Dr. Hutton's Course of Mathemalics. 525 



teachers themselves, whilst they will form in the bond fide student 

 a regard for good order, a judicious discrimination between different 

 methods of operation, that cannot fail to be of the utmost future use 

 to him. The almost universal use of Hutton's Course both in pri- 

 vate schools and by private students, therefoi"e, will be rendered 

 still more conducive to the general diffusion of good mathematical 

 taste, by the publication of the present appendage to it. 



"We have not space to enter into an analysis of the contents of the 

 551 pages contained in Mr. Davies's M'ork — filled, as it is, with ori- 

 ginal views on every branch of elementary mathematics. The author 

 has even touched in various places on the matter of scientific history, 

 and we value this innovation as much as any. How preposterous is 

 it to despise the labours of our predecessors in whatever field of li- 

 terature or science we are labouring ! As this portion of Mr. Davies's 

 work is more immediately open to criticism than any other, perhaps 

 it will not be considered irrelevant if we devote a few lines to its 

 consideration. 



The author's observations on the middle-age abacus are sensible 

 and valuable. The change between the manual abacus and the 

 membranaceal tablets is, indeed, easily conceived ; and In all proba- 

 bility was transferred in that manner to the Arabian system of com- 

 putation. " lliough this mode of notation," as Mr. Davles observes, 

 " may never have been necessary, and very rarely employed by chro- 

 niclers and other persons merely literary, it would be of extreme 

 value in the performance of computations. Amongst these expedi- 

 tion M^ould be of great consequence, and this would often be facili- 

 tated by writing the symbols in ruled columns, Instep.d of placing 

 the dice upon the abacus. This, again, would lead to running the 

 several component letters of any one number into a single and con- 

 tinuous figure, which would represent the number." We must, 

 however, observe. In all this, that we prefer /«c^s to wholesale con- 

 jecture, however pretty and ingenious this last may be. 



The derh^atlons of the signs + and — as given at pp. 11, 13, 

 are, we think, very Improbable, and show that the late Professor 

 Rigaud and Mr. Davles, who have worked together on this subject, 

 are not well versed in ancient handwriting. On a point of this na- 

 ture, where the subjects in dispute were Introduced five centuries 

 ago, it Is necessary, we humbly submit, to take into consideration 

 the mode of writing at the period, — if, Indeed, the symbols are not 

 altogether arbitrary,- — and not reason on the et and the P of the 

 present day, as if our rough- writing were the same with that of the 

 Itahans in the fifteenth century. We are sorry to speak dispara- 

 gingly of what we infer to be a favourite theory with our author, but 

 its very Improbability is quite sufficient to bring with It a condem- 

 nation, and perhaps might eventually have done so from leas mer- 

 ciful critics. 



We beg our readers to study attentively the various remarks 

 tending to the completion of the new method of solving numerical 

 equations. The method of synthetic division, which forms the basis 

 of that process, is here developed at length, and traced to the com- 



