"an ultimate analysis brings us down," and on which "a rational synthesis must build up." From this first principle come as consequences two correlative principles, viz.: uniformity of law, which is simply the persistence of the relations between forces, manifested under identical forms and conditions; and the principle of the equivalence of forces, inductively established within the last twenty years. The researches which resulted in the establishment of this principle rest implicitly on the persistence of force, inasmuch as they measure all the precedent forces, which have disappeared, and all the consequent forces, which have been produced, by the aid of a unit supposed to be constant. If we add two other corollaries, the one relating to the direction of motion in the line of least resistance, the other to the form of motion, which is always rhythmic, we have, with the principles of the continuousness of motion and of the indestructibility of matter (these representing under two correlative forms the principle of the persistence of force), the sum total of the primary truths which serve as a basis for knowledge in general. But these principles, however general, are only analytical truths; though they are essential to a philosophy, they do not constitute a philosophy. They are the laws of the action of forces separately considered. The universal synthesis which is to constitute philosophy must express the total operation accomplished by the cooperation of these factors. The law which shall formulate this synthesis must be a law of the changes in forces under the two phases, matter and motion, by which they are manifested to us: it must be a principle of dynamics holding good both for the whole of the cosmos, and for its every detail. The changes of an object are all produced by new arrangements of the matter constituting it, and by a new distribution of the forces which belong to it. Their necessary direction is given in evolution in virtue of two principles, both of them corollaries of the primary principle of the persistence of force: the law of the instability of the homogeneous and the law of the multiplication of effects.
Every body tends to pass into a more heterogeneous state, because each of the units that constitute it is of necessity differently affected from the others by the combined action of the others upon it; because the resulting difference places each unit in different relations with the incident forces; finally, because these units, owing to their respective positions, cannot all receive the action of an external force in the same direction and with the same intensity. This law, which accounts for the commencement of the changes, accounts also for its continuance.
At the same time a uniform external force, acting on a body, is there dispersed; acting on unlike parts, it breaks up into forces differing in quality and intensity in proportion to the number and diversity of these parts. The same is to be said of each fraction of the force; the process of dispersion goes on increasing, and the result is expressed by the law of the multiplication of effects.
