May 27, 1886] 
NARORLE: 
93 
two long focus microscopes, whose axes produced intersect the 
divided circle at the extremities of a diameter. They are read 
by means of a pointer and spider-line micrometer, whose head 
is divided into 300 parts, each of which represents one second 
of arc. The microscopes are carried at such a height that they 
easily pass the collimator, and they can be read in any position, 
and the light from the collimator passes clear under the girder. 
J. E. A. STEGGALE 
THE ABACUS IN EUROPE AND THE EAST 
At a late meeting of the Asiatic Society of Japan (reported 
in the Fafan Mail), Dr. Knott read a paper on ‘“* The 
Abacus, and its Scientific and Historic Import.” A portion of 
the paper described the various arithmetical processes connected 
with the sovoban, the form of the abacus employed in Japan. 
The writer pointed out that in all arithmetical operations up to 
the extraction of the cube root, the sovoban really possessed 
dis‘inct advantages over ordinary ciphering. This in itself ex- 
plained why the instrument, which in Europe is suggestive of 
an infant school, has in the East survived till the present day. 
The rest of the paper was a discussion of the peculiar position 
which the abacus, used in its widest signification, holds in the 
history of the progress of arithmetic and mathematics, and of 
science and civilisation generally. The following is an abstract 
of the argument, the ultimate object of which was to explain 
why the abacus had died in Europe but lived in China, and 
why the cipher system of numerals had grown up in India but 
not in China. 
The abacus, as used in China and Japan, bears, on the sur- 
face of it, evidence of a foreign origin. The numbers are set 
down on it with the larger denomination to the left—a method 
which could hardly be believed to have been invented by the 
Chinese, who tend to work from right to left, and who have 
always named their compound numbers beginning with the 
higher denominations, The Chinaman says ‘‘one hundred 
forty-five,’ as the Englishman does ; but the Englishman once 
said ‘‘one hundred five-and-forty,” as the German still does ; 
while ‘in some of the Aryan languages of India, and in the 
Arabic of to-day, the number is named ‘‘five-and-forty and one 
hundred.” The Arab writes from right to left, so that, had the 
abacus been invented by such a people who, so to speak, both 
wrote and spoke inversely, it would have indicated the number 
as it does. In fact, the abacus could only have arisen in its 
present form amongst a people who either wrote and spoke 
directly, or wrote and spoke inversely. As a matter of history, 
the geographical home of the abacus is India, but, unless there 
is conclusive evidence to the contrary, we cannot regard it as 
an invention of Aryan Indians, who, although they wrote 
directly, spoke inversely. They probably borrowed it from the 
Semitic merchants, and these, with their inverse speaking and 
inverse writing, may have invented it, or perhaps received 
it from a direct-speaking, direct-writing people, such as 
the highly-cultured Accadians seem to have been. The 
abacus was evolved, no doubt, from the human hand, which, 
with its ten fingers, was the only counting-board used by 
primitive man. Its course of development is quite distinct from 
that of the symbolic representation of numbers. These latter 
we can trace through four stages, which may be called the pic- 
torial, the symbolic, the decimal, and the cipher. The pictorial 
we find in the Egyptian hieroglyphic and the Accadian cunei- 
form ; the symbolic in the hieratic, Phcenician, Hebrew, Greek, 
Roman, and the host of systems which grew up with the deve- 
lopment and spread of alphabets and syllabaries, and the decimal 
in the simplification of these which live to-day in the Chinese 
and Tamilic systems. Once the decimal stage was reached, its 
general similarity to the abacus indications suggested bringing 
_ them into still closer correspondence. This took place amongst 
_ the Aryan Indians, who, along with their brethren of the West, 
-yery soon discarded the abacus for the, to them, more convenient 
_ cipher notation. With the Chinese and Tamils, however, no 
~ advance was made in this direction, a fact especially surprising 
‘in the case of the latter, who have lived in close contact with 
_ peoples that have long used the cipher system of numerals. One 
reason for the Chinese conservatism in so adhering to an un- 
_wieldy notation might be their vertical mode of writing, with 
which no very striking similarity between their symbolising of 
numbers and the abacus columns would appear. But this does 
not explain the conservatism of the Tamils, who write from left 
to right, nor yet the persistence of the abacus for centuries face 
_ to face with the Indian cipher system. 
