272 



NA TURE 



[September 2, 1909 



was an obscure phrase even to a Greek, and that it 

 was meant to refer to what we may call the indifferent 

 distribution of points and lines on a line and a plane 

 respiclively. At any rate, Proclus's explanation is 

 clearlv wrong, though it very likely contains the sub- 

 stance of what a teacher would often say in coni- 

 menting on Euclid's text. 



Another very interesting note is that on the Greek 

 notion of " angle." As this included curvilinear 

 angles, it led to a variety of discussions and some 

 paradoxes; for example, taking a semicircle AMB 

 and a tangent BT at one end of the diameter AB, it 

 was argued that the angle at B between the circle 

 and diameter is less than the rectilineal angle ABT, 

 because BT is outside the circle, while, on the other 

 hand, any acute rectilineal angle can be proved less 

 than the curvilinear angle in question. However 

 (p. 176, bottom), there is some evidence of a way of 

 looking at angles such as we should now express in 

 terms of the differential calculus. 



To the famous postulate 5 (generally referred to as 

 the nth axiom) eighteen pages are devoted. Here 

 it must suffice to say that suffir^nt references are 

 given to the principal authori*'.os on the theor\' of 

 parallels and non-Euclidean geometry, and that atten- 

 tion is properly directed to the work of the Jesuit 

 Saccheri. 



The books least familiar to students are, of course, 

 the arithmetical books (vii.-ix.) and Book x. With 

 regard to the former. Dr. Heath has given diagrams 

 consisting of straight lines, just like those in Book v. ; 

 this is rather misleading, and it would surely have 

 been better to give rows of dots, or, at any rate, 

 graduated straight lines to the same scale. In this 

 part of the work. Dr. Heath gives algebraical para- 

 phrases of the less obvious propositions ; these will be 

 found very helpful to those not familiar with Greek 

 methods of reasoning. 



As De Morgan said long ago, the most remarkable 

 (and in some ways most characteristically Greek) book 

 of the " Elements " is the tenth. If we turn its 

 propositions into algebra, we find that they contain 

 an exhaustive classification of a certain set of irra- 

 tionals (or irrational ratios), all, of course, construc- 

 tible from a given line by means of rule and compass. 

 Dr. Heath, in his introductory note, gives the irra- 

 tionals in question in an algebraic form, which is 

 perhaps the best suited for comparison with the pro- 

 positions, but hardly so neat as De Morgan's in his 

 article (" Penny Cyclopjedia ") on " Irrational Quanti- 

 ties," which is still worth careful reading. 



It should be mentioned that there is an appendix 

 containing the spurious Book xiv. (by Hypsicles), and 

 a note on the so-called Book xv., two elaborate in- 

 dexes, and a beautiful facsimile of a page of the 

 Bodleian MS. D'Orville 301. 



Those who are really interested in Greek geometrv 

 will be deeply grateful to Dr. Heath for putting to- 

 gether, in such an attractive form, such a large 

 amount of historical information, and thus saving 

 students from an immense amount of toilsome re- 

 search. Finally, the excellence of the diagrams, espe- 

 cially in Book xiii., should not be overlooked. 



G. B. M. 

 NO. 2o;g, VOL. 81] 



HYPNOTISM AND OCCULTISM. 

 Hynotism, including a Study of the Chief Points of 

 Psycho-therapeutics and Occultism. By Dr. Albert 

 Moll. Translated from the fourth enlarged edition 

 by /\. F. Hopkirk. Pp. xvi + 610. (London and 

 Felling-on-Tyne : The Walter Scott Publishing Co., 

 1909.) Price bs. 



THIS book is a translation from the fourth edition 

 of the original work. The author presents his 

 readers with a survey of all that is most important 

 in the whole province of hypnotism, and indeed has 

 left little unsaid which could be of any value. An 

 opening chapter on the history of hypnotism indicates 

 the gradual progress of the science from the stage 

 in which it was almost hopelessly mixed up with 

 superstitious quackery, through periods of utter 

 neglect on the part of the scientific world, to the era, 

 which is even now only dawning, in which the sub- 

 ject is submitted to the strictest critical examination 

 of physiologists and psychologists. The literature 

 that has grown up round the subject is enormous, 

 and its volume almost daily increases. 



Dr. Moll's work is not one which is likely to appeal 

 to the general reader, and, indeed, we are of opinion 

 that this is one of its greatest merits. In this country 

 hypnotism has too long been a subject in which a 

 certain class of mind has taken an interest alterna- 

 tively to spiritualism, "Christian Science," or other 

 occult system of the day. To such, a carefully atten- 

 tive and balanced criticism is positively repellent, and 

 it is, unfortunately, in this class that hypnotism has 

 hitherto had its vogue. Dr. Moll deals in very con- 

 siderable detail with the symptoms of hypnosis. In- 

 deed, by far the longest chapter of his book is devoted 

 to a minute account of the psychological, physiological 

 and even anatomical changes which may be noted 

 during, or as a result of, hypnosis. The various 

 explanations which have from time to time been put 

 forward as to the hypnotic state are subjected to 

 searching analysis, and the confident assertions of 

 many of them are shown to have no foundation. 

 What we know about mental processes is confined 

 to a few concomitant phenomena, while the real 

 nature of such processes appears for ever debarred 

 us, and to our author the endeavours of some inves- 

 tigators to explain mental processes by means of our 

 present knowledge of the central nervous system indi- 

 cate a disquieting tendency to overestimate the gifts 

 of physiology. It is, at any rate, plain that authorities 

 take up diametrically opposite sides in their hypo- 

 theses as to the nature of the hypnotic phenomena. 



The medical and legal aspects of hypnotism are 

 dealt with at much length, and an important con- 

 clusion that emerges from the consideration of hyp- 

 notism from these points of view is that its practice 

 should be confined to those who are properly trained 

 in the diagnosis of the affections w-hich it is sought to 

 treat. To hypnotise those who should not be 

 hypnotised, and to seek to cure disease which is not 

 amenable to such treatment, is to bring hyp- 

 notism into disrepute and to wrong the sufferer. 

 Dr. Moll winds up his work with a chapter 

 upon occultism, not because there is any in- 



