8 THE STRUGGLE FOR EXISTENCE 



ralists themselves, several empirical generalizations became estab- 

 lished to which we have become so accustomed that they appear to us 

 almost self-evident. 



"Among these generalizations the following must be recorded. 

 Firstly, the multiplication of all organisms can be expressed by geometric 

 progressions. This can be evaluated by a uniform formula: 



2 bf = N t 



where t is time, b the exponent of progression and N t the number of 

 individuals existing owing to multiplication at a certain time t. Param- 

 eter b is characteristic for every kind of living being. In this 

 formula there are included no limits, no restrictions either for t, for b, 

 or for N t . The process is conceived as infinite as the progression is 

 infinite. 



"This infinity of the possible multiplication of organisms can be 

 considered as the subordination of the increase of living matter in the 

 biosphere to the rule of inertia. It can be regarded as empirically estab- 

 lished that the process of multiplication is retarded in its manifestation 

 only by external forces ; it dies off with a low temperature, ceases or 

 becomes weaker with an insufficiency of food or respiration, with a lack 

 of room for the organisms that are being newly created. In 1858 

 Darwin and Wallace expressed this idea in a form that had been long 

 clear to naturalists who had gone into these phenomena, for instance, 

 Linnaeus, Buff on, Humboldt, Ehrenberg and von Baer: if there are 

 no external checks, every organism can, but at a different time, cover 

 the entire globe by its multiplication, produce a progeny equal in 

 size to the mass of the ocean or of the earth's crust. 



"The rate of multiplication is different for every kind of organisms 

 in close connection with their size. Small organisms, that is organisms 

 weighing less, at the same time multiply much more rapidly than large 

 organisms (i.e., organisms of a great weight). 



"In these three empirical generalizations the phenomena of multi- 

 plication are expressed without any consideration of time and space 

 or, more precisely, in geometrical homogeneous time and space. In 

 reality life is inseparable from the biosphere, and we must take into 

 consideration terrestrial time and space. Upon the earth organisms 

 live in a limited space equal in dimensions for them all. They live 

 in a space of definite structure, in a gaseous environment or a liquid 

 environment penetrated by gases. And although to us time appears 



