, and for astronomical
tables.

A second system of this kind is still used in the pagination of manuscripts
in Ceylon, Siam, and Burma, having also had its rise in southern India. In
this the thirty-four consonants when followed by _a_ (as _ka_ ... _la_)
designate the numbers 1-34; by _[=a]_ (as _k[=a]_ ... _l[=a]_), those from
35 to 68; by _i_ (_ki_ ... _li_), those from 69 to 102, inclusive; and so
on.[140]

As already stated, however, the Hindu system as thus far described was no
improvement upon many others of the ancients, such as those used by the
Greeks and the Hebrews. Having no zero, it was impracticable to designate
the tens, hundreds, and other units of higher order by the same symbols
used for the units from one to nine. In other words, there was no
possibility of place value without some further improvement. So the
N[=a]n[=a] Gh[=a]t {41} symbols required the writing of "thousand seven
twenty-four" about like T 7, tw, 4 in modern symbols, instead of 7024, in
which the seven of the thousands, the two of the tens (concealed in the
word twenty, being originally "twain of tens," the _-ty_ signifying ten),
and the four of the units are given as spoken and the order of the unit
(tens, hundreds, etc.) is given by the place. To complete the system only
the zero was needed; but it was probably eight centuries after the
N[=a]n[=a] Gh[=a]t inscriptions were cut, before this important symbol
appeared; and not until a considerably later period did it become well
known. Who it was to whom the invention is due, or where he lived, or even
in what century, will probably always remain a mystery.[141] It is possible
that one of the forms of ancient abacus suggested to some Hindu astronomer
or mathematician the use of a symbol to stand for the vacant line when the
counters were removed. It is well established that in different parts of
India the names of the higher powers took different forms, even the order
being interchanged.[142] Nevertheless, as the significance of the name of
the unit was given by the order in reading, these variations did not lead
to error. Indeed the variation itself may have necessitated the
introduction of a word to signify a vacant place or lacking unit, with the
ultimate introduction of a zero symbol for this word.

To enable us to appreciate the force of this argument a large number,
8,443,682,155, may be considered as the Hindus wrote and read it, and then,
by way of contrast, as the Greeks and