524; Mr. Davies's Solutions of the Questions of 



LXXX. — Notices respecting New Books. 



Solutions of the principal Questions of Dr. Huttons Course of Ma- 

 thematics ; forming a general Key to that work, designed for the use 

 of Tutors and private Students. By Thomas Stephens Davies, 

 F.R.S., Lond. and Edinb. Royal Military Academy, Woolwich. 



^HE work of Dr. Hutton is too well known to require any de- 

 tailed description in our pages. Drawn up half a century ago 

 for the use of the gentlemen cadets of the Royal Military Academy, 

 its object was to remove the inconvenience which had been felt to 

 arise from the use of detached parts of a multitude of v/orks on dif- 

 ferent branches of mathematical science. Compiled, too, for the use 

 of boys who entered the institution at the age of fourteen, and whose 

 periods of study varied from two to four years, — for boys who beside 

 mathematics were instructed in their applications to mechanical and 

 physical science, — the course was necessarily rendered a brief one. 



Those of our readers who have paid attention to the history of ma- 

 thematical science in this country, do not need to be told that, at 

 the time of its first publication, it was by far the best treatise on the 

 subject existing in our language. During the time which has elapsed, 

 many improvements have been introduced into it by Dr. Gregory, 

 to keep pace with the progTess of science ; but in the last edition 

 the alterations M'ere much more extensive and important than any 

 which had preceded them. The number of new questions which 

 were introduced into that edition have rendered it one of the most 

 valuable books of examples in any language ; and many subjects 

 were treated there which for the first time found their way into an 

 elementary book, — amongst which may be particularly specified 

 Horner's general method of solving algebraical equations with nu- 

 merical coefficients. 



The work before us contains either the entire or indicated methods 

 of solution of all the questions in this edition where it appeared 

 likely that there could arise the least difficultj% We have always 

 thought that such works were useful to teachers, and to private 

 students of honest purpose ; but we saw a drawback to this utility 

 in the probability of their falling into the hands of pupils themselves. 

 In the present case, however, we do not anticipate this evil ; for the 

 work cannot be used for the purpose of deception when any master 

 exercises common vigilance, inasmuch as no student can proceed 

 through the writing and especially filling the occasional blank steps 

 without at least understanding the solution, and seeing its application 

 to collateral problems. To a mere boy of ordinary capacity this is 

 the utmost that can be accomplished even by the most diligent 

 teacher : and hence, in this case, the labour of the master will be 

 diminished and the acquirements of the pupil still secured. 



To both we consider this work invaluable. We were much struck 

 with the general elegance of the solutions, and much pleased with 

 the systematic working formulae adapted to numerical application. 

 Such examples are calculated to improve the mathematical taste of 



