Sixthly, since the conception of an individual substance in general, which I have given, is as clear as is the conception of truth, the conception of corporeal substance will be clear also, and consequently that of substantial forms. If, however, this should not be so, we should be obliged to admit a good many things whose knowledge is not so clear and distinct. I hold that the conception of extension is much less clear and distinct; witness the remarkable difficulties found in the composition of the continuum. And it can, indeed, be said that there is no definite and precise form in the body because of the actual subdivision of the parts. With infinite subdivision the body would be doubtless imaginary and a mere appearance, if there was only the material and its modifications. Nevertheless, it is useless to make mention of the unity, the concept, or the substantial forms of bodies when it is a question of explaining the particular phenomena of nature, just as it is useless for Geometers to examine the difficulties of the continuum when they are at work in solving some problem. These things are nevertheless important and worthy of consideration in their place; all the phenomena of the body can be explained mechanically or by the corpuscular philosophy in accordance with certain assumed mechanical principles without troubling oneself as to whether there are souls or not. In the ultimate analysis of the principles of physics and mechanics, however, it is found that these assumed principles cannot be explained solely by the modifications of extension, and the very nature of force calls for something else.

Finally, in the seventh place I remember that M. Cordemoy, in his treatise on the distinction between the body and the soul, in order to save the substantial unity in the body, feels himself obliged to assume atoms or indivisible extended bodies, so as to have something permanent to constitute a simple being; but you rightly concluded, M., that I did not share this opinion. It appears that M. Cordemoy made an approach to the truth, but he did not yet see in what the true notion of a substance consisted and this latter is the key for most important knowledge. The atom, which consists of only an imagined mass with an infinite duration, an idea which I hold conforms no more to the divine wisdom than does a vacuum, cannot contain in itself all its past and future states and much less those of the whole universe.

I come to your observations upon my objection to the Cartesian principle regarding the quantity of motion, and I grant, M., that the acceleration of a body comes from the impulse of some invisible fluid and that it is like a ship which the wind causes to go at first very slowly and then faster; my demonstration, however, is independent of any hypothesis. Without troubling myself at present as to how the body has acquired the velocity which it has, I accept it such as it is, and I say that a body weighing one pound, which has a velocity of two degrees, has twice as much force as a body weighing two pounds which has a velocity of one degree, because it can raise the same weight twice as high. I hold that in distributing the motion between bodies which come into contact, regard must be had, not to the quantity of motion, as is the case in the Cartesian principle, but to the quantity of the force; otherwise, we should obtain perpetual motion in mechanics. For example, (See Illustration) suppose that in a square LM a body A goes along the diagonal 1A 2A to strike two equal bodies B and C at the same moment in such a way that at the moment of contact the three centers of these three spheres are found in an isosceles right triangle, the whole being in a horizontal plane. Suppose now that the body A remains at rest after the contact in the place 2A, and imparts all its force to the bodies B and C. In this case B would go from 1B to 2B, having the velocity and direction 1B2B, and C from 1C to 2C, with the velocity and direction 1C2C. That is to say, if A takes one second of time to pass with uniform motion from 1A to 2A before contact, then in one second after contact B will pass to 2B, and C to 2C. The question is, what is the length of 1B2B or 1C2C, which represent the velocity. I say that it will be equal to AL or AM sides of the square LM, for the bodies, being supposed equal, the forces would be only as the height from which the body would have to descend in order to acquire these velocities, that is to say, as the squares of the velocities. Now, the square of 1B2B and 1C2C taken together are equal to the square 1A2A. Hence, there is as much force after as before the contact. But we see that the quantity of motion has been augmented; for, since the bodies are equal, the quantity of motion can be estimated by their velocities. Now, before the contact this was the velocity 1A2A but after the contact it is the velocity 1B2B plus the velocity 1C2C; 1B2B plus 1C2C, however, is greater than 1A2A; it must needs be, therefore, that, according to M. Descartes, in order to maintain the same amount of motion the body B would go from 1B only to b, or from 1C only to k, in such a way that 1B b or 1C k shall each be equal to half 1A2A. In this way, however, there will be as much force lost as the two squares of 1B b and of 1C k, taken together are less than the square 1A2A.

And, on the other hand, I will show that by another means force can be gained through the contact. For, since according to M. Descartes, the body A with the velocity and direction 1A2A gives by hypothesis to the bodies at rest B and C velocities and directions 1B b and 1C k so that it may come to rest in their place, reciprocally if these bodies should return and come in contact with the body A resting at 2A with the velocities and directions b 1B and k 1C and should come to rest after the contact, they would make A move with the velocity and direction 2A1A. In this way, however, perpetual motion would be inevitably attained for, supposing that the body B, weighing one pound with the velocity b 1B could rise to the height of one foot, and C the same, there would be before the shock a force capable of lifting two pounds to the height of one foot, or one pound the height of two feet, but, after the contact of 1B and 1C with 2A the body A weighing one pound and having a double velocity (that is to say, the velocity of 2A1A, double the velocity of b 1B or of