May 20, 1886} 
51 
some respects Euclid’s prolixity, recalling over-and over 
again propositions which have gone before, does much to 
fix them in the memory of the learner and prevent loose- 
ness in reasoning, and though we think Euclid’s style 
admits with advantage of some pruning, we feel that Mr. 
Nixon, with overstrained regard to the examination hall, 
has used the knife too freely, and has run the risk by his 
style and free use of abbreviations and signs of letting 
the young pupil believe, as he is only too glad and ready 
to do, that mathematical work should be written after the 
fashion of a telegram, grammar disregarded, articles and 
little words omitted, and what should be sentences written 
without verb or copula. 
Mr. Nixon has deliberately omitted the usual marginal 
references, on the ground that “learners (1) very gener- 
ally ignore them; and (2) will gain greater benefit by 
having to hunt up the references themselves.” We believe 
he has thereby seriously injured the value of his book. 
Because many boys, in the hands of a careless teacher 
and left to themselves, ignore the references, is hardly a 
good reason why they should not be supplied for those 
who would use them, or who would be required by their 
teacher to use them; and they would be exceptional 
pupils under exceptional teachers who could be depended 
on, or find it easy, “to hunt up the references themselves.” 
Doubtless the exercise of doing this is excellent, but the 
beginner needs some help in doing it. 
We have thought it would be most useful to dwell at 
some length on Mr. Nixon’s revision of Euclid’s text, and 
can only notice generally the exercises and addenda, 
which occupy more than half the book. The collection 
of exercises appears to be very well chosen and complete, 
though we should have been glad to see more of them 
interspersed among the propositions from which they 
naturally flow. 
The addenda include all the more important develop- 
ments of the elementary geometry, as well as an intro- 
duction to many of the methods of the higher geometry. 
As a collection of results in the geometry of the straight 
line and circle this part of the book appears to us from a 
cursory perusal to be excellent, giving a full account of 
the important relations of the triangle and its associated 
circles, centres of similitude, coaxial circles, &c. ; while 
for methods the elementary notions and use of cross 
ratios, harmonic ranges, inversion, poles and polars are 
explained and applied to such an extent as to prepare the 
student naturally for their application to geometry beyond 
that of the straight line and circle. We fail, however, to 
find such prominence given to the great principles of 
duality and reciprocity as their importance, scarcely less 
in elementary than in the higher geometry, appears to us 
to demand. 
The typography, and the accuracy and clearness of the 
figures, are to be commended as worthy of the Clarendon 
Press. RB 
OUR BOOK SHELF 
Practical Histology and Pathology. By H ‘ i 
5 a . By Heneage Gibbes 
M.D. Third Edition. (London: H. K. Lewis, 1885.) 
THE text in this edition does not, on the whole, differ 
much from that of the previous editions, some new useful 
formule of staining and a more comprehensive arrange- 
ment of the subject-matter being the chief differences. 
The tables given at the end of the book as to the con- 
version of degrees of Centigrade into Fahrenheit and 
vice versa, as to the conversion of English weights and 
measures into French, are in some points incorrect, and 
might have been easily correctly copied from any standard 
work. E. KLEIN 
Farm Live-Stock of Great Britain. By Robert Wallace, 
F.C.S. F.H.A.S., &c., Professor of Agriculture and 
Rural Economy in the University of Edinburgh. 
(London: Simpkin, Marshall, and Co.; Edinburgh: 
Oliver and Boyd, 1885.) 
WITHIN 200 pages octavo, of rather large type, does Prof. 
Wallace condense much useful information upon farm 
live-stock. It must, however, be evident that to treat of 
cattle, sheep, swine, and horses, from a biological, an 
agricultural, and an economical point of view would at 
least require double the number of pages, containing 
twice the number of words, and folded quarto. Brevity 
has been said to be the soul of wit; but in a work such 
as this we cannot but feel that it must be intended by its 
author either for those who know nothing or for those 
who know something of the subject. It appears to us to 
fall short of the requirements of each of these classes of 
readers. Four and a half lines—forty words, in fact—upon 
the Devon breed of cattle cannot be considered adequate, 
however terse and compressed they may be (and to the 
point they undoubtedly are), to giving a good word-picture 
of this race. Besides, Prof. Wallace must excuse us for 
differing from him as to his statements even in this very 
short description. Heis wrong in saying “colour blood- 
red, no white.” There is white upon the fore-udder in 
almost all Devon cattle, and it is unfortunate that there 
should be a manifest error in this very short description 
of an important breed. 
The book aims at too much, and is too vague in its 
general plan. The writer is successful in being concise, 
but he is not free from érrors, and a greater amplitude in 
his observations would have both conferred a greater 
general interest upon his pages, and been more satis- 
factory to an earnest student of agriculture. Let us 
hope shortly to see an enlarged edition. 
Common-Sense Euclid. Books 1. and II. Part I. By 
the Rev. A. D. Capel, M.A., St. John’s College, Cam- 
bridge. (London: Joseph Hughes, 1886.) 
THE object of this book, as the author tell us, is to point 
out, especially to teachers and those teaching themselves, 
the portions of the treatise which either present difficulties 
to the beginner or escape their notice altogether. 
The propositions are explained in a very clear and 
concise way, some of them being even worked backwards 
and their analysis being made in every case; explana- 
tions are given, here and there, where they are most re- 
quired, and are put in the easiest possible way. Problems, 
at the end of each proposition and also at the end of the 
book, are given, making a total of 300, followed by hints 
for their solution. 
The figures are not placed opposite each proposition, 
as they are in most editions, but all together at the end. 
The plan adopted is avery good one, it being understood 
that the student must construct the figures for himself. 
Arithmetic for Schools. By the Rev. J. B. Lock, M.A. 
(London: Macmillan and Co., 1886.) 
THIS is a carefully prepared school-book, forming, as to 
scope, a sort of arithmetic mean between Hamblin Smith’s 
and Brook Smith’s or Muir’s. It contains the usual 
rivulets of text ending in seas of examples. In the purely 
arithmetical part of the book logical accuracy is attempted 
with considerable success. Want of grasp is much more 
evident in the part which deals with the applications. 
j There the division into subjects is strangely illogical, and 
