vi OBITUARY NOTICES OF MEMBERS DECEASED. 



appeared in ])rint shortly after his death, he shows how to reduce 

 one of the problems regarding the existence of periodic orbits to a 

 geometric problem, which, however, he was unable to solve. He 

 apologizes for putting forth such an incomplete result on the ground 

 that at his age (he was onl}- 58) he could not feel confident of re- 

 turning to the problem in the future and solving it completely. One 

 cannot avoid the impression that he felt that his career was very 

 nearly at an end. It will doubtless interest this audience to know 

 that a proof of Poincare's theorem has already been found by a 

 young American mathematician. Professor G. D. Birkhoff, of 

 Harvard. 



We cannot here dwell longer on the astronomical work of Poin- 

 care. We must pass over without particular mention his work on 

 the figure of the earth, on the tides, and on the lunar theory, as well 

 as his recent book on cosmogony. 



Poincare is the author of at least fourteen advanced text-books 

 in various branches of physics. Among the titles we find Capillarity, 

 Elasticity, Vortices, Heat, Thermodynamics, Optics, Electricity, 

 Wireless Telegraphy, etc. These are chiefly reproductions of his 

 courses of lectures at the Sorbonne. He also wrote a large number 

 of papers and memoirs on physical topics, especially on Hertzian 

 waves and on the theory of electrons. On the whole, however, his 

 work in physics cannot be compared in importance with his funda- 

 mental contributions to mathematics and astronomy. His work on 

 the dififerential equations of physics and on Dirichlet's principle, 

 which one might be expected to mention here, is of more conse- 

 C|uence to mathematics than to physics. 



We must now turn to another main division of his work in a 

 domain of pure mathematics. Already in 1883 he had published an 

 important paper (in the Acta Mathematica) laying the foundations 

 of the theory of functions of two complex variables. In 1887 he 

 published his memoir on the residues of double integrals, which 

 furnished one of the chief tools for the theory of algebraic functions 

 of two variables, a theory which has since been built up chiefly by 

 his colleague Picard, by Poincare himself, and by many brilliant 

 Italian geometers. 



