754 ANNUAL REPOKT SMITHSONIAN INSTITUTION, 1912. 



its being. So those who fear that their end will be hastened by that 

 of the solar system may be reassured. The retinue of the sun once 

 disappeared, does that mean that other analogous and distant sys- 

 tems, scattered here and there like a living dust, will not exist in- 

 definitely ? That is a question much discussed at present, but which 

 we can not answer. 



The problem of the shape of a star resolves itself into that of a 

 fluid mass rotating and subject to various forces. Next to the 

 problem of three bodies it is the most important one of celestial 

 mechanics. Here, too, Pomcare made remarkable discoveries. They 

 mark an epoch in the study of the subject, as Sir George Darwin 

 remarked the day he presented to Poincare the gold medal of the 

 Koyal Society of London. Formerly but two figures of equilibrium 

 were known for rotatmg fluids, the elipsoid of revolution and that of 

 Jacobi with three unequal axes. Poincare found through his calcula- 

 tions an infinite number of others which are stable and shaped like 

 pears, whence the name apiodes given to this class of bodies. The 

 pear-shaped bodies discovered by Poincare appear to have an im- 

 portant place in nature, as proved by the evidence from certain nebulee 

 and close double stars. They enable us to get some idea of the mech- 

 anism of that bipartition, somewhat analogous to that of organic 

 cells, which may have given birth to a great number of binary sys- 

 tems and which successively separated the earth from the sun and 

 then the moon from the earth. 



Finally Poincare showed that no form of equilibrium is stable 

 when the velocity of rotation exceeds a certain limit. He at once 

 applied this fact to that enigmatic marvel, the ring system of Saturn. 

 Maxwell showed that the rings could not be solid and if fluid that 

 their density could not exceed three one-hundredths that of Saturn. 

 Poincare proved that if the rings are fluid they could not be stable 

 unless their density is greater than one-sixtieth that of Saturn. He 

 concluded that the only alternative is to suppose that they are formed 

 of a multitude of small satellites, gravitating independently. We 

 know how spectrum analysis subsequently proved this marvelous 

 deduction of this mathematical genius. 



A small portion only of Poincare's scientific work is included in that 

 just described. Even a superficial description of all would require 

 volumes, it is so vast. Before turnmg to another branch of his work, 

 that which will reveal his philosophy, I feel almost a kind of remorse 

 as I find myself obliged, by the limitations of this tribute, to pass 

 over in silence all those great" discoveries which he has so generously, 

 almost indifferently, if I may use that word, worked out, always 

 with the same mastery, in such different branches of science, in 

 optics, in thermodynamics, in electricity, or in astronomy; some- 

 times with daring strokes he treated of the relations between the 



