98 



NATURE 



[June 4, 1903 



otherwise. So long as |a-| <i, Lambert's series de- 

 nes a function of ;t: ; calling this/(jr), a prime number t 

 is distinguished by the fact that it makes 



D,P(A-) = 2p[p !) 



when x=o. There are many remarkable instances of 

 arithmetical truths derived by constructing an enumer- 

 ative series (purely symbolical, in the first instance) and 

 then investigating its properties as a function of ;tr. Ulti- 

 mately, of course, the results obtained must depend upon 

 purely arithmetical considerations ; but transcendental 

 analysis supplies, in such cases, a kind of machine, by 

 which, with slight effort, theorems are verified, or even 

 suggested, although the proof of them by strictly arith- 

 metical methods may be very difficult. Whether 

 Lambert's series can be used in this way to simplify the 

 problem of the frequency of primes still remains an open 

 question. G. B. M. 



A PLEA FOR INTERACTION. 



Geist und Korper, Seele und Leib. Von Ludwig 

 Busse. Pp. x + 488. (Leipzig : Verlag der Diirr'schen 

 Buchhandlung, 1903.) Price 8.50 marks. 



IN this book the author aims at finally establishing a 

 doctrine of "interaction." Previous expositions 

 in less comprehensive form have already been criticised 

 by eminent writers ; to these objections the author now 

 replies. The result is a veritable encyclopaedia of 

 views on this question ; authors of all nationalities are 

 here cited to defend themselves against criticisms 

 which are throughout shrewd and relevant. In the 

 mass of material the author's particular theory is 

 apt to be obscured; a strictly methodical procedure 

 has to some extent obviated this defect. After a 

 refutation of materialism, adequate for Its purpose 

 as entrde, we come to the piece de rdsistance, entitled 

 "Parallelism or Interaction?" Here parallelism is 

 discussed under the heads modality (Is parallelism a 

 metaphysical doctrine or merely a hypothesis?), quan- 

 tity (must It be partial or complete?), and quality 

 {materialistic, realistic-monistic, idealistic-monistic, 

 and duallstic forms). From this catalogue there 

 finally emerge as " valid forms " only the complete, 

 the realistic-monistic, the idealistic-monistic, and the 

 duallstic forms. The method of criticism employed 

 is called by the author "immanent." Internal dis- 

 sensions reduce the various doctrines to the vanishing 

 point; those alone survive which do not contain in 

 themselves any elements contradictory to parallelism. 

 The crucial point comes when the idealistic-monistic 

 form is discussed. The author holds an idealistic- 

 spiritualistic doctrine, and is therefore concerned to 

 show that this does not necessitate parallelism, that 

 interaction is not only possible, but preferable. He 

 relies mainly on the unity of consciousness, and the 

 necessity of including activity as subjectively known 

 in our view of the Whole. The arguments against 

 *' conservation of energy," " continuity," and natural- 

 istic positions in general are then brought forward. 

 The author is emphatically opposed to any com- 

 promises. Between mind and matter the break is abso- 

 NO. 1753, VOL 68] 



lute; activity without expenditure of energy, the ex- 

 tension downwards to the unconscious or to quelque 

 chose d'analogique — In short, compromise of all kind 

 is rejected. Philosophy must here take its stand upon 

 experience, and claim that interaction alone does justice 

 to the facts. The rejection of a preestabllshed har- 

 mony makes It necessary to assert that ultimately we 

 must formulate any given series of events, not as one 

 or as two homogeneous series, either physical (as 

 a b c . . .) or psychical (0/87..), but as a com- 

 pound series of the form a P c S, &c. Similarly the 

 rejection of any development of mind from lower 

 elements' Is followed by the conclusion (after Lotze) 

 that It supervenes on a certain development of " Zellen- 

 gruppe. " It follows that so far as interaction is con- 

 cerned we must assert a dualism ; the two systems 

 which interact must be kept distinct; the ultimate 

 unity Is not to be found In their nature, but in the fact 

 of their Interaction ; we have not to piece together the 

 world, but to accept its living unity. 



Clearly such a theory claims attention more for the 

 consequences to which It looks than for the advantages 

 It attains. So far we must regard the Weltans- 

 chauung of the closing section as much more than 

 a " dessert." Here there appears an " AU-Geist," and 

 with it new possibilities; unfortunately the binder 

 omitted some pages here, and criticism must therefore 

 turn upon him rather than upon the author. As an 

 exposition of how experience may be treated in the 

 interests of a Weltanschauung, we have here an admir- 

 able discussion. Much of It Is common property among 

 writers on the philosophy of psychology. But refuta- 

 tion has before now proved a two-edged sword, and 

 on the crucial points, the subjects of activity and of 

 development, the author seems to glide from proof 

 (o assertion. The Idealistic treatment of the two 

 factors said to interact presumably forms the ground 

 of a final unity; the question " how " Is more easily 

 solved ambulando than cogitando. It seems to re- 

 quire more than the author's theory of Thing-monads 

 and Soul-monads — more even than the binder can have 

 omitted. G. S. B. 



THE NEW ENCYCLOPEDIA. 

 Encyclopaedia Britannica. Vol. xxxi. New volumes. 

 Vol. vil. Mos— Pre. (London : A. and C. Black ; 

 and the Times Office, 1902.) 



THE prominence given to scientific subjects in the 

 seventh. of the new volumes of what has long been 

 regarded as our national encyclopaedia serves in a 

 measure to indicate how large a part the work of men 

 of science has taken in the increase of knowledge 

 during the last quarter of a century. Among articles 

 of prominent importance in this volume, so far as the 

 student of science is concerned, are those dealing with 

 palaeobotany, pathology, and physiology, though there 

 are many other articles of a less exhaustive kind deal- 

 ing with problems of great scientific interest. Techno- 

 logical questions receive due attention, and are repre- 

 sented, among others, by essays on navies,- ordnance, 

 paper manufacture, petroleum, photography, and elec- 



