310 MEMOIRS OF THE NEW YORK BOTANICAL GARDEN 



center of the cell, and there will thus be formed an invagination 

 or projection of the plasma membrane from the center of each of 

 its triangular faces toward the center of the cell. Now let the 

 accompanying diagram represent the cell at the stage just described: 



Text-figure i. Diagram of mother-cell before division. 



Let a, b, c, and d be the four nuclei, and let e be a point on the 

 plasma membrane equidistant from a, b, and c. The cell is shown 

 in its three dimensions, and these must be kept in mind during 

 the discussion. Two of the four nuclei, a and c, are on either side 

 of the plane of the diagram. Let xy be a plane tangential to the 

 plasma membrane at the point e, and let x be the point of inter- 

 section of the perpendicular dropped from b to the plane xy. By 

 actual measurement of the cells, ed is about i6 microns, cb is 14 

 microns, and xb is 7 microns. Now if there is an attraction be- 

 tween each of the nuclei and the point e, this point would tend to 

 move along the line ed. Let EB represent the force exerted by b 

 to draw e along the line ed. Then the force exerted by a and c 

 respectively would also be equal to EB; therefore the total force 

 exerted by the three nuclei, a, b, and c will be t,EB. Let EB 

 represent the force exerted by b. The force exerted by a and c 

 respectively will also be EB. Xow the angle xeb may be shown 

 ge(;metrically to be one-half of a right angle. Therefore the 

 resultant of the forces exerted by the three nuclei, a, b, and c, 

 will be about 2EB. Xow ed is less than 2eb, and therefore, since 

 the force is inversel>' proportional to the scjuare of the distance, 



