Aug. 7, 1873) 
vented schools from adopting it up to the present time as 
_a text-book ; it presupposes too much special talent on 
the part of the teacher, and contains but few of the modern 
methods of calculation. 
Two main points should ever be kept in view in teach- 
ing a subject like arithmetic : first, its principles ; secondly, 
the application of these principles to the affairs of life. 
In our opinion, the former is undoubtedly the more im- 
portant if the subject be regarded as an instrument of 
education. For arithmetical principles are, if properly 
explained, so very readily comprehended, that a beginner 
is not likely to find a more delightful path along which he 
may proceed to the extensive domains of mathematics ; 
but, being generally regarded as a mere catalogue of em- 
pirical rules and as a means for exercising the memory, 
arithmetic becomes, not educational, but instructive, an 
act of drudgery, and of no more real assistance as a 
branch of education than needlework or spelling. Explain 
the ordinary system of numeration to a pupil, let him 
thoroughly understand the meaning of digit-value and of 
grade-value, and he will then require but little deep 
thought, though it will be excellent mental training, to find 
out for himself the reasons of the four simple rules with 
respect both to integers end decima/s. Or, in some cases, 
let him construct a rule for himself. We do not remember 
to have ever seen what could fairly be called an arithme- 
tical rider ; ordinary problems are not riders, for they are 
scarcely more difficult than a geometrical theorem with 
the position and letters of the figure altered. The teacher 
would occasionally be called in to assist at these exer- 
cises ; but assistance sought for is far more valuable than 
that which is spontaneously proffered, and its effect more 
lasting. Mr. Hensley’s “Scholar’s Arithmetic” is one of 
the very few books in which we find decimals discussed 
in their proper place ; indeed it is difficult to understand 
how this branch of the subject can be logically postponed 
till a later period if our system of numeration is rationally 
explained, as of course it should be, at the very com- 
mencement of the course. 
Pursuing the subject systematically, the pupil should be 
introduced next to othcr systems of numeration ; and 
should have at least a little practice in such complex 
contrivances as long measure <nd troy weight. Certainly 
the contrast would be abundantly sufficient to mould any 
young rational being into a most ardent advocate of the 
metric system, But we cannot say that Mr. Hensley 
brings out so strongly as perhaps he might the vast 
difference between the two methods; his chapter on 
decimals, treating as it does of conceptions and quantities 
almost unknown to the great majority of British pupils, is 
somewhat too abstract. Yet we are glad to recognise in 
him an outspoken adherent of a universal decimal system, 
and he seems to look with becoming contempt upon our 
insular stupidity in fondly cherishing our marvellous 
weights and measures. 
Fractions and proportion are the only other important 
branches of elementary arithmetic ; and, when these are 
mastered, not only is the attainment of a first-rate know- 
ledge of mental and commercial arithmetic a matter that 
requires merely time and practice, but algebra becomes 
thereby most highly attractive as a now comprehensible 
generalisation, and geometry more alluring even to the 
unmathematical pupil, 
NATURE 
281 
The above-mentioned fundamental divisions and their 
applications to business, the reader will find fully and 
ably discussed in the “Scholar’s Arithmetic” ; and Mr. 
Hensley has wisely interspersed these all-essential chapters 
with a few on short methods of calculation, processes of 
verification, engaging problems, and other similar topics 
which usually attract the attention and excite the interest 
of a thoughtful student. There is a short though very 
lucid chapter on involution and evolution ; but, as Mr. 
Hensley remarks in his preface, he has intentionally 
passed over subjects which are most easily explained 
algebraically. There! are also more than thirty pages of 
examination papers from various sources, over and above 
the numerous examples scattered through the book, as 
well as a short though sufficient index and glossary. The 
book is perhaps rather too bulky, and in parts very un- 
equal as regards the difficulty of adjacent sections; but 
these are trivial failings which will not interfere with its 
use in schools, and we feel no hesitation in pronouncing 
it to be one of the most attractive educational works that 
have appeared on this subject, and it will doubtless be of 
very great assistance to every earnest teacher. 
TEMPLE ORME 
OUR BOOK SHELF 
The Human Mind ; A System of Mental Philosophy for 
the General Reader, By James G. Murphy, LL.D., 
Author of Commentaries on Genesis, Exodus, and 
Leviticus. (Belfast: William Mullan.) 
THIS book shows that its author possesses at least 
one common characteristic of mental philosophers, 
namely, an inordinately good opinion of his own ability. 
And, lest the reader should not discover for himself what 
Prof. Murphy has actually done in psychology (which 
might happen), he is explicitly told in the preface that, 
while building on the foundations laid by Reid and 
Hamilton, Prof. Murphy has, in his own opinion, pro- 
duced a work which he can venture to submit to “the 
mental philosopher, as a somewhat nearer approach to 
the real character of the mind than that of Reid, the 
founder, or even Hamilton, the lucid and eloquent expo- 
sitor and defender, of the true system of mental philo- 
sophy.” Another recommendation put forward in the 
preface is that this treatise is “among the briefest of 
those that have gone over the whole field of the mind. 
Perhaps, we cannot tell. But to us the marvel is that 
the book should have ever come to an end. We have 
made several honest attempts to read portions of the re- 
spectable looking volume, but have never been able to 
get beyond a few sentences ; for we felt as if launched on 
ashoreless ocean where we might sail on and on, or 
round and round for ever, and we could not keep our 
eyes open on the prospectless outlook, We fear some of 
the mental philosophers, to whom the book is submitted, 
will not give it very earnest consideration. What seems to 
bea main object with Prof. Murphy, and which is, as it ap- 
pears tous, rather inconsistent with a scientific treatment 
ofthe phenomena of mind, is to establish the existence and 
discover the attributes of Deity. But there are few readers, 
we should think, who will find much interest or pleasure 
in his mode of handling this part of his theme. There is 
not a little of the irreverent jargon with which meta- 
physical theologians have so often shocked all truly 
religious people. Here, for example, is a reflection that 
ought perhaps to leave no doubt as to the honesty of the 
Almighty, whatever other effect it may have on a reli- 
gious mind: ‘He is the Creator of all actual things, 
which are therefore already His own by an absolute and 
indefeasible right. He has therefore no temptation to 
take that which does not belong to Him,” 5, 
