524f Mr. Davies’s Solutions of the Questions of 
LXXX. — Notices respecting Nem Books, 
Solutions of the principal Questions of Dr. Hutton s 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 Acddemy, Woolwich. 
T 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 works 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 progress of science ; but in the last edition 
the alterations were 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 difficulty. 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 
