When we study magnitude by itself, apart, that is to say, from the gradual changes to which it may be subject, we are dealing with a something which may be adequately represented by a number, or by means of a line 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,ãlength 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 ãplane projectionã of the object. In other words, what we call Form is a ratio of magnitudes, referred to direction in space.
When in dealing 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, 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 ãgrowsã hot or cold. When in a two-dimensional diagram, we represent a magnitude (for instance length) in relation to time (or ãplotã {51} length against time, as the phrase is), we get that kind of vector diagram which is commonly known as a ãcurve of growth.ã We perceive, accordingly, that