The causes that determine the position of the amphiaster are scarcely known. It has been proved by experiment that in some cases this position may be determined by mechanical causes. Thus, Driesch has shown that when the eggs of sea-urchins are flattened by pressure, the amphiasters all assume the position of least resistance, i.e. parallel to the flattened sides, so that the cleavages are all vertical, and the egg segments as a flat plate of eight, sixteen, or thirty-two cells (Fig. 135). This is totally different from the normal form of cleavage ; yet such eggs, when released from pressure, are capable of development and give rise to normal embryos. This interesting experiment makes it highly probable that the disc-like cleavage of meroblastic eggs, like that of the squid or bird, is a mechanical result of the accumulation of yolk by which the formative protoplasmic region of the ovum is reduced to a thin layer at the upper pole ; and it indicates, further, that the unequal cleavage of less modified telolecithal eggs, like those of the frog or snail, are in like manner due to the displacement of the mitotic figures towards the upper pole. Even here, however, the hypothesis of a merely mechanical displacement probably does not touch the root of the matter ; for it will not account for the eccentric position of the spindle in the formation of the polar bodies or in teloblasts. Neither will it explain the eccentric position of the horizontal spindle in such cases as the first cleavage of the annelid egg. In Nereis, for example (Figs. 43, 122), the inequality of the first cleavage is predetermined long before actual division both by an eccentric position of the spindle and an inequality in the asters, neither of which can be referred to an unequal horizontal distribution of the yolk.' In this and many similar cases we must assume more subtle causes lying in the organization of the cytoplasmic mass, or rather of the egg as a whole ; but these deeper causes still lie beyond our grasp. Unequal division, which plays so important a part in development, still therefore awaits a final explanation, and until this is forthcoming we have but a vague comprehension of the primary factors of growth.
Hertwig's Development of Sachs's Law.—We have now to consider two additional laws of cell-division formulated by Oscar Hertwig in 1884, which bear directly on the facts just outlined and which lie behind Sachs's principle of the rectangular intersection of successive division-planes. These are : i. The nucleus tends to take up a position at the centre of its sphere of influence, i.e. of the protoplasmic mass in which it lies.
2. The axis of the mitotic figures typically lies in the longest axis of the protoplasmic mass, and division therefore tends to cut this axis at a right angle.
The second law explains not only the mode of division in flattened eggs, but also the normal succession of the division-planes according to Sachs's second law. The first division of a homogeneous spherical egg, for example, is followed by a second division at right angles to it, since each hemisphere is twice as long in the plane of division as in any plane vertical to it. The mitotic figure of the second division lies therefore parallel to the first plane, which forms the base of the hemisphere, and the ensuing division is vertical to it. The same applies to the third division, since each quadrant is as long as the entire egg while at most only half its diameter. Division is therefore transverse to the long axis and vertical to the first two planes.
Hertwig's second law has caused much discussion and has been shown to have many exceptions, as for instance in the cambium-cells of plants and in columnar epithelium. While undoubtedly one of
the most important laws of cell-division thus far determined, it only pushes the analysis a stage further back, and leaves unexplained the nature of the forces that determine the position of the spindleaxis. Pfluger assumed that this position must be that of least resistance to the elongation of the spindle, which is obviously in the long axis of the protoplasmic mass ; and the same view has been advocated by Braem and Driesch. Now, there can of course be no doubt that the final direction of the spindle, like that of any body, is the position of least resistance, i.e. the position of equilibrium determined by the resultant of all the forces operating upon it. The undetermined point is whether these forces are of a simple mechanical nature, such as pressure and the like, or of a more subtle physiological character. Roux seeks them in the "tractive forces" of the protoplasmic mass modified by an innate predisposition to a particular form and succession of divisions that has its seat in the nucleus. Heidenhain identifies them with conditions of intracellular tension determined by the astral rays.
It cannot be doubted that all these forces may play a part in determining the position of the spindle, but it must be confessed that the problem is still very far from a solution. In some cases Hertwig's law is directly opposed to the facts, the spindle lying transversely to the axis of the protoplasmic mass. In other cases, as for instance in the division of some Protozoa (Euglypha, t. Schewiakoff) and in segmenting ova (Crepidula, t. Conklin), the protoplasmic elongation leads the way, and may be fully determined before the spindle is formed. In still other cases the reverse is true, as in the formation of the polar bodies, where the spindle forms and rotates into position before the egg shows any corresponding change of form. In many ova we can assign no mechanical cause for the rotation, such as the pressure of deutoplasm and the like ; and even when deutoplasm is present, its position is such that we should expect a horizontal rather than a vertical position of the .polar spindles were it a mechanical result of the presence of deutoplasm.
The ultimate determination of the planes of division is probably to be sought in those influences that determine the movements of the centrosomes. Sachs's law of rectangular succession is primarily a result of the fact that the daughter-centrosomes typically diverge, and so determine the spindle-axis, in a line which is at right angles to the axis of the mother-spindle ; hence the ensuing cleavage is vertical to the What we do not really understand is the principle by which this typical succession is modified. The pressureexperiments prove that the modifications may be produced by simple mechanical means. The history of division in the cambium-cells and columnar epithelium seems to show that neither direct pressure nor the shape of the cells caused by it can be the ultimate cause. The succession of divisions, always in the same plane, in apical cells and in teloblasts, is directly related with a deeply lying law of growth that affects the whole developing organism, and we cannot at present distinguish in such cases between cause and effect ; for whether the apical growth of the body as a whole is caused by local conditions within the apical cells, or the reverse, is undetermined. This unsatisfactory result shows how far we still are from an understanding of the fundamental laws of growth and their relation to celldivision, and how vast a field for experimental research lies open in this direction.