CHAPTER III, 



THE RATE OF GROWTH 



When we study magnitude by itself, apart from the gradual 

 changes to which it may be subject, we are deahng with 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 point 

 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, 

 our diagram plots magnitude in one direction against magnitude in 

 another — length against height, for instance, or against breadth ; and 

 the result is what we call a picture or outhne, 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 growth; and 

 it is evident that this term growth has wide meanings. For growth 

 may be positive or negative, a thing may grow larger or smaller, 

 greater or less; and by extension of the concrete signification of 

 the word we easily arid 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" length 

 against time, as the phrase is), we get that kind of vector diagram 

 which is known as a "curve of growth." We see that the pheno- 

 menon which we are studying is a velocity (whose "dimensions" are 

 space/time, or L/T), and this phenomenon we shall speak of, simply, 

 as a rate of growth. 



In various conventional wa-ys we convert a two-dimensional into 



* In Aristotelian logic. Form is a quality. None the less, it is related to qiuirUity't 

 and we jfind the Schoolmen speaking of it as qualitas circa quantitatem. 



