1. It is shown, by an investigation of the movements of blinking in the normal individual, that the distribution of interblink periods (intervals between successive blinks measured in seconds) is remarkably constant for the individual under constant experimental conditions. 2 The movements are not reflex, and do not depend on the integrity of the second, third, fourth, fifth, or sixth cranial nerves. They are centrally controlled, and dependent on intermittent impulses passing from the region of the basal ganglia. 3. The rate of blinking is closely related to the “mental tension” of the subject at the time, and in all probability the movements constitute a kind of relief mechanism, whereby nervous energy, otherwise unutilised, passes into a highly facilitated path.

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THE purpose of this series of papers is to show to what extent the phenomena of sedimentation and rouleaux formation of red blood cells may be explained on simple physical principles. A perusal of the literature on the subject makes it clear that the extent to which such principles operate requires investigation and clarification.We shall require, in the meantime, the following expressions to cover certain possible cases: 1. A Spherical Body falling in a Fluid. -Let the radius of the body be R, and of small dimensions, and let the specific gravity be s,. If the body falls through a fluid of viscosity ', and of specific gravity 82, with velocity V, we have a balance between the forces tending to produce the fall and forces resisting the fall, -4R3 . g . (SI-S2)=6-aqRV, the gravitation constant being g, and the quantities being expressed in the C.G.S. system. This balance of forces gives us Stokes' formula, V = 2(s, -S OR 2 . 9g ( which gives the constant velocity of fall of a small sphere in a fluid. 2. A Flat Elliptic Disc falling in a Fluid. -Such a body falls in the most stable position, which is broadside on, this being the position of most resistance. Let the axes be a, b, and c, and let the body fall in the direction a. As regards the resistance to its fall the disc will behave like a sphere of radius,

From this short study of rouleaux formation several points have emerged. The first condition for rouleaux formation, and one which is fulfilled under all but unique circumstances, is that there shall be collisions among the cells. The frequency of these collisions plainly depends on such factors as the movements in the fluid, the number of cells present per unit volume, the viscosity of the fluid, and the size of the cells. The second condition is that the collisions shall result in permanent cohesions. Such cohesions will not occur if the surfaces of the cells are not sticky, if the repulsive forces between the cells are very great, or if the cells collide with one another so that the surfaces which come into contact are small. If, on the other hand, the collisions bring large surfaces into contact, permanent cohesions are likely to occur, for not only are there large surfaces over which the cohesive forces between the cells can act, but separation of these surfaces entails a considerable amount of work. The consideration of these points indicates why cells collect in rouleaux, and not in aggregates of roughly spherical form, for all contacts except those which occur at the ends of the shorter rouleaux are not permanent, whereas all contacts in which the cells are broadside on result in lasting cohesions. To this must be added the fact that discoid cells moved by a fluid orient themselves broadside on, and therefore collisions in this position are encouraged. From the mass of work on the potential difference between the red cells and the suspending fluid, it appears that, if the potential difference be reduced below a certain point, agglutination of the cells occurs, all contacts being permanent, in whatever position they occur. From this may be drawn the deduction that the repulsive forces accompanying this potential difference are sufficient to prevent the permanence of all contacts except those which involve a large extent of surface in connection with which considerable surface and cohesive forces are called into play. Before this explanation is regarded as the correct one, however, it must be shown that those electrolytes, and other substances which reduce the potential difference, do not also increase the stickiness of the cell surfaces. The cases of CaCl2 and MgCl2, which reduce the potential difference and yet do not cause agglutination, and the instance of heated plasma, which increases rouleaux formation without decreasing the potential difference, show how necessary it is to take account of this latter possibility, the importance of which has been clearly recognised by such investigators as Oliver and Barnard and Northrop. As regards the kinetics of rouleaux formation, we have found that a simple equation containing one easily evaluated constant is sufficient to describe the course of the phenomenon under such conditions as are extremely suitable for experimental purposes. This research was carried out under a grant from the Royal Society.

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