THE CONCEPTUAL WORLD 35 



the system, motionless earth and moving moon at the 

 time ti, and motionless earth and moving moon at the 

 time ^2, are separated by an interval of time dt, which 

 is smaller than any finite interval that we can conceive. 

 We must then integrate the differential of the position 

 difference so as to obtain the real difference in the 

 condition of the system after the finite interval of time 

 ti to ^2 has elapsed. Thus mathematics, incapable 

 of dealing with real intervals of time, evades this diffi- 

 culty by considering tendencies, not real occurrences. 



Things that happen in a part of inorganic nature 

 arbitrarily detached from the rest, and investigated by 

 the methods of mathematical physics, do not endure. 

 Let us suppose that we take some silver and add nitric 

 acid to it : the metal dissolves. We can then add 

 hydrochloric acid to the solution and precipitate the 

 metal in the form of chloride ; and we can then fuse 

 this chloride with carbonate of soda, or some other 

 substance, and so obtain the metal again. If we work 

 carefully enough we can repeat this series of operations 

 again and again and the original portion of silver will 

 remain unchanged both in nature and in mass. All 

 the chemical reactions into which it has entered have 

 not affected it in any way ; that is to say, these reactions 

 have not endured. 



If we inject a serum, containing a toxin, into the 

 blood stream of a susceptible animal, certain things 

 happen. The animal will become ill, but, provided 

 that the amount of serum which has been injected was 

 not too great, it will recover. If the toxin be again 

 injected a reaction occurs, but the animal does not 

 become so ill as on the first occasion, and after a number 

 of injections the dose administered may be so great as 

 to kill a susceptible animal but may yet produce no 

 effect on the animal which is the subject of the process 



