194 
IN ATA T ELS, 
[ DECEMBER 27, 1906 
the selected intervals form a set of potency c. Similar 
theorems apply to areas and volumes: thus, if we 
take a unit square it is possible to ‘* black out” a 
definite region within it, the area of which may be 
less than any given quantity, in such a way that no 
circle, however small, can be placed within the square 
without covering some at least of the black region, and 
so that the points not within the black region form a 
set of potency c. It should be specially noticed that al- 
though the black region is, or may most conveniently 
be, constructed by an infinite process, it is perfectly 
definite, in the sense that we can say whether any 
given point (x, y) lies within it or not. 
Another point to which attention may be called is 
the definition of ‘‘ curve’’ (p. 219) as a set of points 
having certain properties. This is quite distinct from 
the idea of a path traced by a continuously moving 
point, and leads to very curious and interesting pro- 
blems relating to rectification and quadrature. 
Enough has been said to show how interesting 
and novel are the contents of this treatise; the ex- 
amples and figures are of great help in making the 
general arguments intelligible, and the bibliography 
will enable the reader to consult all the literature 
relating to the subject. Finally, the appendix should 
not be overlooked, as it contains some important 
additional matter, besides a few corrections. To the 
latter may be added ‘‘ chap iv., § 20,’’ instead of 
“chaps ives 913,45 On pene G. B. M. 
METAMORPHOSES OF PLANTS. 
Jugendform und Bliitenreife im Pflanzenreich. By 
Dr. L. Diels. Pp. 130; with 30 illustrations in text, 
each with several figures. (Berlin: Gebriider Born- 
traeger, 1906.) Price 3.80 marks. 
N this work the author has presented much interest- 
ing information from the point of view of an in- 
quiry into the relations between sexual maturity and 
the conditions attained by the vegetative organs, especi- 
ally where these from any cause show tendencies to 
marked changes of aspect during the development of 
the plants. Many of his examples are drawn from 
his personal investigations, the inquiry having sug- 
gested itself to him during a residence in Western 
Australia, where peculiarities in these relations appear 
to be remarkably frequent, and to be often traceable 
to the environment. He has also made a careful 
study of such published works as bear on this subject, 
and has used the materials derived’ from them with 
good effect as regards both the facts and the causes 
of abnormal conditions, and the inferences to be 
drawn from them. His statement of the whole sub- 
ject, and of the conclusions that he believes can be 
fairly based on what is yet known of it, is well and 
clearly put, and shows the need of further inquiry, as 
well as the risk of pressing inferences beyond their 
fair limits at times. 
The book is deserving of attentive perusal, and will 
suggest to the careful reader parallels among our 
own plants to some of the cases described, and ques- 
tions in need of investigation from the new stand- 
point. The book opens with a discussion of the 
NO. 1939, VOL. 75 | 
conditions that favour the attainment of sexual 
maturity in the normal course of development, and 
also prematurely, as measured by the stage of de- 
velopment of the vegetative organs. By selected ex- 
amples it is shown how variable are the stages of 
progress, when judged by the leaves especially, at 
which sexual reproduction may occur. Attention is 
also directed to the assemblages of different species 
that exist on dry, poor soil, and that are distinguished 
by the production of precocious flowers and fruits 
on ill-nourished dwarfs, as well as to the production 
of flowers in cultivated seedlings of various trees, as 
in the Swietenia Mahagoni, recorded by Mr. Hemsley 
(Hooker’s ‘‘ Icon.,’’ 2786), where deficiency of water 
appears to be the exciting cause. 
The unusual precocity of reproduction is most evi- 
dent where there is naturally a succession of leaf- 
forms before the normal period of flowering is 
reached, some of these being regarded as character- 
istic of the immature, and others of the adult plant. 
For the definite grades in such a succession Dr. Diels 
employs the term ‘‘ Helikomorphie,’’? the whole being 
included in the ‘‘ Heteroblastie ’”? of varied forms of 
parts having the same morphological value. The sig- 
nificance of the helicomorphies, where not of the 
grade usually associated with flowering, is shown to 
differ in different plants. In some even those char- 
acteristic of the normal immature plant may not 
be fully exhibited. In others these may be fully 
shown; but those of the adult may remain unde- 
veloped or arrested. The causes that lead to such 
departures from the usual course can be shown to lie 
in the environment in some cases; but in others they 
cannot yet be explained. Among the more frequent 
causes of arrest and retention of immature character- 
istics are influences that interfere with growth, such 
as deficiency of water in dry soils, inclement weather 
at high elevations, shading and overcrowding, the 
plants grown under such conditions showing an un- 
usual tendency to flower while having leaf-organs of 
the normal immature grade. 
A comparison of allied species shows that the normal 
youthful helicomorphy of one may be very similar to 
the normal adult condition of another that lives in 
less favourable surroundings, e.g. in Ranunculus 
sceleratus and R. pygmaeus. 
The importance of a thorough comprehension of 
these variations, of their significance in the life of 
each species, and of their value as indications of re- 
lationships between species or larger groups in classi- 
fication, is self-evident. Embryology has not afforded 
like help in systematic botany to that obtained from 
it in zoology. In some cases seedling plants for a 
brief time show characters very unlike the adults, 
and suggestive of the structure of less modified allied 
forms, as in the well-known- examples of Ulex and 
Acacia. All such deserve careful study; and Dr. Diels 
has shown how they throw light on the value of 
“species,” as in the forms of Limosella, and of 
‘‘genera,’? as in the relation of Regnellidium to 
Marsilia. His discussion of the relations of certain 
species of Hakea, of Grevillea, and of numerous 
others, largely on the basis of his personal observa- 
