4 io SCIENCE PROGRESS 



Let c t (o)) be such a factor that 



X ( clco)A(o = X t clp lt p 2 , . . . )Ap l} Ap* . . . Ap r (3) 



gives the mass of that portion of the species for which the 

 parameters p 1} pz . . . p r are comprised within the limits 



p l and p x + ApA 



p2 and pi + Ap\ . . 



p r and p r + Ap r J 



The increments Ap may be infinitesimals if the conditions of 

 the case commend such choice. 



The character of the species being thus defined, it is evi- 

 dent that evolutionary change in character of the species is 

 only one aspect of the redistribution of matter in the system 

 comprising that species — it is that particular phase of the 

 redistribution which occurs within the confines of the species 

 itself. We may speak of this phase or part of organic evolu- 

 tion as intra-species or intra-group evolution. 



In contradistinction with this we may speak of the phase 

 of evolution to which the system of equations (2) refers as 

 inter-species or inter-group evolution — i.e., the redistribution 

 of matter among the several species of matter of which the 

 system is composed. 



The relations which connect the several factors of intra- 

 group evolution are evidently more complex than those which 

 exist between the factors of inter-group evolution. 



It is therefore expedient to consider the latter first. 



We are thus led, primarily, to a consideration of the system 

 of differential equations (2). 



In physico-chemical dynamics it is customary to study 

 processes taking place at constant pressure and temperature, 

 or at constant volume and temperature. 



We shall here introduce a similar restriction, and consider 

 the case of inter-group evolution taking place at constant 

 parameters P {e.g., constant extension-in-area and constant 

 climatic conditions). 



Furthermore, a simple case which naturally invites first 

 attention is that in which the changes in the parameters Q (in 

 the character Q of the several species) take place very slowly 

 as compared with the changes in the variables X—i.e., as com- 

 pared with the changes in the distribution of matter among 

 the several species. 



In this case we may, as a first approximation, regard the 

 Q's also as constant. 



