reduced to a mechanical agent, and entering into the machinery of physical forces, of being in fact itself only a movement of the universal transformation of the dynamical forces of nature; and this is just what Determinism affirms. The question in dispute is precisely this: Can the soul act in any other way?

The doctrine of conservation of force, theoretically established by Leibnitz, and mathematically demonstrated by Huyghens, has in our days become an experimental truth of the first order, in consequence of the discovery of the mechanical theory of heat. It has been proved by experiment-and a whole new science has sprung therefrom-that the quantity of work spent in a given machine corresponds constantly with the quantity of heat produced; that, to put it in a more general way, friction, concussion, in a word, whatever in a machine is known as those passive resistances which occasion the pure loss in machinery of a notable portion of motive power, generates heat. Heat therefore takes the place of motion, or rather is itself motion, and subject to mechanical laws. Thanks too to it, that portion of the mechanical force of the universe that we might imagine dissipated and lost, since it is never recorded as visible motion, is now found in insensible movements that make on our senses the effect of heat. The great principle of the persistence of force is then universally confirmed. From another point of view Lavoisier, in founding modern chemistry, demonstrated that in all transformations of bodies the quantity of mass or matter invariably remained the same. Thus: same amount of matter, same amount of force, is the double fundamental law that rules the universe. The famous nihil ex nihilo is no longer a metaphysical axiom, it has become a palpable overwhelming truth, the basis of science and industry, the foundation of all our industries and all our dealings with nature.

Thus, then, the universe is one vast machine, whose operations are subject to mechanics, and whose movements are determined by anterior movements; all of them, even such as are called voluntary, have been infallibly prescribed, it would seem, in the first movements originally imparted to nature. In this vast wheelwork, subject to inflexible fatality, what becomes of human will?

We seem to be reduced to the following dilemma: Either will is utterly powerless, or it can only act as being itself a part of the general system,—that is to say, in the character of a mechanical, blind, and fatal force; but if so, there is an end of human freedom.

There was, however, one issue which Leibnitz with profound sagacity discerned, and this was the origin of a theory that has passed for an absolutely chimerical one, for want of sufficient attention to the profound motive that suggested it ;-we mean the theory of pre-established harmony. It does, indeed, seem to result from the preceding train of thought that the soul can neither create nor direct motion; but if there be no direct action, there may at least be correspondence. Why should not the First Cause have so calculated the series of movements

in the universe that at a given moment such a movement should correspond with such a volition? and, reciprocally, why should not God have laid down for souls such an internal law of development that, with such and such external movements, such and such sensations should invariably correspond? The voluntary act would be purely internal, and would not need any mechanical force to act externally. The laws of mechanics themselves would have been so determined as to serve our wills. According to this hypothesis, the most absolute. mechanism would not be in contradiction with free-will. It is true that Leibnitz's doctrine of pre-established harmony did not save freedom, because he admitted an internal determinism in souls, as well as the external determinism of which we have been speaking; but this is a different train of ideas, with which we have not to occupy ourselves here.

Thus pre-established harmony was able to disengage moral liberty from the bonds of mechanics: so much is evident; but at what cost was this done? At the cost of the most exorbitant assertions and the

strangest consequences. To begin with, this hypothesis not only contradicts common sense, but also that inner consciousness which appears most incontrovertibly to assert a direct action of our will on our bodily organs. Moreover, if it be true, as Leibnitz tells us, that whatever occurs in souls occurs as though there were no body, and in bodies as though there were no souls, does it not follow that the whole material universe might be destroyed without our perceiving it? Thus, were it God's pleasure to annihilate all the world with the exception of one single monad, would not that monad alone persist in being the whole universe? But if so, what need is there of a universe at all? And why should we suppose that anything exists besides this one monad? Conversely, if it pleased God to annihilate souls while letting bodies subsist, history would go on none the less in its destined course; and, to an external observer, nothing would be changed. Think of it! these revolutions, wars, great political undertakings, parliamentary conflicts, eloquent orations-all these accomplished by soulless bodies, by automata without life and without thought. Is such a division of the world into two halves so independent, so separate, so alien, that they cannot assure each other of their respective existence,-is such an hypothesis, resembling as it does a universal somnambulism, much preferable to fatalism itself, or does it afford any solid security for morality to base it thus on one of the most extraordinary conceptions of the human mind?

