Abstract
1. The present paper is the first of a series dealing with the birefringence of mitotic figures in the eggs of the sea-urchin Psammechinus miliaris. 2. Living eggs have been examined using time-lapse photography, and retardation curves for the mitotic figures constructed from densitometric measurements made on the film negatives. 3. In the case of the aster, an integral equation relating retardation and coefficient of birefringence can be formulated and solved exactly to give coefficient of birefringence. In the case of the spindle, coefficient of birefringence can only be calculated approximately. 4. In both asters and spindles, the coefficient of birefringence is nil at the centres,rises to a maximum at 5 or 6CL out, and then falls to a minimum at the equator of the spindle or the periphery of the aster. 5. The rise in coefficient of birefringence round the centre is not as sharp as might be expected, and there is some evidence that orientation is built up gradually over a distance of a few microns. 6. The fall in coefficient of birefringence away from the maximum is approximately an inverse square in the case of the spindle. In the aster it falls off somewhat more rapidly. Since the density of material does not vary from point to point, this fall must be due to changes in molecular and micellar arrangement, or to a decreasing proportion of oriented material. 7. The classical conception of the spindle and asters as structures built up of discrete fibrils radiating from the centres, would be expected, for geometrical reasons, to give an inverse square fall in proportion of oriented material. While, therefore, a homogeneous structure with varying molecular and micellar arrangement cannot be ruled out, it is possible that the mitotic figure consists of definite fibrils radiating from the centres. 8. Evidence from other sources supports this view, and suggests that the fibrils must be submicroscopic in size.