JUNE 21, 1912] 
outlines are too hard and the colors not quite 
true; there is too much of the mannerism of 
the artist. The colored plates in Professor 
Thomson’s book also seem to me criticizable; 
they look a little out of focus, as it were—much 
as things look to the present writer when he 
has mislaid his glasses. 
On the chance that some of our active 
workers in genetics have not recently read 
their “Selborne,” it may be worth while to 
quote the following pertinent information: 
“One thing is very remarkable as to the 
sheep: from the westward till you get to the 
river Adur all the flocks have horns, and 
smooth white faces, and white legs; and a 
hornless sheep is rarely to be seen: but as soon 
as you pass that river eastward, and mount 
Beeding-hill, all the flocks at once become 
hornless, or, as they call them, poll-sheep; and 
have moreover black faces with a white tuft 
of wool on their foreheads, and speckled and 
spotted legs: so that you would think that the 
flocks of Laban were pasturing on one side of 
the stream, and the variegated breed of his 
son-in-law Jacob were cantoned along on the 
other. And this diversity holds good respec- 
tively on each side from the valley of Bramber 
and Beeding to the eastward, and westward all 
the whole length of the downs. If you talk 
with the shepherds on this subject, they tell 
you that the case has been so from time im- 
memorial, and smile at your simplicity if you 
ask them whether the situation of these two 
different breeds might not be reversed. How- 
ever, an intelligent friend of mine near Chi- 
chester is determined to try the experiment; 
and has this autumn [1773], at the hazard of 
being laughed at, introduced a parcel of black- 
faced hornless rams among his horned western 
ewes. The black-faced poll-sheep have the 
shortest legs and the finest wool.” 
T. D. A. CockERELL 
UNIVERSITY OF COLORADO 
THE HINDU-ARABIC NUMERALS 
Tn a recent number of Science’ I ventured 
to assert the correctness of the statement that 
our present decimal place system with the zero 
1 January 5, 1912. 
SCIENCE 
969 
is of Hindu origin. The veteran historian 
of mathematics, Moritz Cantor, makes sub- 
stantially the same assertion in the latest 
edition (1907) of the first volume of his 
“Vorlesungen iiber Geschichte der Mathe- 
matik,” p. 608. He says, referring to the use 
of words with place value.’ 
This kind of conscious juggling with the notions 
of positional arithmetic together with the zero, is 
most easily explained in the home of these notions, 
which (home) for us is India and this we may 
affirm even if there is question of a second home. 
We mean if both notions were born in Babylon, 
of which there is great probability, and were car- 
ried over into India in a very undeveloped state. 
We niay add that neither Cantor nor any 
other has yet presented any historical evidence 
that these ideas were carried over to India 
from Babylon. Enestrém, the editor of the 
Bibliotheca Mathematica, a journal devoted 
to the history of mathematics, has recently* 
supported the view that the Babylonian arith- 
metic is not of the same nature as our system. 
The Babylonians did not use the zero, so far 
as we know, with the same notion of place 
value for purposes of computation as in the 
Hindu system. The Babylonian multiplica- 
tion tables published by Hilprecht which in- 
elude tables of 1,800 times various numbers 
are an evidence of this fact. In a fully devel- 
oped sexagesimal (60) system this table would 
be replaced by the table of thirty times the 
corresponding numbers, since 1,800 equals 30 
times the unit of higher order, 60. Further- 
more, the Babylonian system was not adapted 
for computation because of the mixture of 
decimal and sexagesimal systems and further 
because of the large base, 60. 
Recently another early document referring to 
the Hindu numerals has been published. This 
document is of prime importance because, 
being written in 662 a.D., it antedates by more 
than two centuries the earliest known appear- 
ance in the ninth century of the numerals in 
Europe. The probability is, too, that the 
?See Smith-Karpinski, ‘‘The Hindu-Arabie Nu- 
merals,’’ p. 39, for an explanation of this system. 
® Bibliotheca Mathematica, Vol. XI. (3), 1911, 
p. 331, 
