Page:Popular Science Monthly Volume 20.djvu/461

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the German physiological school. They believe that the force necessary 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 competent 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 organisms, hesitates to make friends with this conception, fearing, notwithstanding 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 contrary, I attach importance to having precisely designated the condition in which are grounded all the sensible differences that have caused mankind to recognize, although the same forces 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 without 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 Académie des Sciences Morales et Politiques admits the possibility of a mechanical indeterminism on the authority of the three mathematicians. But, when the hypothesis