I should be extending these preliminary considerations too far were I to recall other attempts at reconciliation made by metaphysicians, as, for example, Kant's profound distinction between phenomena and noumena, the former alone being subject to mechanical laws, the latter being understood by Kant as one with beings themselves free; the mechanical world being but semblance, freedom the reality; the former

produced by our sensibility and imagination, the latter constituting our very being, very essence. But laying aside all these metaphysical hypotheses, let us now inquire whether science itself, whether mechanics themselves, may not help us to discern a possible reconciliation.

A philosopher recently lost to science, who was also a man of science -M. Cournot-had put out an important idea which may perhaps be looked upon as the starting point of the theory now under consideration. He had pointed out that man is able by his intelligence displayed in improving and better combining the different wheels of a machine, to lessen indefinitely the amount of physical work that machine has to perform in order to produce a given effect; and by a process of reasoning familiar to mathematicians-the infinitesimal process he came to the conclusion that a case might be conceived possible in which the work should rigorously speaking be nil; for instance, in the case of organized machines-organisms in which purely mechanical physical force should be replaced by what M. Cournot calls the directing power, a power that would, he says, intervene and act, not after the manner of physical forces, not by adding its action to theirs or neutralizing them by a contrary action of the same kind, but by impressing on them an appropriate direction. This, it will be seen, was a return to Descartes' principle, but with this difference: that instead of a rigorously mechanical direction which might have given scope for the objections of Leibnitz, a quite other sort of direction was here contemplated, having nothing in common with mechanical force.

This idea of M. Cournot's, whose penetrating and accurate cast of mind is known to all philosophers, has been accepted and reproduced without his responsibility by another learned member of the French Institute in the section of mechanics, namely, by M. de Saint Venant, who last year, before the Academy of Science-which was much surprised and not perhaps much pleased to find itself thus unexpectedly transported to the cloudy and fluctuating domains of metaphysic-had a curious note, since inserted in the Comptes Rendus, on the "Harmony between Moral Liberty and the Laws of Mechanism." M. Boussinesq himself thus sums up the theory of M. de Saint Venant. The latter, he says,

"reduces from the first the mechanical effect of the will to a very small amount of work done-to which he gives the name of unlinking or unhooking work, because he compares it to that of the workman drawing the click (or hook) that retains a pile-driver at a certain elevation, or to that of a man drawing the trigger of a loaded gun. He next shows that a greater and greater perfecting of mechanism indefinitely reduces this amount of work, and he is of opinion that nature, being more perfect than art, may have succeeded in entirely annihilating it. This comes in point of fact to the opinion held by M. Claude Bernard, who admits the influence of a directing principle while denying its power of creating any force-that is to say, of modifying in any one particular the physical conditions of motion."

In order to be quite exact, we are bound to say that the above

solution has not satisfied all our scientists. It has been doubted whether it was legitimate from work progressively reduced to draw the conclusion of work absolutely nil; it has been asked whether the progressive diminution of work in this case has not had for its cause the anterior work of the workmen who constructed the machine, of the engineer who designed it, and even of the intelligence and will of the inventor of the machine; for it cannot without a petitio principii be assumed that none of these are mechanical forces, this being the very matter in dispute.

Nevertheless, we hold it to be already a great point gained that distinguished and competent scientists so well versed in the question as are M. Cournot, M. de Saint Venant, M. Boussinesq, and others, should have admitted as possible, as involving no contradiction, the hypothesis of a non-mechanical power acting upon matter without adding to or subtracting from mechanical force,-a directing extraphysical power. Such an hypothesis, I repeat, is in itself valuable, if only as an hypothesis. Were this idea to be contested by other scientists, philosophers would always be entitled to refer them the one to the other. But we may now take a step further, and here intervene those labours of M. Boussinesq of which we have not as yet treated, but which we could not possibly have understood or appreciated if we had not previously summarized the order of ideas amongst which they rank, and into which they bring a new element, an ingenious point of view, which may make intelligible the hypotheses of MM. Cournot and Saint Venant, and remove the apparent paradox we seemed to discover in their theories.

