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, so as 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 Yetat du Magnetisme Terrestre a Bruxettes, pendant 

 les douse armies de 1827 a 1839. Par A. Quetelet. 



Sur la Longitude de I ' Observatoire Royal de Bruxettes. 

 Par A. Quetelet. 



Presented by the Author. 



Asiatic Researches. Vol. XX., Part 2. Presented by 

 the Asiatic Society of Bengal. 



