Do you take any interest in Fixt Fate, Free Will &c. If so Boussinesq [of hydro dynamic reputation] 'Conciliation du veritable determinisme mecanique avec l'existence de la vie et de la liberte morale' (Paris 1878) does the whole busi ness by the theory of the singular solutions of the differential equations of motion. Two other Frenchmen have been working on the same or a similar track Cournot (now dead) and de St Venant [of elastic reputation Torsion of Prisms &c.] Another, also in the engineering line of research, Philippe Breton seems to me to be somewhat like minded with these.
There are certain cases in which a material system, when it comes to a phase in which the particular path which it is describing coincides with the envelope of all such paths may either continue in the particular path or take to the envelope (which in these cases is also a possible path) and which course it takes is not determined by the forces of the system (which are the same for both cases) but when the bifurcation of path occurs, the system, ipso facto, invokes some determining principle which is extra physical (but not extra natural) to determine which of the two paths it is to follow.
When it is on the enveloping path it may at any instant, at its own sweet will, without exerting any force or spending any energy, go off along that one of the particular paths which happens to coincide with the actual condition of the system at that instant.
In most of the former methods Dr Balfour Stewarts &c. there was a certain small but finite amount of travail decrochant or trigger-work for the Will to do. Boussinesq has managed to reduce this to mathematical zero, but at the expense of having to restrict certain of the arbitrary constants of the motion to mathematically definite values, and this I think will be found in the long run, very expensive.
But I think Boussinesq's method is a very powerful one against metaphysical arguments about cause and effect and much better than the insinuation that there is something loose about the laws of nature, not of sensible magnitude but enough to bring her round in time.
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