Upon the results of these experiments Driesch based his first proof of vitalism. Let us suppose that there is a mechanism in the developing egg. Now the embryo which results from the latter sooner or later acquires a three-dimensional arrangement of parts: head-end differs from tail-end, dorsal surface differs from ventral surface, and the parts differ on either side of the median plane. The mechanism must, therefore, be one which acts in three dimensions, anterior and posterior, laterally, and dorso-ventrally. We may represent it by a diagram of three co-ordinate axes, _x_, _y_, _z_; _x_ and _y_ being in the plane of the paper, and _z_ at right angles to the plane of the paper. Now in the 2-cell stage the same mechanism must be present, for this stage develops normally into one entire embryo. But since _either_ of the blastomeres may develop into an entire embryo, the mechanism must also be present in each of them, and since in the 16-cell stage each blastomere may develop an entire embryo, it must be present in each of the sixteen blastomeres. A three-dimensional mechanism is therefore capable of division down to certain limits. [Illustration: FIG. 15.] [Illustration: FIG. 16.] Suppose now that we allow the sea-urchin egg to develop normally up to the blastula stage. In this stage it is a hollow sphere, the wall of which is a single layer of cells. It is similar all round, that is, we cannot distinguish between top and bottom, right and left, anterior and posterior regions; but since it develops into a larva in which all these distinctions become apparent very soon, it must possess the three-dimensional mechanism, since the activity of the developmental process is going to produce different structures in each direction. Now the blastula, by very careful manipulation can be divided, cut into parts with a sharp knife. Since it is similar all round the direction of the cut is purely a matter of chance. It can be cut through along the planes 1 2, 3 4, 5 6, 7 8, for instance; really there are an infinite number of planes along which the blastula can be cut into two separate parts, and the direction of the plane is not a matter of choice, but purely a matter of chance. Nevertheless, each of the parts into which the larva is cut becomes an entire embryo. For a time the partial blastula--approximately a hollow hemisphere in form--goes on developing as if it were going to become a partial embryo, but soon the opening closes up and development becomes normal. It does not matter even if the two parts into which it is divided are not alike in size; provided that a part is not too small, it will follow the ordinary course of development. [Illustration: FIG. 17.]