76 THE QUANTITATIVE METHOD IN BIOLOGY 



difference i : 2 will exist between both ; but if we take the 

 number of divisions into account, the difference is only 4 : 5 

 or I : 1-25. There seems, at first sight, to exist a complete 

 disproportion between cause and effect.^ When the last cell- 

 division has taken place the sensitive period of the property 

 number of cells is over. (Compare § 66.) 



(3) When the specimen has reached its equilibrium in 

 respect of the number of cells, the latter have not yet attained 

 their full size. This is certainly the case with their length, the 

 further increase of which may be considerable ^ and is certainly 

 influenced by external causes. The sensitive period of the 

 property length of the cells begins really after the last cell- 

 division and is therefore limited to the last part of the period 

 of development (growth) of the specimen. 



(4) The property number of axes is (as far as we know) inde- 

 pendent from the conditions of existence. 



(5) The properties number of sorts and form of the cells seem 

 to be also independent from external influences, except if the 

 number of cells did not exceed two, which is thinkable (if so, 

 cylindric intermediate cells would not exist). 



We see from the above that the sensitive periods of three 

 groups of properties of Spirogyra (length and breadth of the 

 egg, number of cells, length of the cells) do not coincide. There- 

 fore the three groups are independent from each other with 

 regard to plasticity. It is, for instance, a priori, possible that 

 a small egg produces a specimen with numerous short cells, 

 that a big egg produces a specimen with few long cells, etc., 

 etc. This must be taken into account whenever we wish to 

 investigate any form of correlation between the mentioned 

 properties. 



These principles are, of course, applicable on any animal or 

 vegetable species. (See § 47, p. 56.) 



§60.— FIRST EXAMPLE: SPIROGYRA {continued). -^In 

 Spirogyra a longitudinal axis really exists. I have also sup- 

 posed the existence of a transverse axis in the egg and in each 

 cell, but this axis remains in reahty latent till sexual reproduc- 

 tion takes place. When the moment of reproduction approaches, 

 two specimens of Spirogyra place themselves side by side, the 

 cells facing each other by pairs. Each cell produces a tubular 

 outgrowth which meets the corresponding outgrowth of the 

 opposite cell. The axis of each outgrowth clearly indicates the 

 position of the transverse axis of the cell. Since all the out- 

 growths of each specimen seem to be in the same plane, we may 



^ Compare the law of Weber. 



' I have no information about the further increase of the breadth. 



