CHAPTER III 



THE RATE OF GROWTH 



When we study magnitude by itself, apart, that is to say, 

 from the gradual changes to which it may be subject, we are 

 deaUng Avith a something which may be adequately represented 

 by a number, or by means of a hne of definite length ; it is what 

 mathematicians call a scalar phenomenon. When we introduce 

 the conception of change of magnitude, of magnitude which varies 

 as we pass from one direction to another in space, or from one 

 instant to another in time, our phenomenon becomes capable of 

 representation by means of a line of which we define both the 

 length and the direction ; it is (in this particular aspect) what is 

 called a vector phenomenon. 



When we deal with magnitude in relation to the dimensions 

 of space, the vector diagram which we draw plots magnitude in 

 one direction against magnitude in another, — length against 

 height, for instance, or against breadth ; and the result is simply 

 what we call a picture or drawing of an object, or (more correctly) 

 a "plane projection" of the object. In other words, what we 

 call Form is a ratio of magnitudes, referred to direction in space. 



When in deahng with magnitude we refer its variations to 

 successive intervals of time (or when, as it is said, we equate it 

 with time), we are then dealing with the phenomenon of groivth ; 

 and it is evident, therefore, that this term growth has wide 

 meanings. For growth may obviously be positive or negative ; 

 that is to say, a thing may grow larger or smaller, greater or less ; 

 and by extension of the primitive concrete signification of the 

 word, we easily and legitimately apply it to non-material things, 

 such as temperature, and say, for instance, that a body "grows" 

 hot or cold. When in a two-dimensional diagram, we represent 

 a magnitude (for instance length) in relation to time (or "plot" 



