6 TRANSACTIONS 
OF THE 
TEXAS ACADEMY OF 
SCIENCE 
• 
1 2 
3 
4 
5 
6 
7 
8 
9 
bal tel 
kil 
fol 
lul 
mal 
vel 
jol 
zul 
and for the tens 
10 20 
30 
40 
50 
60 
70 
80 
90 
bals tels 
kils 
Jols 
luls 
mals 
vels 
jols 
zuls 
and we have in addition: 
hundred thousand 
million 
billion 
trillion quadrillion 
turn mil 
balion 
telion 
kilii 
on 
folion. 
In this scheme we observe the following defects ; As regards the 
digits there is no word to express 0. As regards the expressions for 
the denominations, why should the denomination ten be denoted by 
the affix for the plural? It is an arbitrary use of the affix. The other 
names for the denominations are not more systematic than the English 
words ; there is the usual jump from thousand to million; we are not 
told whether telion means thousand million or million million, and no 
words are provided to express fractional denominations. One writer 
even gives telion as meaning two millions, kilion as meaning three 
millions; and he evidently does this from the analogy tels 20 and kils 
30. If tel expresses a multiple of 5, it also expresses a multiple of ion. 
According to English usage, billion means 1000,000 2 , trillion 1010,- 
000 3 , and quadrillion 1000,000*, and so on ; 1000,000 being the base and 
hi, tri, quadri, expressing the index of the power. According to the 
usage of this country and of France billion means 1000x1000,000, that 
is 1000 3 , trillion 1000 4 , quadrillion 1000 5 , while 1000* is expressed by 
million ; in this system 1000 is the base, but the prefixes of the words 
no longer express accurately the index of the power. 
In physical works we meet with the highest development of the 
notation for number; it consists of a series of significant figures, and 
of a positive or negative power of ten. To vocalize this notation 
we require an elementary word for each of the elementary numbers 
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and a series of words for the integer powers 
of ten, and for the fractional powers of ten. As there are five elemen¬ 
tary vowels, ten words for the digits may be obtained by prefixing the 
consonants b and 1. Thus : 
0 123 456789 
ba be bi bo bu la le li lo lit 
The word for a higher number is formed by taking the appropriate 
monosyllables in succession ; for .example : 
11 12 23 123 105 
bebe bebi bibo bebibo bebala 
The integer denominations may be expressed by affixing j to the 
number for the place or power of ten, while the fractional denomina¬ 
tions may be expressed by adding n instead of f, thus : 
