Sitppleinent to ''Nature" October 19, 1905 



entertaining by the copious illustrations and interest- 

 ing through the many novel points which are touched 

 upon. As an example of the latter, the question is 

 raised as to the physiological limits of the rapidity of 

 effective response in fencing and boxing, and experi- 

 ments are cited bearing on this point. 



A more serious, and at the present moment more 

 important, aspect of the subject-matter is that which 

 deals with body movements in relation to the improve- 

 ment of general bodily physique. These are dealt 

 with in the same comprehensive manner as those 

 just referred to, for the author includes most of the 

 gymnastic exercises used in France, Swedish drill, the 

 use of clubs and of apparatus of different kinds. 



The malformation of the body is also referred to, 

 whether due to the under-development or to the over- 

 development of special muscular groups ; as an ex- 

 ample of the first, the malformation of the chest 

 through the weakness of the trunk muscles, abdominal 

 muscles, &c., is conspicuously shown; as an example 

 of over-development, the malformation of the thigh 

 in fencing masters. 



The closing chapters are devoted to the conditions 

 which may be presumed to determine how muscular 

 force can be most economically directed towards the 

 production of body movements. The author realises 

 that it would be undesirable in a treatise of a semi- 

 popular character to present this extremely important 

 subject in detail; nor, indeed, can it be set forth in 

 a very convincing manner, since several questions of 

 a fundamental type are still from the scientific point 

 of view in an unsettled state. Thus it is still a matter 

 of doubt how closely the heat-producing properties of 

 muscle are associated with those of mechanical tension 

 or change of form. M. Demeny is well aware of 

 this, and warns his readers that it is impossible to 

 deduce the energy relationships of the animal 

 mechanism from those of artificially constructed 

 machines. In this as in other departments of 

 physiology the hope of arriving at a more precise in- 

 tellectual standpoint is that expressed by one of 

 Bacon's aphorisms; it will "only be well founded 

 when numerous experiments shall be received and 

 collected into natural history which, though of no use 

 in themselves, assist materially in the discovery of 

 causes and axioms." 



In this spirit the various experiments detailed in the 

 concluding chapter of the book must be approached. 

 Most of these are concerned with the influence of 

 walking with definite loads for definite distances; 

 the points noted were the number of steps per minutei 

 the length of the stride, and the posture of the body.' 

 It appears that when, as in walking, muscular move- 

 ments are repeated many times, then there is an 

 optimum rhythm which, by permitting appropriate 

 reparation, allows the maximum of effect with least 

 expenditure of muscular power. The author considers 

 this to be the case in almost all body movements, 

 although experiments are not given in support of' this 

 generalisation. 



The book as a whole is likely to prove of very con- 

 siderable value in connection with the subject of 

 physical degeneration, which has been for some time 

 NO. 1877, VOL. 72] 



agitating the mind of the public. Methods of educa- 

 tion it is now realised should, from the hygienic 

 point of view, concern themselves with the posture of 

 the body. In the code for 1905 issued by the Educa- 

 tion Department stress is laid upon the importance 

 of " the careful cultivation of a correct posture at 

 writing and other lessons." This tardy awakening 

 of the authorities to the importance of cultivating the 

 bodily physique of the children who are taught in the 

 national schools renders it probable that teachers will 

 desire to instruct themselves in the fundamental 

 scientific aspects of the various methods for improving 

 the bodily structure and functions. In this respect 

 a work such as that now under review is likely to 

 prove of very real service ; it is trustworthy, it 

 approaches the whole question of body posture from 

 a point of view at once scientific and utilitarian, it 

 attacks the fundamental question (that, namely, of 

 the effective action of the muscles), and finally, it is 

 written in a style which makes the subject-matter 

 intelligible without presupposing special technical 

 knowledge on the part of the reader. The only draw- 

 back to its utility is one which is susceptible of 

 removal bv its translation into English. 



F. G. 



GEOMETRY OF POSITION. 

 On the Traversing of Gcnnictrical /•"i^s.'iircw. By 

 J. Cook Wilson. Pp. x+154. (Oxford: Clarendon 

 Press, 1905.) Price bs. net. 



SUPPOSE that an outline figure of any kind is 

 drawn upon a blackboard. In its construction 

 the chalk describes a certain number of closed or open 

 paths, a path being defined as the mark made by 

 the chalk during the whole time of any one of its 

 contacts with the board. But the number of paths 

 thus actually described is not necessarily the smallest 

 by which the figure can be produced, and it is an 

 interesting problem to analvse a given figure into its 

 minimum number of paths, each traversed once. 

 .As a simple example, let two oval paths be drawn 

 intersecting in four points ; the resulting figure can 

 be traversed as one closed path. If two of the inter- 

 sections are joined, the new figure can be traversed 

 as one open path ; if the remaining intersections are 

 joined, the figure cannot be reduced to less than two 

 paths. 



The first two parts of Mr. Wilson's book deal with 

 the problem above stated and various associated 

 questions. The most intercsring result is one of 

 greater generality than might have been expected. 

 Let a point in the figure be called odd or even accord- 

 ing as an odd or even number of lines radiate from 

 it; then a figure with 2n odd points can be analysed 

 into n paths, but no fewer. (To include the case when 

 i? = o a slightly modified statement is necessary, which 

 will be found in the book.) 



In part iii. the author enters upon new ground by 

 applying the principle of duality; this is the most 

 novel part of the book, and a few comments on it 

 may not be superfluous. The results of the first two 

 parts may, of course, be directly reciprocated without 

 introducing any metrical considerations; but this is 



