198 
INGEIRTS C/Tsare 
[ DECEMBER 27, 1906 
to 0-4 of a minute. We suspect that Mr. Goodwin 
knows a good deal more about the capacity of the 
men for whom he is writing than we do. 
NW, Ao JE. 
The Horticultural Note Book. Compiled by J. C. 
Newsham. Pp. xx+418. (London: Crosby Lock- 
wood and Son, 1906.) Price 7s. 6d. net. 
TuHE contents of this book are as disconnected as are 
the words in a dictionary. Anything like a ‘‘ review ”’ 
is, therefore, out of the question. We can only state 
the general nature of its contents and give an opinion 
as to the way in which the compiler has accomplished 
his task. As to its contents, they comprise ‘‘ prac- 
tical rules, data, and tables for the use of students, 
gardeners, nurserymen, and others interested in 
flower, fruit, and vegetable culture, or in the laying 
out and management of gardens.”’ 
This is a fairly comprehensive enumeration, but it 
is not complete, for we also find various tables which 
will be of service to those who have to deal with 
woodcraft or the sale of timber. The compiler has 
done his work well; he is evidently familiar with the 
ordinary requirements of his readers, and he has 
fulfilled them with judgment and accuracy. 
With such a mass of detail to deal with it would 
be wonderful if misprints did not occur, but they are 
remarkably few. On 299 there is, however, a 
crop of such blemishes which should be removed in a 
future edition. We may suggest also that the tables 
on pp. 251, 252 be expunged as inadequate, and in 
point of accuracy not equal to the rest of the volume. 
We are glad to see various metrical tables added. 
No one who compares the regular definite proportions 
of the metrical system with the confusion of the 
ordinary lineal and land measures, to take one in- 
stance, can doubt the advantages of regular system 
over chaos. It is permissible to envy the next genera- 
tion, whose labours will be so materially lightened by 
the general adoption of the new system. 
The author has given not a few ‘‘ miscellaneous 
weights and measures, but he might have added 
more from the Covent Garden repertory, where cab- 
bages are sold by the “‘ mat,’’ carrots by the “ pad,” 
cauliflowers by the ‘tally,’ to say nothing of 
‘“bundles,’’ ‘t bunches,’’ “‘ cases,’’ and other indeter- 
minate measures. A book of this kind is intended 
for reference purposes, and its value must be tested 
by frequent consultation. Tried by this test, we may 
say that we have found the book very serviceable. In 
a future edition a list of the commoner fungi and the 
plants on which they are parasitic would be desir- 
able; for instance, we find no reference either to the 
ordinary or the American mildew attacking goose- 
berries, or to the fungous pests which commit such 
havoc with grapes, tomatoes, and cucumbers. 
By G. Vivanti. 
(Milano: 
” 
Funzioni poliedviche e modulari. 
Pp. viii+437- Manuali Hoepli, 366-367. 
Ulrico Hoepli, 1906.) Price 3 lire. 
Tue author tells us in his preface that he found 
Klein’s ‘‘ Vorlesungen tiber das Ikosaeder’’ and 
Klein and Fricke’s ‘‘ Theorie der elliptischen Modul- 
functionen ”’ ‘‘ pretty stiff reading.’? Probably most 
students will sympathise with him and will give a 
ready welcome to this little book, which is intended 
to prepare the reader for the study of these classical 
treatises. The ground covered is approximately that 
of the last four chapters of Forsyth’s ‘‘ Theory of 
Functions *’ (excluding automorphism), but the sub- 
ject-matter is discussed in much greater detail. The 
first part of the book deals with groups formed by 
substitutions of the form 2! =(az+8)+(yz+4), especi- 
ally with the five finite (polyhedral) types of group 
NOs O30,-VOL. 75] 
and with the infinite (modular) group in which a, B, 7,6 
are integers such that ai—By=r1. In the first few 
pages a group is defined and some of its more ele- 
mentary properties proved. It must be confessed that 
these introductory sections are not quite satisfactory, 
and it is doubtful whether they would be readily 
intelligible to anyone who had no previous knowledge 
of group-theory. For instance, the author fails to 
make clear the distinction between a group and a 
semi-group, or that between an abstract group and 
the particular application he has in mind. The rest 
of part i. is, however, clear and readable, and should 
serve effectively the purpose intended by the author. 
In the second half of the treatise the author dis- 
cusses the invariants of the polyhedral and modular 
groups, the connection of the Schwarzian equation 
with polyhedral and modular equations, and the ap- 
plication of the polyhedral groups to the solution of 
algebraic equations. This part appeals to a very 
different class of readers; in fact, the author assumes 
a knowledge of elliptic functions, Riemann’s surfaces, 
the existence theorem, Noether’s curve, the Galois 
field theory, &c. The lack of balance between the 
two parts in this respect is unfortunate, if unavoid- 
able. There are a few errors; for instance, the state- 
ment of § 104 seems to require modification when 
n=6, while on pp. 208 and 209 the difference between 
(n), [n], and {z} is not at all clear. 
Hermann von Helmholtz. By Leo Koenigsberger. 
Translated by Frances A. Welby, with a preface 
by Lord Kelvin. Pp. xvii+440. (Oxford: Claren- 
don Press, 1906.) Price 16s. net. 
Ture German original of this book appeared in 1903, 
and was reviewed at some length in Narure of July 2 
in the same year (vol. Ixviii., p. 193). The work of 
translation is admirably done in every way, and the 
English public owes a debt of gratitude to the trans- 
lator for enabling it to study in its own language one 
of the most interesting careers of the nineteenth cen- 
tury. A moderate all-round scientific training is 
necessary and sufficient to enable the reader to follow 
the description of the greater part of Helmholtz’s 
work; but, though mathematical symbols are avoided, 
probably no one who has not specialised to some 
extent in applied mathematics will find intelligible 
the account of his more abstruse mathematical 
researches. ; 
Though Herr Koenigsberger makes the very most 
of the space at his disposal, yet the reader lays aside 
a book of 440 pages with a feeling that he has seen 
the merest sketch of Helmholtz’s life. Probably no 
better comment could be made on the industry of the 
great man of science or on the versatility of his 
genius. To do full justice to his career a treatise of 
three times the length would perhaps be needed. As 
it is, the reader is bewildered at the rapidity with 
which his attention is turned from one epoch-making 
discovery to another, and tries in vain to follow the 
steps by which Helmholtz was led from one subject 
to another when, during the space of three years 
largely occupied with his professorial duties, he dis- 
cussed in turn optics, nerve transmission, acoustics, 
hydrodynamics, geometry, electricity, hay-fever, and 
so on. 
Though, on the whole, the book lays more stress 
on Helmholtz’s work than on the details of personal 
interest, yet the author has a true instinct for record- 
ing just those incidents of Helmholtz’s life which 
throw most light on his character and ideals, and 
reveal most clearly the influences which surrounded 
him. We lay down the book with a feeling of very 
real sympathy for the frequent illness and bereave- 
ment which cast a perpetual shadow over the plea- 
