Septembke 19, 1902.] 



SCIENCE. 



469 



economic work to devote a year to pure re- 

 search. The results would extend far be- 

 yond the single year or the single individ- 

 ual. If the Carnegie Institution can ar- 

 range to pay half the salary of an investi- 

 gator, giving him at the same time the 

 best facilities for research at "Washington, 

 at one of our well-equipped universities or 

 abroad, requiring the institiition with 

 which he is connected to pay the other half, 

 its funds would be spent wisely and eco- 

 nomically. 



There are certain men of genius or talent 

 who for one reason or another have not 

 been able to find a place in our organized 

 social machinery. Such men might per- 

 form work of value if given the opportu- 

 nity, and the Carnegie Institution could 

 here assist in a way that is not possible for 

 any other institution. 



The two general principles which I have 

 kept in mind in writing the above are that 

 the Carnegie Institution should do (1) what 

 it only can do, working whenever possible 

 with existing institutions; and (2) should 

 aim to increase the influence of men of 

 science, working with them and through 

 them. 



The executive committee and the trus- 

 tees of the Carnegie Institution mil have 

 before them reports prepared by those 

 most competent to give advice, and their 

 final decisions will be better considered 

 than the views of any individual. I have 

 ventured to print these remarks, based 

 chiefly on the science with which I am en- 

 gaged and the institutions vs'ith which I 

 am more or less familiar, on the supposition 

 that suggestions from all quarters will be 

 welcomed by the officers of the institution. 

 I have of course expressed only my indi- 

 vidual opinions and have in no wise at- 

 tempted to represent the policy of the .jour- 

 nal in which they happen to appear. As 

 responsible editor of this journal, however, 



I urge men of science to join in a discussion 

 of the problem as to how endowments for 

 research, and especially the great endow- 

 ment of the Carnegie Institution, can best 

 be used for the advancement of science. 

 J. McKeen Cattell. 

 Columbia University. 



SCIENTIFW BOOKS. 

 Lehrhuch der Combinatorik. Von De. Eugen 



Netto. Leipzig. B. G. Teubner. 1901. 



Pp. viii + 260. 



At the present time neither European nor 

 American universities offer lecture courses 

 on the subject of combinatorial analysis. 

 This fact is the more noteworthy when we 

 remember that during the first quarter of the 

 nineteenth century nearly every mathematic- 

 al chair in Germany was occupied by a 

 specialist in that field. This Combinatorial 

 School of Germany has passed into deserved 

 oblivion. Under the leadership of C. F. Hin- 

 denburg it represents the culmination of an 

 unfortunate tendency of eighteenth century 

 mathematicians to develop analysis, particu- 

 larly the subject of infinite series, with ref- 

 erence to form only, and to pay little or no 

 attention to the actual contents of formulae. 

 The polynomial theorem was hailed as 'the 

 most important theorem of all analysis.' In 

 combinatorial analysis (combinatoric) the 

 German school was contented with the deduc- 

 tion of rules for the writing down of all the 

 combinations and permutations that are pos- 

 sible under given restrictions. The simple 

 fact that the able and fairly complete treatise 

 now under review hardly mentions the work 

 of Hindenburg shows that what are now con- 

 sidered the substantial parts of combinatoric 

 have been developed outside of the German 

 Combinatorial School. Associated with the 

 early development are the great names of 

 Pascal, Leibnitz, Wallis, James Bernoulli and 

 De Moivre. 



While combinatoric is not now made the 

 subject of lectures in our universities, it is 

 nevertheless of importance. The student ac- 

 quires much of it during the pursuit of other 

 branches. It is touched upon in the study 