M. Boussinesq's idea consists in utilizing in favour of the possibility of moral freedom a theory familiar to geometers under the name of singular solutions, and also sometimes spoken of as Poisson's paradox. Agreeably to this theory, there may be, M. Boussinesq holds, cases of complete mechanical indeterminism, that is to say, cases where a motor, having reached certain points called by the author points of bifurcation, may indifferently take one of two different directions while in either case equally satisfying the mathematical equation. There may be cases in which a body might indifferently remain quiescent, or ascend, or descend, without its preceding state necessarily determining any one of these hypotheses, all three equally satisfying all the principles of mechanics, so that, in order to determine one of the three, no additional work need be expended. Under such a supposition we see that an extra-physical, extra-mechanical action might be the effect of a directing power. The author ingeniously compares the will to an engineer who, "having to construct a canal along the summit of a hill, may at all points of that singular course distribute at pleasure the water of the canal into the one or the other of the two adjacent valleys, without having to make it deviate from its natural tendencies."

There would thus, according to M. Boussinesq, be cases, occurring

only under very special conditions no doubt, and as difficult, even the simplest of them, to produce artificially as to make a cone stand on its' apex, but still cases theoretically possible,-cases I say in which the initial state of a system would not involve completely determined tracks for phenomena; those tracks would admit of numerous bifurcations, which, once given, would reproduce themselves indefinitely, and would thus permit the continual existence of a directing power charged at every moment with the determination of directions. Analysis, indeed, can only demonstrate this theorem in extremely simple cases, as, for example, in a system of two atoms, and in other fictitious systems infinitely less complicated than that of our living organisms can ever be; but nature has resources unknown to art, and analogy may help us to suppose that she has by some transcendent calculation not beyond her power realized systems, not of two atoms, but of millions and billions of atoms, in which previous preparation may have rendered possible millions and billions of bifurcations. Thus the flexibility of life would be compatible with the rigour of mechanical law.

In a word, then, we gather from the preceding theory that mathematics do not exclude, nay, that in certain cases they authorize us to assume, a sort of indetermination, and cases of bifurcation where the mere fillip required to decide the motor in taking one direction or the other might be nil, or at least determine the effect by the aid of work virtually nil, that is, without work. The physicist, the mechanician, who observe the result, would always find the permanent quantity they required. The directing power would not enter into the calculation, and yet its action would be none the less real though not appreciable by the dynamometer.

"We know," says M. Boussinesq, "how much the geometers of the last century were surprised by the singular integrals that they met with in their researches and that analysis gave in reply to certain questions of geometry. I do not think I am mistaken in affirming from my own experience that the same astonishment is still felt in our own day by thoughtful minds when studying for the first time the chapter of Infinitesimal Analysis that treats of these. This astonishment arises from the mysterious and inscrutable property possessed, as we have seen, by singular solutions.

"It would be deemed natural that so extraordinary a property should have called attention to the solutions in question as calculated to represent what there is of spontaneous, extra-physical, and special in the phenomena of life. Does it not seem as though this property ought to have led almost immediately to recognizing in them the special function of expressing the geometrical or mechanical conditions of an existence so marvellous and veritably singular as being endowed with consciousness and free activity in the midst of the immense inorganic world, surrounded by a network of laws apparently regulating all the infinitely small variations of things?

"And yet no one, to my knowledge, had up to the present time put out this so simple and, as it were, so inevitable idea. Though it was known that Nature hardly ever fails to realize somewhere or other analytical facts as widely extended as those of singular solutions, no geometers seem to have inquired what in the visible world might be the peculiar domain and field of application of these solutions.