June 15, 1900.] 



SCmNGE. 



947 



to pass successive events." If such statements 

 as these are warranted by the evidence which 

 is oflfered, then the logic of this science is not 

 that of the other sciences. 



The popular interest in the topic which this 

 volume treats, the obvious intention to gain 

 the ear of the public by recounting tales of 

 merely personal interest and passing them off 

 as scientific data, the confident expression of 

 the author in the certainty of his conclusions, 

 will all combine to circulate the notion among 

 the public at large that the conclusions of the 

 volume represent the final verdict of science on 

 these momentous questions ; and it is in this re- 

 spect that the volume is likely to exert a seriously 

 unfortunate influence. It is difficult enough at 

 best to get the intelligent layman to understand 

 that the ability to interpret soundly and ration- 

 ally phenomena of this field demands, like all 

 expert opinion, a special knowledge and a fit- 

 ness of training and intellect. It is quite idle 

 to expect the layman to distinguish too closely 

 between one scientist and another, or between 

 the methods which they use and the dicta which 

 they express. Possibly (and it were better if 

 one could say probably) M. Flammarion has so 

 seriously overstepped the limits of sound judg- 

 ment and expression in this matter, that his 

 authority will be called into question by the 

 reader who reflects as he reads. There is no 

 good reason why an astronomer with a gift for 

 popularization and an interest in the phenomena 

 of the ' Unknown ' should not prepare as good 

 and valuable an account of these phenomena 

 as the present state of knowledge permits. There 

 is no desire on the part of psychologists to dis- 

 countenance such investigation, whatever its 

 origin. But it is essential that the investigator 

 should thoroughly know what the present state 

 of knowledge really is, and above all, that he 

 should possess the indispensable logical appre- 

 ciation of the conditions of the various problems. 



This logical vigor and discernment, this essen- 

 tial logical insight that is both a natural endow- 

 ment and the result of conscientious training is 

 not the prerogative of any one science nor of 

 scientists at large ; and he who has it has the 

 most important part of the equipment necessary 

 to the participation in such investigations. It 

 is because this volume is conspicuously lacking 



in these qualities, and because it as a conse- 

 quence substitutes for them uncritical collections 

 of narratives and dogmatically stated conclu- 

 sions, that it must be disavowed by those who 

 stand for the thoroughly scientific investigation 

 of the unexplored regions of the psychological 

 universe. It is very certain that if M. Flam- 

 marion and his colleagues had used the same 

 methods in astronomy as he applies to the in- 

 vestigations of this volume, modern astron- 

 omy would be held in very different repute from 

 that which it now enjoys. There is an amateur 

 and an expert exploration of this field, just as 

 there is in geographical exploration, and it will 

 require the best trained and most scientific ex- 

 plorer to reveal the true nature of this ' darkest 

 Africa' of the human mind. 



Joseph Jasteow. 



Histoire des mathematiques. Par Jacques Boyer. 



Geoeges Caere et C. Naud, Editeurs. 



Paris. 1900. Pp. 260. 



The growing interest in the history of science 

 is made manifest by the number of historical 

 works which have appeared in recent years. 

 Perhaps in no science is this movement so 

 marked as in mathematics. During the last 

 twenty years there have appeared not only the 

 monumental works of Moritz Cantor and Maxi- 

 milien Marie, but also a large number of brief 

 histories. The volume before us belongs to the 

 latter "class. 



An attractive feature of this book are the 

 page-portraits of nineteen mathematicians and 

 seven facsimiles of parts of celebrated manu- 

 scripts and of old drawings of mathematical 

 instruments. We know of no other general 

 history of mathematics which furnishes the 

 reader such a treat. So high is our apprecia- 

 tion of this feature that we are ready to forgive 

 the author when we discover that, out of a 

 total number of nineteen mathematicians whom 

 he has honored with portraits, eleven are 

 Frenchmen. 



M. Boyer's history is written in an interest- 

 ing style and will doubtless stimulate more 

 serious study of mathematical history in larger 

 works. But in two respects the author has 

 hardly achieved what might have been ex- 

 pected of him. 



