that their 3n co-ordinates satisfy a system of 3n differential equations of the fourth order (and not of the second, as required by the law of inertia). We know that by introducing 3n variable auxiliaries, a system of 3n equations of the fourth order may be reduced to a system of 6n equations of the second order. If, then, we suppose that the 3n auxiliary variables represent the co-ordinates of n invisible molecules, the result is again conformable to the law of inertia. To sum up, this law, verified experimentally in some particular cases, may be extended fearlessly to the most general cases; for we know that in these general cases it can neither be confirmed nor contradicted by experiment.
The Law of Acceleration.—The acceleration of a body is equal to the force which acts on it divided by its mass.
Can this law be verified by experiment? If so, we have to measure the three magnitudes mentioned in the enunciation: acceleration, force, and mass. I admit that acceleration may be measured, because I pass over the difficulty arising from the measurement of time. But how are we to measure force and mass? We do not even know what they are. What is mass? Newton replies: "The product of the volume and the density." "It were better to say," answer Thomson and Tait, "that density is the quotient of the mass by the volume." What is force? "It is," replies Lagrange, "that which moves or
