
NOTICES AND ABSTRACTS 
OF 
MISCELLANEOUS COMMUNICATIONS TO THE SECTIONS. 

MATHEMATICS AND PHYSICS. 
MATHEMATICS. 
Tue Rev. Dr. Bryce gave an Account of a Treatise on Arithmetic in the Chinese 
Language, by the Rev. Dr. Moncrierr, late of St. Paul’s College, Hong Kong. 
The Chinese have for ages had a character (called Ling) corresponding in part to 
our zero, but used by them only to fill a vacant place, not to give local value. Thus 
they came one step nearer the Arabic notation than the Greeks did. One step how- 
ever remained, which Dr. Moncrieff has taken. The Jesuit missionaries to China 
had printed Vlacq’s Logarithmic Tables in a simplified character, and it has been 
said that a copy of their work was presented to the Royal Society about the year 
1750. Dr. Moncrieff’s letter requesting him to make the present communication, 
had only reached Dr. Bryce on the first day after the present meeting ; and having 
been pretty constant in his attendance on the Sections, he had not had time to 
investigate the matter particularly: however, he had examined all the records of the 
Royal Society within his reach, but could find no notice of the work of those reverend 
gentlemen. He was therefore unable to say whether they had attempted to introduce 
the admirable device of local value, which is the distinctive characteristic of the Arabic 
notation. If they had, Dr. Moncrieff evidently knew nothing of their having done 
s0; which is not wonderful, inasmuch as Dr. Peacock, in his learned and elaborate 
history of the science (Encyclopedia Metropolitana), makes no mention of their 
work, from which we may infer that it was unknown even to him. At all events, 
Dr. Moncrieff found the actual arithmetic of China in the same clumsy condition 
in which it has been for ages, their notation quite unfit for making calculations on 
paper as we do, in consequence of which they were obliged to perform all arithme- 
tical operations on the Abacus*. 
Finding the circle used for another purpose in the written language of China, Dr. 
Moncrieff used a triangle for his ling or zero, and employed it to convert the cha- 
racters representing simple units, into symbols for tens, hundreds, &c., exactly as in 
the Arabic notation. He also introduced our marks of addition, subtraction, mul- 
tiplication, division, involution, evolution, &c., modifying some of them to distinguish 
them from characters already in use for other purposes. 
The work comprises the common rules,—fractions, common and decimal,—invo- 
lution and evolution ; in short, the general scientific principles of arithmetic. He 
_ * Two different figures of the Chinese Abacus are given in the Phil. Trans. for 1686, and 
in Du Halde’s History of China. 
1852. 1 
