532 



SCIENCE 



[N. S. Vol. L. No. 1302 



on without serious interruption; and the out- 

 put of books for the year, as may be seen by 

 reference to the detailed list given in a later 

 section of this report, is rather greater than 

 the average annual output for the past 

 decade. Of the entire list of twenty-nine 

 volmnes issued, only two classes of them, 

 selected mainly for the purpose of showing 

 trends of progress, may be referred to here. 

 The most elementary, the most essential, 

 and hence the most widely used, if not 

 esteemed, of the sciences is arithmetic. It 

 is a fundamental requisite, in fact, of all 

 esact knowledge. Ability to add, subtract, 

 multiply, and divide affords probably the 

 simplest test of capacity for correct thinking. 

 Conversely, inability or indisposition to make 

 use of these simple operations affords one of 

 the surest tests of mental deficiency, as wit- 

 nessed, for example, by numerous correspond- 

 ents who are unable to or who refuse to apply 

 these operations to the finances of the insti- 

 tution. But the familiar science of arith- 

 metic lies at the foundation also of a much 

 larger and a far more complex structure 

 called the theory of numbers. This theory 

 has been cultivated by many of the most acute 

 thinkers of ancient and modern times. It 

 has more points of contact with quantitative 

 knowledge in general than any other theory 

 except the theory of the differential and in- 

 tegral calculus. These two theories are com- 

 plementary, the first dealing with discrete or 

 discontinuous numbers and the second with 

 fluent or continuous numbers. ITaturally, a 

 subject which has attracted the attention of 

 nearly all of the great mathematicians of the 

 past twenty centuries has accumijlated a con- 

 siderable history. The more elementary con- 

 tributions of Euclid, Diophantus, and others 

 of the Greek school; the extensions of 

 Fermat, Pascal, Euler, Nevrton, Bernoulli and 

 many others in the seventeenth and the eight- 

 eenth centuries; and the work of Lagrange, 

 Laplace, Gauss, and their numerous contem- 

 poraries and successors of the nineteenth cen- 

 tury, make up an aggregate which has stood 

 hitherto in need of clear chronological tabu- 

 lation and exposition. This laborious task 

 was undertaken about ten years ago by a 



Eesearch Association of the Institution, Pro- 

 fessor Leonard E. Dickson, of the University 

 of Chicago. A publication under the title 

 "History of the Theory of Numbers" has 

 resulted, and Volume I. (8vo, xii-j-486 pp.), 

 devoted to divisibility and to primality of 

 numbers, has appeared during the past year; 

 and a second volume devoted to diophantine 

 analysis is now in press. This work is remark- 

 able for its condensation of statement. It 

 contains more information per unit area than 

 any other work issued thus far by the insti- 

 tution. It is remarkable also for the care 

 taken by the author and by his collaborators 

 to secure precision and correctness, a niunber 

 of experts having assisted in the arduous 

 labors of verification required during the 

 process of printing. 



It is the object of science primarily to find 

 answers to the question " How ? " rather than 

 to the question " Why ? " ; or, to seek to de- 

 scribe phenomena rather than to try to ex- 

 plain them. Words, however, constitute, in 

 general, a rather imperfect medium for the 

 communication of ideas, and as a consequence 

 the intellectual world, like the political world, 

 often finds itself involved in misunderstand- 

 ings which lead to nothing better than that 

 metaphorical and degenerate form of energy 

 called the heat of controversy. Thus, about 

 a half-century ago there arose, as we now see, 

 a quite needlessly bitter discussion over the 

 question whether and to what extent the phe- 

 nomena of life may be traced back to the 

 properties of matter with which they are ob- 

 viously intimately associated. The new sci- 

 ence of biology was just then arising and the 

 limitations of its domain and the conditions 

 of its existence and development were widely 

 disputed, as is best shown probably by the 

 lay sermon of Huxley delivered at Edin- 

 burgh ISTovember 8, 1868, " On the Physical 

 Basis of Life." In this remarkable address 

 Huxley defines, with prophetic clearness and 

 completeness, the limitations and the condi- 

 tions in question and these, as he defined 

 them, are now generally admitted as essential 

 to all fruitful inquiry. Moreover, the prin- 

 ciples expounded by Huxley have been justi- 

 fied in amplest measure by the extraordinary 



