138 
Mr. Hunt on the Permeahility of 
of Boetius was not introduced by him. It does not appear 
to me that much authority ought to be given to the well- 
known passage of William of Malmsbury,* * * * § as far as it is 
supposed to prove that Gerbert brought the knowledge of the 
abacus from Spain : and, as Professor Peacockf so well ob- 
serves, ‘‘ the passage of this historian contains no certain in- 
timation of the knowledge of the notation by nine figures and 
zero, as the rules which would be thence derived, would tend 
rather to relieve than increase the labours of the sweating 
calculators,” — qucB a sudantihus abacistis vix intelliguntur. 
Now had the question of the Boetian contractions been 
broached when Professor Peacock composed his history of 
arithmetic, he would immediately have seen how evidently this 
passage refers to them, and this supposition would have ex- 
plained his doubts in the remaining part of his argument. 
In the treatise of Berhelinus in the Bodleian library^, the 
Boetian contractions occur explained by Greek numerals,— 
a most singular and important fact, and one which affords a 
very strong argument for what M. Chasles has stated at p. 474 
of his Aperfu Flistoriqiie. En passant^ this is also an argu- 
ment for the antiquity of this artificial abacal system. 
Again, what difference is there between the system of the 
Greeks, the system in the Mentz Manuscript, the system in 
the passage in Boetius as satisfactorily explained by M. 
Chasles, and the Arabic method ? I mean with regard to 
first principles^. All, in fact, are contained in the following 
formula, which is the general expression for any finite num- 
ber : — 
N = -h + ... -f 10 + «o» 
where ••• digits, or integers less than the 
radix 10. 
XXV. On the Permeability of various bodies to the Chemical 
Rays. By Robert Hunt.H 
IITAVING many years since repeated, with much interest, 
the experiments of Wedgwood, Davy, and Wollaston 
on the chemical influence of light, it was with much pleasure 
* Wright’s Essay on Anglo-Saxon Literature (p.'66). 
t History of Arithmetic, p. 415. 
X I possess a transcript of this manuscript, but, having mislaid it, am 
compelled to defer any commentary on it till M. Chasles has published 
his edition. 
§ M. Chasles, Apergu Historiquey p. 474. 
II Communicated by the Author. 
