THE SEVEN WORLD-PROBLEMS. 445 



the German physiological school. They helieve that the force neces- 

 sary for the release of absolute motion may be not only relatively very 

 small, but even equal to nothing. M. Boussinesq has indicated certain 

 differential equations of motion, the integrals of which permit singular 

 solutions of such a kind that the sense of further motion becomes 

 equivocal or quite indefinite. An example of this kind is the case in 

 which a grave point at the periphery of a perfectly smooth paraboloid, 

 having a perpendicular axis and its apex pointing upward, retains, in 

 ascending in a plane drawn through the axis, the tangential velocity 

 which it had acquired in falling to the same place. It then reaches 

 the apex with a velocity of zero, and remains there till it pleases some 

 directing principle residing there to give it an impulse in a required 

 direction, which, although it is equal to nothing, shall yet be com- 

 petent to let it glide down the paraboloid again. 



Cournot believed that the releasing force, equivalent to zero, M. 

 Boussinesq that the integral, with singular solutions, was needed as a 

 means of explaining, in connection with the directing principle, the 

 diversity and indeterminableness of organic processes. The German 

 physiological school, accustomed to see only simple mechanism in or- 

 ganisms, hesitates to make friends with this conception, fearing, not- 

 withstanding the protestations of its friends, that the vital force that 

 is always, under one form or another, coming to the surface in France 

 might be lurking behind the " directing principle." I may remark 

 here that M. Boussinesq misunderstands me when he makes me say in 

 the " Grenzen des Naturerkennens " that an organism is distinguished 

 from a crystalline form only by its greater complication. On the con- 

 trary, I attach importance to having precisely designated the con- 

 dition in which are grounded all the sensible differences that have 

 caused mankind to recognize, although the same foi'ces rule in both, 

 two distinct kingdoms in living and inanimate nature. This condition 

 is, that, in the inorganic individual, the crystal, matter exists in stable 

 equilibrium, while in the organic individual a more or less complete 

 dynamic equilibrium sways the matter, sometimes with a positive, 

 sometimes with a negative balance. While the stream of matter 

 coursing through the animal promotes the conversion of potential into 

 kinetic energy, it also explains the dependence of life upon external 

 conditions, the integrating stimulus of the older physiology, and the 

 perishability of the organism as opposed to the eternity of the crystal 

 lying inert in itself. 



In our opinion, the theory of an unconscious life can subsist with- 

 out a forking integral and without a directing principle. On the other 

 hand, it is doubtful if anything can be gained in the controversy be- 

 between free-will and necessity with these aids or with the theory of 

 release. M. Paul Janet's report to the Academie des Sciences Morales 

 et Politiques admits the possibility of a mechanical indeterminism on 

 the authority of the three mathematicians. But, when the hypothesis 



