December i6, 1909] 



NA TURE 



185 



hospital consisted of two divisions similar in every 

 respect, except that in the first division the women 

 were attended by the students and in the second 

 division by midwives. Semmelweis found, over a 

 period of five years, that the mortality in the first 

 division remained three times as high as that in the 

 second. What was the cause of this? A significant 

 entrj' occurs in his note-bool< : — " All is doubt and 

 difficulty. Only the great number of the dead is an 

 undoubted reality." 



In 1S47 Semmehveis's friend Prof. Kolletschka 

 died of septicsemia from a scratch on the finger 

 received at a post-mortem examination. The cir- 

 cumstances of this tragedy, its origin from the 

 introduction of a poison into a wound surface, the 

 course of the illness, and the pathological results 

 revealed by examination of the body after death 

 brought illumination to Semmelweis. This was a 

 similar condition to the " fever " of puerperal women ; 

 both were due to inoculation of putrid organic matter, 

 hence the terrible mortality among women attended 

 by students fresh from the mortuary and the better 

 results obtained by the midwives. In 1847 " the 

 eternally true doctrine " was announced, but no wide 

 publicity was given to it, and it failed to obtain 

 general acceptance. Had Semmelweis been a ready 

 speaker or writer, had his personality been different, 

 inore ambitious, perhaps even more winning, the 

 great truth might have been accepted by the pro- 

 fession. Instead of this he died unrecognised, after 

 years of embittering and acrimonious discussion. 

 Sir William Sinclair's book is of the greatest interest, 

 and we are glad to welcome an adequate English 

 appreciation of Semmelweis, who certainly ranks 

 among the "heroes of medicine." 



NON-EUCLIDEAN GEOMETRY. 

 The Elements of Non-Euclidean Geometry. By Dr. 



J. L. Coolidge. Pp. 292. (Oxford : Clarendon 



Press, 1909.) Price 155. net. 

 "T^HIS work will be found really valuable by all 

 J- students of geometry, especially by those who 

 know little or nothing of the non-Euclidean theories. 

 First of all we have a discussion of the elementary 

 axioms; in this the plane is deduced from what may 

 be called a triangular frame, in the manner of Peano 

 and Schur, Then comes the discrimination of the 

 three cases, according as the sum of the angles of a 

 plane triangle is equal to, greater than, or less 

 than two right angles ; and this is followed by the 

 fundamental trigonometric formulae for a triangle, 

 deduced very neatly from Saccheri's isosceles birectan- 

 gular quadrilateral. It is also proved at this stage 

 that the •non-Euclidean plane can be developed upon a 

 surface of constant curvature in Euclidean space. 



The author next proceeds to a discussion of higher 

 spaces (in three dimensions), the absolute, and groups 

 of congruent transformations. The treatment here is 

 entirely analytical, and for the beginner, at any rate, 

 this is doubtless the proper course to take. In fact, 

 most will feel that the analytical treatment of the 

 subject has the great advantage of preserving us from 

 fallacies and vicious circles. 

 NO. 2094, 'VOL. 82] 



The next chapters contain developments relating to 

 curves and surfaces of the first and second orders ; 

 in particular, there is an interesting chapter on the 

 higher line-geometry. In some respects this is 

 analogous to Staudt's representation of an imaginarv 

 line of the second kind; but it should be said that 

 there is only a very brief sketch (pp. 127-30) of the 

 interpretation of imaginary coordinates in non- 

 Euclidean space. 



The chapter on areas and volumes is remarkably 

 good and clear. The formula for the area of a 

 triangle is obtained by a method which is both ele- 

 mentary and rigorous ; and there is a very interesting 

 discussion of the volume of a tetrahedron. 



Chapters xv. and xvi. are on differential geometry, 

 and here again the treatment is admirable. For one 

 thing, the quantities usually denoted by D, D', D" 

 present themselves in a natural way instead of result- 

 ing from a long and tedious calculation. Among the 

 prettiest results of these chapters are the extensions 

 of Meunier's theorem and of Gauss's theorem on the 

 total curvature at any point on a surface. 



There is a brief discussion of multiply connected 

 spaces, and two final chapters, each of which is, in 

 fact, an independent presentation of the subject, one 

 from the projective point of view, and the other, like 

 that of Riemann's famous essay, based on the pro- 

 perties of a quadratic differential form. The reader 

 cannot fail to profit from these various ways of re- 

 garding the subject; their agreement in results will 

 help to free him from the natural prejudice which 

 many entertain — that non-Euclidean geometry is a 

 mere juggling with symbols, having no relation to the 

 properties of space as it actually is. .\iter the recent 

 critical work on the foundations of geometry, the con- 

 clusion is inevitable that there are no grounds at 

 present, and probably never will be, for asserting that 

 the space of physical phenomena is Euclidean or non- 

 Euclidean ; while in the realm of speculation the three 

 kinds of space are coordinate, and equally possible. 



G. B. U. 



COLOUR PHOTOGRAPHY. 



L'bcr Farbenphotographie nnd verwandte nattir- 

 u'issenschaftliche Frageii. By Prof. Otto Wiener. 

 Pp. 88. (Leipzig : J. .\. Barth, 1909.) Price 2.40 

 marks. 



THERE is, perhaps, no more remarkable recent 

 scientific achievement than the realisation of 

 the problem of photography in colours, which has 

 occupied the thoughts and aspirations of many 

 workers since the day when Nicephore Niepce, the 

 founder of photography, told the Marquis de Jouffroy 

 that one day he would reproduce his likeness just as 

 he saw it in a mirror. 



In this reprint of a discourse on colour photography 

 and kindred physiological questions, delivered at the 

 Congress of Naturalists in Cologne in September, 

 1908, Dr. Otto Wiener has given a brief sketch of the 

 principles of the various methods of colour photo- 

 graphy, with additions, chiefly of omissions from the 

 discourse itself, together with copious notes and r<^ 

 ferences to the literature, and further details of the 



