Suppose we are given, the premises--_All P is M_, and _All S is M_--the middle term is undistributed.

But take the obverse of the contrapositive of both premises: All m is p; All m is s: .'.

Some s is p.
Here we have a conclusion legitimately obtained; but it is not in the terms originally given.
For Mediate Inference depending on truly logical premises, then, it is necessary that one premise should distribute the middle term; and the reason of this may be illustrated even by the above supposed numerical exceptions.

For in them the premises are such that, though neither of the two premises by itself distributes the Middle, yet they always overlap upon it.

If each premise dealt with exactly half the Middle, thus barely distributing it between them, there would be no logical proposition inferrible.