The second thing upon which I should like to be enlightened is your statement, "In order that the body or matter should not be a simple phenomenon, like a rainbow, nor a being brought together by accident or by an accumulation, like a pile of stones, it must not consist merely in extension, and there must needs be something which is called the substantial form and which corresponds in some sort to what is called the soul." There are a good many things to ask upon this point.

1st. Our body and our soul are two substances really distinct. Now, if we put into the body a substantial form aside from this extension, we cannot imagine how there should be two distinct substances, we cannot see therefore that this substantial form has any relation to what we call our soul.

2nd. This substantial form of the body must be either extended and divisible or not-extended and indivisible. If we should say the latter, it would seem to be as indestructible as is our soul; and if we should say the former, it would seem that nothing would be gained toward making the body a unum per se, any more than if it consisted only in extension. For it is the divisibility of extension into an infinity of parts which presents the difficulty of conceiving it as a unit. This substantial form therefore would not remedy this difficulty at all so long as it also is divisible like extension itself.

3rd. Is it the substantial form of a block of marble which makes it one? If this is so, what becomes of that substantial form when it ceases to become one, after it has been cut in two? Is it annihilated, or does it become two? The first is inconceivable, if this substantial form is not a mere manner of being, but is a substance; and it cannot be said that it is a manner of being or a mode, because then the substance, of which this form would be the mode, would be an extension. This apparently is not your thought. And if this substantial form should become two instead of one, why would not the same be said of the extended alone without this substantial form?

4th. Do you give to extension a general substantial form such as has been admitted by certain Schoolmen who have called it

formam corporeitatis? Or do you wish that there should be as many different substantial forms as there are different bodies and are these different in kind when the bodies are different in kind?

5th. In what do you put the unity which is attributed to the earth, to the sun, or to the moon, when we say that there is only one earth which we inhabit, one sun which lightens us, only one moon which turns about the earth in so many days? Do you think that this earth, for example, made up of so many heterogeneous parts must necessarily have a substantial form which is appropriate to it and which gives to it this unity? It does not seem that you believe this. I should say the same thing of a tree, of a horse, and still further I would instance mixtures; for example, milk is composed of the serum, of the cream, and of the portion which hardens. Are there here three substantial forms, or is there only one?

6th. Finally, it will be said that it is not worthy of a philosopher to admit entities of which there are no clear distinct ideas; and there are no such clear and distinct ideas of these substantial forms. And furthermore even, you do not let them be proved by their effects, since you acknowledge that it is by a corpuscular philosophy that all the particular phenomenon of nature should be explained, and that there is no advantage in bringing up these forms.

7th. The Cartesians in order to find unity in bodies have denied that matter was divisible to infinity and they have held that indivisible atoms must be accepted; but I think that you do not share their opinion.

I have examined your little brochure and I find it very subtle, but take care lest the Cartesians should reply that it brings nothing up against their position, because you posit something which they think false- namely, that a stone, in descending, gives to its own self this greater velocity which it acquires as it descends. They will say that this acceleration comes from the corpuscles, which, in rising, cause everything that they find in their way to descend and impart to them a part of the motion which they had; and therefore there is no cause for surprise if the body B, four times the weight of A, has more motion when it has fallen one foot than the body A when it has fallen four feet, because the corpuscles which have pressed upon B have communicated to it a motion proportioned to its mass and those which have pressed upon A, in proportion to its mass. I do not assure you that this reply will be valid, but I think at least that you ought to see if there be anything in it. I shall be very glad to know what the Cartesians have said to your brochure.

I do not know whether you have examined what M. Descartes says in his letters in regard to the general principle of mechanics. It seems to me that when he wishes to show why the same force can lift by means of a machine twice or four times as much as what it can lift without a machine, he declares that he has not taken into consideration the velocity. My recollection about it, however, is very confused, for I have gone into those things only from time to time and at odd moments, and it is more than twenty years since I have seen any of those books.

I do not wish you, M., to turn away from any of your occupations however important, in order to reply to the two objections which I have brought forward. You may do as you please about them and at your leisure.

I should like very much to know if you have not given the finishing touches to the two machines which you invented while at Paris. The one in the province of arithmetic seemed to be much more perfect than that of M. Pascal, and the other was an absolutely correct watch.

I am yours devotedly,

XII: Count Ernst von Hessen-Rheinfels to Leibniz

Rheinfels, 21/31, Oct., 1686.

Monsieur: