302 



NATURE 



[June 14, 1917 



is not represented in a single reproductive cell, 

 for the organism is always a double structure. 

 On the other hand, we know that certain physical 

 characters are definitely inherited upon Mendelian 

 lines ; for instance, colour in plants and animals, 

 certain hair and feather characters, leaf forms, 

 the presence or absence of horns in cattle, the 

 shape of potato-tubers, are thus inherited ; as are 

 also brachy-dactyly, nyctalopia, and other condi- 

 tions in man. 



Although certain abnormal characters in. 

 individuals may be conveniently described 

 as dominant or recessive, this is far • from 

 being a full explanation of neuropathic inherit- 

 ance. The "coupling" and "repulsion" known 

 to exist between different factors, the explanation 

 of " sex-limited " diseases, and even the causation 

 of sex itself, fail to be explained upon evidence 

 which is founded upon Mendelian lines alone. In 

 regard to Mendelism we think there is too much 

 stress laid in the text-book upon the statement 

 that "actual findings in mental disorders are 

 alongside of theoretical expectations." As yet we 

 know too little to be able to state that Mendel's 

 law applies to all characters of all living organ- 

 isms. Mental disorders in themselves are too 

 vague as well as too subtle and complicated to 

 be classified into definite heritable unit-characters. 

 All we can say is that we must not expect simple 

 Mendelian results from the study of insane in- 

 heritance, which is a product of many factors, 

 each of which may possibly be independently 

 heritable, but all of which have certain definite 

 effects that must necessarily interfere with the 

 practical application of Mendelism. The irregu- 

 lar dominance of some abnormal mental states 

 shows that there is no definite segregation of 

 mental characters. 



The references to cerebral syphilis in the 

 manual are the only long quotations from any 

 English authority, and these do not point out 

 that mental symptoms, such as cerebral irritation, 

 restlessness, excitement, anxiety, and depression, 

 occur in no fewer than 80 per cent, of all cases 

 of syphilis, and mostly during the secondary 

 stage ! It is agreed by English authorities that 

 these mental symptoms occur within six months 

 from the date of primary infection. The author 

 is too optimistic about the Wassermann reaction 

 remaining negative after one or two injections of 

 salvarsan. Exceptionally this may be so, but the 

 present treatment of syphilis extends to more than 

 one hundred days, and consists in the intravenous 

 or intramuscular injection of salvarsan, neo-salvar- 

 san, gallyl, luargol, or kharsivari, combined with 

 mercury ; and cerebral syphilis receives identical 

 treatment. No reference is made to the numerous 

 exp)eriments made with salvarsanised serum, and 

 we share the author's doubt as to the permanent 

 arrest of general paralysis or of locomotor ataxia. 



The Binet-Simon tests of mental deficiency are 

 Introduced and occupy about twenty pages, but it 

 would have been more helpful if the author had 

 added fuller comments upon their interpretation 

 and practical utility. No mention is made of the 

 NO. 2485, VOL. 99] 



Montessori method of treating mental deficiency^ 

 for this would have been appropriate in a work 

 purporting to cover all inherent mental weakness. 

 A useful sub-section is given to the technique of 

 the Wassermann reaction, but, although the 

 haemolytic system is used to explain the bacterio- 

 lytic, the description needs simplifying for the 

 general practitioner, in spite of the fact that this 

 reaction is in essence only a quantitative chemical 

 test for the presence of "complement." Psycho- 

 analysis finds a short place in the text-book ; it is 

 described as a "time-robbing task," and the 

 author shows a dignified reserve in its discussion, 

 merely indicating briefly the methods employed to 

 carry it out. Figures of the dead neuron (Betz 

 cells) are introduced from the drawings of Adolf 

 Meyer, but no reference is made to the altogether 

 different structure of the living neuron. On the 

 whole, the manual is a trustworthy text-book for 

 the psychiatric clinic, and the new edition brings 

 the work fairly up to date, although there is no 

 mention of " shell-shock " or the mental effects 

 of the war. Probably the recent development in 

 American politics will soon remedy this defect. 

 Robert Armstrong-Jones. 



PHILOSOPHY AND PARADOX. 

 (i) Fermat's Last Theorem. By M. Cashmore. 

 Pp. 63. (London: G. Bell and Sons, Ltd., 

 1916.) Price 25. net. 



(2) The Elements of Non-Euclidean Plane Geo- 

 metry and Trigonometry. By Prof. H. S. 

 Carslaw. Pp. xii+179. (London: Longmans,. 

 Green and Co., 1*916.) Price 55. net. 



(3) The Algebraic Theory of Modular Systems. 

 By F. S. Macaulay. Pp. xiv+112. (London: 

 At the Cambridge University Press, 1916.) 

 Price 45. 6d. net. 



(i) npHE main fallacy of Mr. Cashmore 's 

 -»- paradoxical tract is this : — " Let f, <f> be 

 polynomials in x, and A a constant different from 

 zero; then, if /, cf> have a common factor (x—a), 

 x = a may be regarded as a solution of f/(l> = X. 

 Conversely, if //<^ = A has a root a, then (x — a) 

 must be a common factor of / and ^." (See p. 18.) 1 

 (2) By this time it is fairly well known among f 

 mathematicians that ordinary geometry is a sort 

 of border-line between two equally consistent 

 theories, in each of which Euclid's axiom of 

 parallels is false. In one of these the sum of 

 the angles of a " rectilinear " triangle exceeds 

 two " right " angles ; in the other it falls short of 

 it, and may even converge to zero. If "similar" 

 triangles are defined by parallelism of sides, we « 

 have the sums of their angles differing according" I 

 to a fixed law; and, similarly, if we define them 

 by proportion of sides (generally according to a 

 different law). These non-Euclidean geometries j 

 apply to three-dimensional space as well as to the | 

 plane, and the question for teachers is to make 

 them intelligible to the student by intuitional 

 methods. As regards the case when the sum of 

 the angles of a triangle is less than two right 

 angles, nothing can be better than to take as 



