Mathematics s 6 ^ 



0^0 



ner numerous researches in pure mathematics. As a corollary, 

 almost, has resulted also a more or less complete correlation 

 of the sciences of heat, light, electricity, and magnetism ; and 

 a still further correlation, if not a complete unification, is con- 

 fidently expected. In the rational investigation of physical 

 phenomena the question of the energy involved is everywhere 

 uppermost; and no such investigation meets the requirements 

 of the present day unless the source, the transformations, and 

 the resultant form of the energy are accounted for. 



Along with the rapid growth and multiplication of the sci- 

 ences which have been such prominent characteristics of the 

 civilization of the past half-century, there is noticeable also a 

 rapid growth in the interrelations of those sciences. Chemis- 

 try, for example, has come to be closely allied to physics ; 

 physics is largely applied mechanics ; geology shades off by 

 easy gradations into physical geodesy ; physical geodesy is 

 only a branch of dynamical astronomy ; while mathematics 

 is an indispensable instrument for all of them, and biology 

 must evidently in the near future draw heavily on most of 

 them for the solution of its problems. It is in this growth 

 of interrelations that one may discern the beginnings of cor- 

 relations and generalizations which will simplify and unify the 

 appalling aggregate of knowledge now presented by the 

 sciences. And it is thus that the evils of specialization, which 

 have been somewhat deplored of late, evils necessary to the 

 fact-gathering stage of the sciences, will find their proper 

 correction. 



If such have been the characteristic features of the progress 

 of science in general during the past fifty years, what role is 

 to be assigned to the mathematical work which has been pro- 

 moted directly or indirectly by the Smithsonian Institution in 

 the fields of American science ? To the casual reader of the 

 bulky catalogue of the "Contributions to Knowledge," "Mis- 



