archives of 
the City Companies, or in the office of the City 
Chamberlain? If there do, these would go far 
towards settling the question. 
3. When in the public offices of the Govern- 
ment? It is probable that criteria will be found 
in many of them, which are inaccessible to the 
public generally. 
4. When in the household-books of royalty and 
nobility ? This is a class of MSS. to which I have 
paid next to ne attention; and, possibly, had the 
query been in my mind through life, many frag_ 
Ee eee 
