474 
NATURE 
(Jury x21, tome 
their mode of working, and the principles under- 
lying the construction, but he gives the actual 
construction by working drawings and excellent 
pictures and detailed instruction required in the 
workshop. 
The space available for this review does not 
permit of an enumeration of the contents in detail ; 
it must therefore suffice merely to mention the 
main headings. The first three chapters deal with 
continuous current. We find here measuring in- 
struments, switchgear, rheostats, accumulators, 
D.C. machines, special types of motors as used on 
railways and for winding engines, speed control, 
and the use of D.C, apparatus generally. The rest 
of the book is taken up with A.C. work. Here, 
again, we start with measurement and the con- 
struction of measuring instruments, then follow 
switchgear and safety appliances, the construction 
and testing of generators, parallel working, con- 
verters, transformers, synchronous and asynchron- 
ous motors, starting and regulating devices, and 
finally commutator motors. It is an excellent book 
and will be found useful by all practical men who 
work on scientific principles. | GisperT Kapp. 
PRINCIPIA MATHEMATICA. 
Principia Mathematica. By Dr. A. N. White- 
head, F.R.S., and Bertrand Russell, F.R.S. 
Volume il. Pp. xxxiv+772. (Cambridge: 
The University Press, 1912.) Price 30s. net. 
HE main features of this important work 
have been described in a previous notice 
(August 31, 1911, p. 273). In the present volume 
the authors come more directly into contact with 
what may be called traditional arithmetic and 
algebra, the three parts being devoted to cardinal 
arithmetic, relation-arithmetic, and series respect- 
ively. Our old familiar friend, the family of 
natural numbers, appears under the head of ‘in- 
ductive cardinals”; besides this, and preceding it, 
we have a discussion of various types of cardinals, 
definitions of addition, multiplication, and ex- 
ponentiation valid for transfinite, as well as finite, 
numbers; thence we proceed to the study of inter- 
vals, progressions, the first transfinite cardinal, 
and the axiom of infinity. 
The section on relational arithmetic almost 
brings us back to formal logic again; it is a sort 
of analogue to ordinal arithmetic, and, as the 
authors point out, it is in the present context 
mainly important as a preparation for the doctrine 
of series, which immediately follows. The mathe- 
matical reader will be struck by the fact that 
a relation which generates a series is analysed into 
one which possesses three separate and independ- 
ent properties. Important technical terms here 
NO. 2228, VOL. 89] 
‘ 
are “section” and “segment” (pp. 624 et seq.), 
and in all this connection the contributions of 
Dedekind and Cantor make themselves felt. The 
final section brings us to the general problems of 
convergence, limit, and continuity ; and the reader 
who has the courage to learn the new symbolism 
will now find that there has been a real philo- 
sophical advance in the period between Cauchy 
and Cantor; or perhaps it would be better to say 
that Cantor has initiated a new era of research, 
so far as any one man Is truly an initiator. 
Analogies are always dangerous, and in nothing 
more so than in pure mathematics; but one can- 
not help feeling that all this recent investigation 
of the elements of mathematics has some affinity 
to the chemical analysis of molecules into their 
atoms. Perhaps it may not be absurd to carry 
the metaphor a little further. Electricians have 
proved that the atom of the chemist is a much 
more complicated entity than he imagined; it is 
possible that the present irreducibles of the mathe- 
matician may dissociate, if subjected to still 
severer tests. If this be so, the resolver will be 
either a mathematician or a metaphysician, or a 
combination of both; and even he may not (indeed, 
probably will not) arrive at ultimate conclusions 
with which the human spirit will rest content. 
It would be very unfair not to point out that 
the authors, by immense and ungrudging work, 
have fused together the discoveries of many 
searchers (including themselves) into as near a 
homogeneous whole as_ present circumstances 
permit. G: Bae 
DISEASE-DISSEMINATING ARTHROPODS. 
Entomology for Medical Officers. By A. Alcock, 
C.I.E., F.R.S. Pp. xx+ 347+ 136 text-illustra- 
(London: Gurney and Jackson, 1911.) 
Price gs. net. 
tions. 
T has well been said that tropical medicine is 
nowadays largely a matter of entomology, 
and it is to the recognition of this fact that the 
volume before us owes not only its appearance, 
but also much of the knowledge epitomised in its 
pages. The term “entomology” is interpreted 
by the author in the ‘old inclusive Latreillian 
sense,’ and we consequently find ourselves con- 
cerned not merely with insects, but with the 
Arthropoda as a whole, or rather with those 
groups of this enormous phylum with which the 
medical officer in the tropics at the present day 
must needs have a nodding acquaintance or some- 
thing more. 
In view of the transcendent importance of the 
Diptera in connection with disease, it 1s not sur- 
prising to find that nearly half of the volume is 
