138 Mr. Hunt on the Permeability 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," — quce a sudantibus ahacistis 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:j:, 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 Aperpi Historique. JLii '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 = a,„10'" + «;n-ilO"'-' +a„,_2lO'''-2 + ... + a, 10 + «o> 



where «q, Wj, Cj, ... am are digits, or integers less than the 

 radix 10. 



XXV. On the Permeability of various bodies to the Chemical 

 Rays. By Robert Hunt.|| 



tTAVING 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, Jperpu Historique, p. 474. 



II Communicated by the Author. 



