1026 



SCIENCE. 



[N. S. Vol. XI. No. 287. 



social and a moral universe as well as a phys- 

 ical one ; the facts of experience with which he 

 starts are found in his relations to his fellows 

 as well as in those of the material world. In 

 these facts, too, he must iind laws, and through 

 laws he must pass to the conception of that moral 

 system, in which alone he can find the true free- 

 dom of rational and self-realizing activity." 



Having set forth his view of the function 

 of logic and of education, Mr. Welton is pre- 

 pared to discuss their relation to each other. 

 The points which logic emphasizes in educa- 

 tional theory, he says, are (1) ' that all true 

 education must be relative to the society in 

 which it is given' ; and (2) ' that logic equally 

 with psychology, teaches the educator that 

 the attainment of knowledge is the result of 

 mental exertion.' 



That these are fundamental principles of a 

 rational educational theory, every one will ad- 

 mit. Both deserve strong emphasis ; and at the 

 present stage of the development of educational 

 theory, particularly the first. I say particularljr 

 the first, because the second has been empha- 

 sized from time immemorial, while the first has 

 only recently come to receive the attention it 

 deserves at the hands of writers and speakers 

 on education. Education is primarily a social 

 study, like economics, or government. The 

 development of the individual is fruitless unless 

 it proceeds with constant reference to his mem- 

 bei'ship in the contemporary social organism ; 

 and the maintenance, organization, and direc- 

 tion of education constitute one of the most 

 important functions of society. 



Both of these points are discussed briefly by 

 Mr. Welton. One finds himself regretting that 

 so little space is devoted to the discussion of 

 these important topics ; and the value of the 

 book consists, not in a fresh contribution to 

 educational theory, nor in a discussion of the 

 relation of logic to educational theory ; but in 

 the general intellectual stimulus such a book 

 must give to every earnest teacher. 



The teacher may learn from this book what 

 knowledge is, and how knowledge is tested and 

 assimilated. But he will not find in it an 

 enumeration of the kinds of knowledge to be 

 sought, nor a discussion of the relative efficacy 

 of different kinds of knowledge in promoting in- 



dividual and social well being. He will get from 

 it no teaching devices, but he may expect to 

 derive from it valuable assistance toward grad- 

 ually developing within himself the right pro- 

 fessional attitude throughout the whole range of 

 his activity. p^^L H. Hanus. 



Harvard University. 



The Theory and Practice of Interpolation, includ- 

 ing Mechanical Quadrature and other Impor- 

 tant Problems concerned with the Tabular 

 Values of Functions, with the requisite tables. 

 By Herbert S. Eice, M.S., Assistant in the 

 Oflice of the American Ephermis, and Profes- 

 sor of Astronomy in the Corcoran Scientific 

 School, Washington, D. C. Lynn, Mass., 

 The Nichols Press. 1899. 

 Perhaps the first impression which this book 

 produces is one of surprise that the author has 

 found enough material relating to interpolation 

 to fill 234 pages of small quarto. A brief in- 

 spection, however, shows that we have to do 

 with a work dealing with most if not all of the 

 important problems which arise in connection 

 with the formation and use of the numerical 

 tables which play so conspicuous a part in ap- 

 plied mathematics. In short, we find here a 

 development not only of the familiar processes 

 of interpolation, but those of numerical differ- 

 entiation and integration, with a variety of ap- 

 plications to astronomical and other problems. 

 The author's preface informs us that he has 

 attempted no marked originality, either in sub- 

 ject matter or method. " Indeed, sufficient has 

 hitherto been written of interpolation, quadra- 

 tures, etc., to firmly dissuade one from such an 

 endeavor." * * * " But while viewing the 

 matter in this practical sense, the writer re- 

 gards his work as no mere compilation." 



In the development of the subject the deriva- 

 tion and discussion of the important formulfe of 

 Newton, Stirling and Bessel naturallj' consti- 

 tute the basis of the structure. As this work 

 progresses we have each important step illus- 

 trated by a number of numerical examples, to- 

 gether with the development of such precepts^ 

 as are important in the practical application. 

 For instance, in the great majority of cases we 

 have to do with numerical quantities which, like 

 the familiar logarithmic and trigonometrical 



