836 



SCIENCE. 



[N. S. Vol. XX. No. 520. 



theories to the role of mere practical recipes ; 

 these equations express relations, and if the equa- 

 tions remain true it is because these relations 

 preserve their reality. They teach us, now as 

 then, that there is such a relation between such 

 a thing and such another thing; only this some- 

 thing which formerly we called movement we now 

 call electric current. But these appellations were 

 only images substituted for the real objects which 

 nature will eternally hide from us. The veritable 

 relations between these real objects are the only 

 reality that we can attain, and the only condition 

 is that the same relations exist between the ob- 

 jects as between the images by which we are 

 forced to replace them. If these relations are 

 known to us, what matter if we deem it con- 

 venient to replace one image by another. 



That some periodic phenomena (an electric 

 oscillation, for example) is really due to the 

 vibration of some atom which, acting like a 

 .pendulum really moves in this or that sense, is 

 neither certain nor interesting. But that be- 

 tween electric oscillation, the movement of the 

 pendulum and all periodic phenomena there ex- 

 ists a close relationship which corresponds to a 

 profound reality; that this relationship, this 

 similitude or rather this parallelism extends into 

 details; that it is a consequence of more general 

 principles, that of energy and that of least ac- 

 tion, this is what we can affirm; this is the 

 truth which will always remain the same under 

 all the garbs in which we may deem it useful to 

 deck it out" (pp. 189-191). 



Our author has thus discussed the question 

 of the degree of reality in various branches of 

 science from four points of view. In arith- 

 metic vee have necessary truth developed 

 a priori in the mind; in geometry we have to 

 do with conventions, conveniently related to 

 the material world, but not themselves amen- 

 able to direct experimental treatment; in 

 mechanics we have likewise to do with con- 

 ventions, but they are amenable to direct ex- 

 periments; while in physical sciences we seek 

 under various images to exi^ress relations 

 which are profound realities. 



It is impossible to give a summary of a 

 work which is itself so summary. What pre- 

 cedes is an inadequate attempt to present a 

 few characteristic views which may serve to 

 indicate the general spirit of the work and the 

 style of treatment. The larger part of the 



rich mass of material has necessarily re- 

 mained untouched. 



The work is characterized throughout by 

 masterly clearness and by the skill with which 

 the overgrowth of unessentials and conse- 

 quences is stripped off and the fundamental 

 idea presented in a few phrases. In its tone, 

 the work addresses the non-scientist. Little 

 technical knowledge is requisite to read it, 

 but still it will hardly prove inviting to those 

 who have not in some way attained a certain 

 facility in following strict reasoning. To 

 these it will furnish an excellent and stimu- 

 lating discussion of some fundamental prin- 

 ciples of modern science apart from the 

 technicalities, while the scientist will welcome 

 this presentation in connected form of care- 

 fully thought out views which have already 

 aroused much interest in their earlier publica- 

 tion in various journals. 



The work is also remarkable for the ease 

 and directness of its style and for the genial 

 manner in which the illustrative examples are 

 chosen and treated. M. Poineare is a past 

 master of that most difficult art of giving the 

 central thought of a large theory in a few 

 words without sacrificing lucidity. 



It is to be hoped that the work will receive 

 in America that wide and thoughtful reading 

 which it deserves equally on account of the 

 subjects treated and the stimulating orig- 

 inality of the treatment. An English transla- 

 tion of the book and of the notes of Lindemann 

 is a desideratum. 



Of the German translation little need be 

 said. It is faithful and quite close, and 

 acquits itself remarkably well of the difficult 

 task of conveying the delicate and precise 

 thoughts of the author into the German 

 tongue. The task was of course much 

 facilitated by the remarkable clearness of the 

 original, in which there is seldom opportunity 

 to question just what is meant, though the 

 domain is one where few can avoid involved 

 ideas and entangling phraseology. The im- 

 perative requirement that every shade of 

 meaning be faithfully reproduced effectually 

 restrains the translator from any of those para- 

 phrases which must be permitted if the trans- 

 lation is to conform itself, unhampered, to 



