CONSTANCY AND INDEPENDENCE 14/15 



water is being swallowed (ml. /sec.) by a land animal observed 

 over several days. The sexual activities of a stag during the 

 twelve months. The activity in the mechanisms responsible for 

 reflexes which act only intermittently : vomiting, sneezing, 

 shivering. 



14/14. The property of ' threshold ' leads often to behaviour of 

 part-function form. For if x dominates y, and if, when x is less 

 than some value, y remains constant, while if, when x is greater 

 than the value, y fluctuates as some function of x, then, if x is 

 a full-function and fluctuates across the threshold, y will behave 

 as a part-function. In the nervous system, and in living matter 

 generally, threshold properties are widespread ; part-functions 

 may therefore be expected to be equally widespread. 



Systems containing part-functions 



14/15. Having earlier examined the properties of systems con- 

 taining null-functions (S. 7/7), and step-functions (S. 7/8 et seq.), 

 we will now examine the properties of systems containing part- 

 functions. It is convenient to suppose at first that the system 

 is composed of them exclusively. 



Even when not at a resting state, some of such a system's 

 variables may be constant. If the system is composed of part- 

 functions which are active for most of the time, the system will 

 show little difference in behaviour from one composed wholly of 

 full-functions. But if the part-functions are active only at in- 

 frequent intervals then, as the system traverses some line of 

 behaviour, inspection will show that only some of the variables 

 are changing, the remainder being constant. Further, if observed 

 on two lines of behaviour, the set of variables which were active on 

 the first line will in general be not the same as the set active 

 on the second. That this may be so can be seen by considering 

 its field. 



The field of an absolute system which contains part-functions 

 has the peculiarity that the lines of behaviour often run in a 

 sub-space. Thus, over an interval when all the variables but 

 one are inactive, the line will run in a straight line parallel to 

 the axis of the active variable. If all but two are inactive, the 

 line will run in a plane parallel to that which contains the axes 



163 



