78 ROBERT W. HEGNER 



from an abnormal increase in the ratio (i.e., in the growth of 

 the nucleus), and Rhizopoda and Infusoria in which this con- 

 dition was induced by overfeeding either died or else regained 

 the normal ratio by direct elimination of nuclear material or 

 by conjugation. The intervals between successive divisions 

 were divided by Hertwig into two periods: 1) a period of 

 'funktionelles Wachstum/ during which the cytoplasm grows 

 more rapidly than the nucleus, leading to an abnormal K/P 

 ratio, and, 2) a period of 'Theilungs-wachstum,' during which 

 the normal K/P ratio (the 'Kernplasma-Norm') is regained by 

 the rapid growth of the nucleus, and at the end of which cell 

 division occurs. The end of the period of functional growth 

 when the K/P ratio is abnormal is the moment of 'Kernplasma- 

 Spannung.' Popoff ('08) believes he has proved by experi- 

 ments on Frontonia and other ciliates that division and the 

 plane of division are determined at the moment of nucleo- 

 cytoplasmic tension. For example, if pieces of cytoplasm 

 were removed during the period of functional growth, the cyto- 

 plasm continued to increase until the nucleocytoplasmic norm 

 was established, but if they were cut away during the period 

 of division-growth, division occurred without the regaining of 

 the nucleocytoplasmic norm and the organism divided into 

 unequal parts in the plane which was median before the 

 operation. 



Many external and internal conditions are supposed to affect 

 the normal K/P ratio. Thus Hertwig found that the ratio 

 was increased if the organism were subjected to low tempera- 

 tures and was diminished at higher temperatures. For 

 example, the average K/P ratio for Dileptus gigas at 8°C. was 

 1/7, and at 25°C. was 1/13. Similar results were obtained by 

 Popoff ('08) on Stylonychia. This investigator used the ratio 

 P/K (cytoplasm /nucleus) and found that the ratio decreased 

 as the temperature decreased; e.g., it was 80.7 at 25°C., 77.4 

 at 17°-19°C., and 74 at 10°C. Rautmann's ('09) experiments 

 on Paramecium also confirm Hertwig's conclusions. He found 

 that at temperatures above 25°C. the K/P ratio decreased. 

 The confirmation offered by Prandtl's ('06) studies on Didinium 