The explanation is 
rather to be found in the system of nomenclature, which, being 
direct both among the Chinese and the Tamils, fitted perfectly 
with the abacus indications. For this reason the manipulation 
of the abacus in China and Japan is more rapid and certain than 
ciphering, and hence, there being no advantage for simple arith- 
metical operations in tne latter, the cipher system did not de- 
velop in these countries, and even when introduced from the 
West in all its vigour could not displace ‘‘the rod and the 
beads.” An Aryan Indian, with his inverse-speaking, could 
never work the abacus with the same facility as the Japanese 
unless he worked from right to left, a mode of procedure quite 
foreign to his nature. It is not so foreign to the Chinese and 
Japanese, however, to work from left to right, as shown in the 
formation of each individual ideograph employed in writing. 
Hence the abacus suited the Chinese language better than it did 
any of the Aryan languages in their original mode of number- 
naming. The influence of the notation which was developed 
from Semitic sources under the influence of the abacus, has in 
later times compelled many of the Aryan languages to assimilate 
as far as possible to the direct mode of numeration ; but in the 
English fi/teen, the German /frizfzehn, and the French guinze, we 
still have the relics of the original inverse mode of naming, alike 
peculiar to Aryan and Semitic peoples. 
In the course of the discussion which followed, it was men- 
tioned that Chinese mathematics were first studied in Japan 
about 900 A.D., and that the Japanese ascend by powers of 
10,000 in their treatment of larger numbers. 
THE GAZETTEER OF RUSSIA? 
E have received the concluding fascicule of the ‘ Geogra- 
phical and Statistical Dictionary of the Russian Empire,” 
published by the Russian Geographical Society, and edited by M. 
P. Semenoff. This monumental work, which was begun more 
| than twenty years ago, has been now concluded in five large 
octavo volumes, and will remain for many years the most trust- 
worthy and complete source of information for the geography of 
the empire, exclusive of Poland, but inclusive of the former 
Russian dominions in America. It may be regretted that the 
editor of the ‘* Dictionary” has been diverted by so great a 
variety of geographical, statistical, and administrative work from 
this undertaking, and that therefore the last fascicule appearing 
twenty-three years after the first, the statistical information con- 
tained in the first fascicules and volumes has become out of date. 
But notwithstanding that, the ‘‘ Dictionary ” has not become old. 
Its value is not in the statistical data it contains ; it is much 
more in the excellent geographical descriptions of the localities 
treated—that is, of each separate government of Russia, Siberia, 
Turkestan, and Caucasus—of the seas that border Russia, and 
their islands. Several articles are excellent and most complete 
monographs, and we need only mention those on the Amur, 
Caucasus, Sakhalin, the Northern Ocean, or Turkestan to 
remind geographers of these excellent descriptions of whole 
regions. The geology, the flora and fauna of each region 
have received much attention. These descriptions will not soon 
be old—they can be only completed. 
At the end of each article there is, moreover, a most com- 
plete bibliography of the larger geographical works in which the 
place described in the article has been mentioned, as also 
of monographs dealing with it, and of newspaper articles. This 
bibliography is invaluable for the geographer. On the whole, 
the equally high standard of all geographical descriptions and 
the unity of conception in all of them—the whole being the 
work of the editor himself, assisted only by M. Zverinsky and 
very few occasional contributors—make this ‘‘ Dictionary” 
occupy one of the first ranks among like publications. An ap- 
pendix is promised, which will contain descriptions of such 
regions as the Thian-Shan, Ferganah, and Transbaikalia, which 
were much explored during the publication of the ‘‘ Dictionary.” 
They will embody all recent information. 
UNIVERSITY AND EDUCATIONAL 
INTELLIGENCE 
Con vocaTION of the University of London met on Tuesday 
evening to consider the report of a Special Committee which 
proposed several important changes in the constitution of the 
* “ Geographitchesko-Statistitcheskiy Slovar Rossiyskoy Imperii,’ P. P. 
Semenoya. 
