The Rate of Multiplication 



85 



foraminifera. During growth, larger chambers are 

 successively formed by the individual. Measurements 

 of the linear dimensions of these chambers show that 

 the ratio between the last old one and the first new 

 one tends to be constant (table 6). In a number of 



Table 6. 



Ratios of Linear Dimensions in Successive Chambers of Foraminiferan 

 Shells. Data of Rhumbler ('09-' 11) 



instances the linear ratio is, at least on the average, 

 very nearly 1.26, as was shown by Rhumbler ('09-'ll). 

 Przibram ('13) pointed out that this number is the 

 cube root of 2; in other words that the volume of the 

 protoplasm exactly doubles at each new chamber-for- 

 mation. It is the peculiar fact that the volume doubles, 

 rather than increases by some other multiple, which 

 makes this resemble a sort of reproduction which is 

 really expressed only as growth; an Arcella, for in- 

 stance, likewise suddenly doubles the volume of its 

 protoplasm by imbibing water at the time of reproduc- 

 tion, and differs from the foraminiferan in that it 

 separates into two parts soon afterward. 



The nuclear conditions among the foraminifera 

 have not been thoroly described. According to Schau- 

 dinn ('03) a multinuclear condition may prevail in the 

 species Polystomella crispa. He also described nu- 

 clear divisions as occurring at times other than the 



