387 
tained in the following extract: “ It would be impossible, 
with the few materials yet brought to light, to conjecture with 
any great probability, how far these Boetian contractions may 
have influenced the introduction, or cooperated with the 
Arabic system, to the formation of our present numerical no- 
tation. It appears to me highly probable that the two sys- 
tems became united ; because the middle age forms of the 
figure five coincide with the Boetian mark for the same 
numeral, and those of two others are very similar. The idea 
of local position, again, may have had an independent 
European origin; the inconveniences of the abacus on paper 
would have suggested it by destroying the distinguishing 
boundaries, and inventing an arbitrary hieroglyphic for the 
representation of an empty square.” 
The author then proceeded to adduce evidence from some 
documents recently discovered in support of these views. He 
showed from the Mentz MS. in the Arundel collection, in 
what manner the mode of operation with the abacus had 
been improved, soas to lead naturally to the present system. 
He then brought forward some passages from MSS. illustra- 
tive of the first employment of the zero; and concluded by , 
adducing an instance from a MS. of the translation of Euclid 
by Athelard, of the fourteenth century, belonging to the 
Arundel collection, in which the number 15 is written in 
these contractions, and without a division. 
DONATIONS. 
Catalogue des Principales Apparitions des eloiles filantes. 
Par A. Quetelet. 
Sur etait du Magnétisme Terrestre a Bruxelles, pendant 
les douze années de 1827 a 1839. Par A. Quetelet. 
Sur la Longitude de Observatoire Royal de Bruxelles. 
Par A. Quetelet. 
Presented by the Author. 
Asiatic Researches. Vol. XX., Part 2. Presented by 
the Asiatic Society of Bengal. 
