The national leader., 1889-02-02
What Numbers Does it Take to Make
Billion?

De6n introduced Dy the lCallan arlLn-
meticians early in the fourteenth CEN
tury. Peacock, in his admirable his
tory OF arithmetic ("Encycloped.
Metropol. vol. i,) states that the
Italians made ''a great addition to their
former numerical language by the use
Of the word 'millione' (which properly
signifies great thousand to denote the
square of one thousand, and which was
followed by the words billions, ,
'trillione,' etc.. deduced Immediately
from the former by pursuing the natural
analogies of the languages: A series
of numerical terms was thus formed,
proceeding not by tens, but by
Millions" The new terms were slowly
adopted by the nations of Europe, but
In every case in their original and
chronological sense.
In Spain these terms were used pro.
badly not long after their establishment
in Italy: in France they were adopted
not much before the opening of the 10Th
century; In Germany. early IN the 10th
century; in England not until the close
OF the 18th century, and in Russia,
early in the 18th century. Locke, who
published his great essay in 1890, COM
plains that his countrymen were accus-
toned to speak of millions of millions of
millions instead of using the more con-
venient term, ''trillions," and he gives
an example or the proper notation to
60 places of figures. divided into sex
tuple periods, and duly named up to
mon1llions. 1.-THE ordinary way of
naming the number in English will be
the often repeating OF millions of
millions of millions Of Millions" &c.
C'Human Understanding" book ii,
chap. 16, sect. g.. 1t is important to
observe that, wherever introduced, the
term 'billlon" uniformly designated
the bis power of the million-a value,
the prefix to twelve places of figures.
In the Italian dictionary of the
Accademici della Crusca, the word.
'bllione" Tor ''billione') is defined sun
milione di milioni." In the Spanish
dictionary Of the Academia Espanola,
the word "bion" Is defined sun million
de miliones," or million multiplied
by itself. In the German dictionary
of DR.. Daniel Sanders. "billion" is
defined ''millional Million" And in
Littre's "French Dictionary" after
defining the word, it is stated: "The
forms billion, trillion, etc., were devised
in the sixteenth century to signify
periods of six to six figures; counting
from the right, units were represented
by the first six places of figures, the
millions were represented by the figures
from the seventh to the twelfth places,
the billions were represented by the
figures from the thirteenth to the eigh-
teenth places, and so on. Est. De
La Roche's ''AIithmetique" is quoted
as stating billion is equal to a million
Millions" LittTe adds without expla-
nation), 1t was not till the middle Of the
seventeenth century that the rule of
separating into periods of six was
changed to separating into periods Of
three figures, and the original billion
was divided by 1000" 1t is not a little
surprising that our cOmpilers Of school
arithmetics, whether smitten with
Franco-mania or with Anglophobia)
have almost unanimously adopted the
modern French perversion OF the
terms ''billIon,' ''trillion," etc. And
thus business men are in the habit of
numeratlng ''illlons" by places of three
(after the million placel. while astrono-
mers and mathematicians preserve the
original and logical numeration by
places Of six figures. 1t needs but a
bare inspection Of the terms themselves
to see that this French neologism (of
the two last centuries) is not only
anomalous, but wholly irrational. The
form of the words million, "billion, :"
''trillion, ,""quadrillion, ,"''quintillion, :"
etc.. necessarily denotes some co-ordina-
tion of numerical progression. What
can it possibly be on the pedagogue's
systemr The expression l, 900, 600, 900
Zone thousand million) does not admit
any logarithmic dissection. How can it
then, be in any sense billion? If it
be any kind of a bis. what is its pri-
maryY It is an impossible second
power. having surd for its root. Had
the French arithmeticians cut down at
the same blow the million to the mile,
the scheme would at least have been
consistent. A true billion is evidently
second order of million, and the only
rational order is the second power.
To any rejecting mind the school,
book enumeration is simply absurd. and
its prevalence is very puzzling phe-
nomenon.