€02 
NATURE 
[AUGUST 15, 1912 
take these observations seriously, particularly as | 
they necessitate the abandonment of every 
generally accepted belief with regard to mitosis. 
Surely Flemming, Boveri, Strasburger, and a 
hundred others were competent observers, and 
with regard to the fundamental facts connected 
with mitosis, and disputed by Mr. Ross, all are 
agreed ! 
The further descriptions of cell phenomena given | 
in the present volume only serve to make clearer 
the obvious necessity of at least an elementary 
knowledge of a subject before undertaking original 
research therein. Various cytological terms are 
used in a manner which suggests that-the authors 
are unfamiliar with the structures these terms 
were invented to specify. With regard to their 
statement that what they call Altmann’s granules 
go to form the chromosomes, no better advice 
could be given than that they should study the 
already voluminous and rapidly growing litera- 
ture relating to chondriosomes, to which the chief 
contributors are perhaps Benda, Meves, Duesberg, 
Prenant, Fauré-Frémiet, and G. Arnold. 
(4) Mr. Green beiieves that “the lie of the 
ground seems to have a mysterious influence on 
the Jocal incidence of cancer,” and that this “can 
only be explained by its relation to the elimination 
and removal of products of coal combustion from 
the houses or from their neighbourhood.” He 
claims, perfectly correctly, that houses built in 
hollows or on the sides of hills are most likely 
to suffer from smoky chimneys, and hence that 
people inhabiting such houses are most subject to 
the action of the products of coal combustion. He 
produces statistics and other evidence professing 
to show that cancer is most prevalent in towns 
situated in hoilows and on steep or hilly sites. 
That various superficial forms, such as chimney 
sweep’s and Kangri cancer, may be caused by 
some local irritant not unconnected with the com- 
bustion of coal or some other substance is prob- 
able, but it is difficult to connect internal cancers 
with coal. Again, Mr. Green’s classification of 
towns is not altogether in accordance with fact. 
Glasgow has one of the lowest death-rates from 
cancer. Mr. Green places it among the towns 
occupying a flat site, as his theory, of course, 
demands. A considerable portion of Glasgow is 
probably as hilly as any town in the United King- 
dom, and the hills are of that steep nature most 
likely to produce smoky chimneys. The Royal 
Cancer Hospital, itself in the middle of the town, 
is surrounded by inclines so steep that it is practi- 
cally unapproachable by wheeled vehicles except 
in one direction. 
Ca ES We 
A 
0. 2233, VOL. 89] 
| (4) Examples in Arithmetic. 
SCHOOL MATHEMATICS. 
(1) Geometry for Schools. Vols. i.-iv. By W. G, 
Borchardt and the Rev. A. D. Perrott. (Cam- 
bridge Mathematical Series.) Pp. xiv + 325 + xiv. 
(London: G. Bell and Sons, Ltd., 1912.) Price 
3s. 6d. 
(2) Algebra for Beginners. By C. Godfrey, 
M.V.O., and A. W. Siddons. Pp! xi+272: 
(Cambridge University Press, 1912.) Price 
2s. 6d. 
(3) A School Algebra. Parts ii and ii. By 
H. S. Hall. With answers. Pp. x+301-550+ 
xxxix—lix. (London: Macmillan and Co., Ltd., 
1912.) Price 2s. 6d. 
Part ii. Taken 
from “A School Arithmetic.” By H. S. Hall 
and F. H. Stevens. Pp. v+117—281+xxiii-— 
xxxix. (London: Macmillan and Co., Ltd., 
1912.) Price 2s. 
(5) The Calculus for Beginners. By W. M. Baker. 
(Cambridge Mathematical Series.) Pp. viii+ 166. 
(London: G. Bell and Sons, Ltd., 1912.) Price 
BS. 
UR mathematical reformers are to-day fairly 
well agreed on the teaching of school 
mathematics; their opinions may be found in the 
various reports of the Mathematical Association 
and in the Report on the Geometry Syllabus by 
the American ‘“‘ National Committee of Fifteen.” 
It is an interesting study to consider how far 
writers of text-books adopt these opinions, why 
they deviate from them, and what an author who 
holds these reforming opinions may do to advance 
them. 
It is, for instance, remarkable with what unani- 
mity the early introduction of solid geometry is 
recommended—only less remarkable than the rarity 
-with which one finds that recommendation carried 
out. Messrs. Borchardt and Perrott (1) make a 
noble effort, and give, in the first six pages, a 
valuable little explanation of a number of three- 
dimensional terms; but the remainder of the 325 
pages now before us appear to be restricted to 
two dimensions. And we have noticed a similar 
falling off in other authors. What is the explana- 
tion? The truth is that three-dimensional work 
is difficult and little suited to the capacity of the 
beginner. Little is possible at an early stage 
beyond the occasional discussion of a problem in 
which the data are in three dimensions, but the 
reasoning in reality two-dimensional. 
The book on algebra by Messrs. Godfrey and 
Siddons (2) leaves us wondering. To avoid mis- 
apprehension, we say at once that it is a good 
book, undoubtedly good, for these authors could 
not write anything but good. But for the work 
aie 
