EVIDENCE PKOVING THE STATEMENT OF THE CASE 41 



to be of such a density that each cubic centimetre weighs 

 exactly one gramme. Now the physicist divides the 

 100 grammes by the 100 cubic centimetres and obtains 

 a quotient of the "numerical value" of 1. A very 

 useful order of thought and one which has produced 

 great results; but what does the unit (1), " the 



numerical value," represent ? Why absolutely nothing 



M 

 in Nature. The physicist expresses the above thus, ^-3. 



That is, weight is divided by volume. If we attempt 

 to effect such a process, it is found to be impossible. 



We can multiply a process, when it is repeated, by 

 time ; and every process or operation takes time. 

 Thus, if we move an 1 apple from one part of space to 

 another in a second of time, and repeat that process 

 ten times by adding apple to apple, we shall be able, in 

 a sense, to multiply time by the objects. Thus one 

 apple multiplied by ten units of time the second (or 

 apple added to apple ten times, and this is all multipli- 

 cation can mean) produces ten apples in ten seconds. 

 In no other way can mathematics be really applied to 

 Nature. Nature recognizes only addition to and sub- 

 traction from atoms in a certain locality, and the 

 addition and subtraction of the forces inherent in 

 atoms. These processes always follow in equations, 

 thus 



If 1 apple = 1 second, 

 then : 10 apples = 10 seconds. 



Both sides of the equation are multiplied. Even in 

 commerce we have a similar order of things. We 

 make an invoice thus 



s. d. 

 ^ dozen oranges @ 12s. per dozen = 6 



