7/15 



THE ULTRASTABLE SYSTEM 



(3) If a piece of rubber is stretched, the pull it exerts is approxi- 



mately proportional to its length. The constant of pro- 

 portionality has a definite constant value unless the elastic 

 is stretched so far that it breaks. When this happens 

 the constant of proportionality suddenly becomes zero, 

 i.e. it changes as a step-function. 



(4) If strong acid is added in a steady stream to an unbuffered 



alkaline solution, the pH changes in approximately step- 

 function form. 



(5) If alcohol is added slowly with mixing to an aqueous 



solution of protein, the amount of protein precipitated 

 changes in approximately step-function form. 



(6) As the pK is changed, the amount of adsorbed substance 



often changes in approximately step-function form. 



(7) By quantum principles, many atomic and molecular variables 



change in step-function form. 



(8) Any variable which acts only in ' all or none ' degree shows 



this form of behaviour if each degree is sustained over a 

 • finite interval. 



7/15. Whether a real variable may or may not be represented 

 by a step-function will usually depend on the method and perhaps 

 instrumentation of observation. Observers and instruments do 

 not, in practice, record values over both very short and very long 

 intervals simultaneously. Thus if the honey-gathering flights of 

 a bee are being studied throughout a day, the observer does not 



B 



Time — >• 



Figure 7/15/1 : The same change viewed : (^4) over one interval 

 of time, (B) over an interval twenty times as long. 



89 



