186 



SCIENCE. 



N. S. Vor.. XL Mj. 283. 



utilitarian tendency, together with Blundau's 

 manifest aversion to cross the threshold of 

 higher mathematics, that to the disciples of 

 Gauss, Lagrange aad Tissot (who care more for 

 the theory than for the application of pro- 

 jections), the treatment of ' autogonal ' or ' con- 

 formal ' projections is not altogether satisfac- 

 tory. He should have introduced the elements 

 of the theory of functions without which a 

 proper treatment of these projections is impos- 

 sible. He should at least have said that the 

 coordinates of a sphere («, v) are connected 

 with those {x, y) of Mercator's projection by the 

 relation 



x-\-iy = u-\-i log tang {^+ -^J 



and that by suitably taking *, the coordinates of 

 any other autogonal projection (X, Y) are given 

 by the relation 



X+iY=i{x + iy). 



If4>( ) = e*" *a stereographic projection 

 is obtained in which the north or south pole is 

 the center of the map. If to this stereographic 

 projection we apply * ( ) = — K -\- en ~'( ), 

 we obtain Peirce's quincuncial projection, etc. 



A. LiNDENEOHL. 

 December 28, 1899. 



The Euolution of General Ideas. By Th. Ribot. 



Translated by Fkanoes A. Welby. Chicago, 



Open Court Publishing Company. 1899. Pp. 



231. 



The scope and mode of treatment of Pro- 

 fessor Ribot's monographs are well known ; and 

 this one follows closely the general plan of those 

 which have preceded it. The topic itself is a 

 most interesting one ; the genesis of the powers 

 of abstraction and the evolution of the general 

 ideas which represent the fruit of such abstrac- 

 tion. The material for the early forms of the 

 process is to be found in the mental operations 

 of animals, of children and savages, and of 

 deaf-mutes before education. These have, in 

 common, the absence of words and the depend- 

 ence of the abstraction upon the generic images 

 formed by sense-experiences. The intermedi- 

 ate stage involves the use of words and is re- 

 flected in the character and growth of language. 

 The word fixes the material basis of the ab- 



straction and aids the mind in focusing upon 

 the 'abstracted' relation. In the highest 

 stages of abstraction the element of repre- 

 sentation has faded away, and the word practi- 

 cally constitutes its entire content. Follow- 

 ing the description and illustration of these 

 processes is a special consideration of the de- 

 velopment of the special concepts of number, 

 space, time, cause, law and species. The funda- 

 mental insistence upon experience as the basis 

 of such development and the suggestiveness of 

 the genetic point of view find apt application 

 in this part of the thesis. 



But iu spite of a well-chosen theme and of a 

 discerning utilization of the literature ; in spite 

 of much interesting material and suggestive 

 modes of treatment, the general impression of 

 the book is a rather unsatisfactory one. There 

 is a judicious occupation of points of advantage ; 

 skirmish lines are thrown out in various direc- 

 tions, a campaign is carefully planned — and the 

 planning is rather too freely discussed — but there 

 is no vigorous nor successful attack upon the real 

 stronghold of the situation. None the less, the 

 monograph will be a helpful one to the student, 

 who will appreciate the significance of the 

 problem, as Professor Ribot outlines it, and 

 who will be led by the interest of the exposition 

 to assimilate the essential factors involved in 

 the growth and functioning of the powers of 

 abstraction. His attention may be specially 

 directed to a point touched upon in the last chap- 

 ter, but worthy of more extensive treatment ; 

 namely, that the criterion of the utility of ab- 

 straction is not to be sought merely in its products 

 — such as the higher mathematics or metaphysics 

 — but as well in the process itself, by which the 

 individual learns to focus the attention at will 

 upon any aspect of a complex experience which 

 may become important. And, in the same 

 chapter, he should not overlook the suggestive 

 delineation of the parts played by theory and 

 practice, by the incentive of genius and by 

 gradual development, in the actual history of 

 the sciences depending upon abstraction. 



Of the translation, the best that can be said 

 is that it is barely satisfactory. A good trans- 

 lation of a psychological work involves the ab- 

 sorption and re-expression of the author's 

 perspective of ideas, not of his words alone ; 



