196 
NATURE 
[ Dec. 28, 1882 
a considerable portion of each number of some mathe- 
matical publications. Mathematical investigations that 
are really valuable can never be made elementary, and 
the questions that can be treated by elementary mathe- 
matics are too trivial to deserve recognition in a scientific 
journal. 
We may notice a demonstration of Euclid i. 47, by the 
late General Garfield, which appears in the first number. 
If the figure is completed it is in fact an intuitive seome- 
trical proof that (a+ 4)? = c*+2a46, where a and & are 
the sides and ¢ the hypotenuse of a right-angled triangte. 
The construction is to divide the four sides of a square 
each into two parts, @and 4, in the same order, and to 
join the points of division, Each of the joining lines is 
thus equal to the hypotenuse c, and the whole square, 
(a + 6)*, is evidently equal to the inside square, c?, and 
the four triangles in the corners, each of which is equal 
to}aé. The figure is practically the same as in the well- 
known proof in which the squares a” and 4? are placed 
side by side and divided by only two lines in such a 
manner that the parts may be moved by mere translation 
(without rotation) so as to form the square <, but the 
special features which give this proof its remarkable 
elegance are absent. Garfield’s proof is Indian in its 
character, and must have been known to Bhascara, but in 
the rather more elegant one given in the Vija Ganita 
(1150) the lines are drawn from the angles of the square 
¢ parallel to the sides of the triangle, and include a square 
(a — 6)’, each of the triangles in the corners being $a as 
before, so that the theorem proved is c? = (a — 6)?+2a4. 
If the points of division in the figure in § 150 of the Vija 
Ganita, in which it is shown that (a+ 4)? — 4ab=(a— 6)? 
are joined, the figure includes both Garfield’s and the 
Hindoo constructions. The construction given by Garfield 
must have been of course discovered over and over again, 
and, on its own account, it is so self-evident as only to be 
interesting historically in connection with the Indian 
proofs. 
If therefore we include among journals one published 
at such long intervals as half a year there are now no less 
than four journals, devoted exclusively to mathematics, 
published in the United States. 
With reference to fhe list of mathematical journals 
given in the previous article in NATURE, it may be men- 
tioned that the Belgian journal, the Wouvelle Corréspona- 
ance Mathématique, which was edited by M. Catalan, with 
the co-operation of MM. Mansion, Brocard, Neuberg, and 
others, was discontinued at the end of 1880, It has been 
replaced by a new journal, /athes7s, which has since been 
published monthly under the editorship of MM. Mansion 
and Neuberg, and has now completed its second volume. 
In this journal the titles of elementary articles are marked 
by across ; there are not on the average more than one 
or two so marked in each number. 
A new Scandinavian mathematical journal is shortly 
to appear under the editorship of Prof. H. G. Zeuthen, of 
Copenhagen, and Prof. Mittiag-Leffler, of Stockholm. It 
is to be hoped that it has a great scientific career before 
it, and assuredly no journal will bear on its title-page the 
names of more illustrious mathematicians, or will have 
started under more favourable auspices. 
J. W. L, GLAISHER 
QUAIN’S “ ANATOMY” 
Quain’s Elements of Anatomy. Edited by Allen Thom- 
son, E, A. Schafer, and G. D. Thane. Two volumes. 
Ninth edition. (London: Longmans, Green and Co., 
1882.) 
Lehrbuch der Neurologie. Fortsetzung von Hoffmann’s 
“Lehrbuch der Anatomie.” Von Dr. G. Schwalbe. 
(Erlangen: Eduard Besold, 1880 and 1881.) 
HE appearance of a new edition of Quain’s Anatomy 
is always regarded with attention and interest by 
teachers of anatomy. The high reputation of its succes- 
sive editors, Richard Quain, William Sharpey, G. V. 
Ellis, Allen Thomson, and John Cleland, and the care 
which has been taken to revise each edition and to incor- 
porate with it the latest additions to anatomical know- 
ledge, have caused this work to be universally regarded 
as an authority, and have gained for it the position of a 
standard treatise on Human Anatomy. 
The new edition, the ninth, which has just appeared, 
has been prepared under the editorial supervision of Pro- 
fessors Schafer and Thane, and Dr. Allen Thomson, 
The first volume, which has been revised by Prof. Thane, 
contains the descriptive anatomy of the bones, joints, 
muscles, blood-vessels, but not the heart ; cerebro-spinal 
and sympathetic nerves, but not the brain and spinal 
cord; with a chapter on superficial and topographical 
anatomy, in which the editor has been assisted by Mr. 
R. J. Godlee. The second volume has been for the most 
part revised by Mr. Schafer, and contains the histology, 
and the anatomy of the viscera, including the heart and 
central organs of the nervous system; whilst a special 
chapter on embryology has been written by Dr. 
Thomson. 
The separation of the anatomy of the heart from that 
of the other parts of the vascular system, as well as of the 
anatomy of the brain and spinal cord from the nerves which 
arise from them, and from the sympathetic system, both of 
which are so intimately connected both anatomically and 
physiologically with both brain and cord, was first made 
in the eighth edition; for prior to that time they had 
always been described along with, and as parts of their 
respective systems. This arrangement, which is also 
carried out in the present edition, is, in our judgment, 
most unphilosophical, for it both destroys the continuity 
of description, and leads the student to dissociate in his 
mind the origin of the nerves and blood-vessels from their 
distribution, Such a dissociation might indeed, as re- 
gards the nervous system, have been excusable at the 
time when both the distributory portions of the cranial and 
spinal nerves and the sympathetic system were believed 
to be developed quite independently of the cerebro-spinal 
axis, and only to become connected with it secondarily. 
But now-a-days, since through the researches, more espe- 
cially of the much-lamented F. M Balfour, both the 
cranial and spinal nerves and the sympathetic have been 
shown to be true offshoots of the cerebro-spinal axis, and 
like it of epiblastic origin, to dissociate them, even for 
descriptive purposes, in a systematic text-book, is, we 
believe, injurious to real progress. The editors of 
“Quain’’ would, we suppose, scarcely think of de- 
scribing in one volume the gangliated cord of the 
sympathetic, and in another the nerves which arise 
