It may well be that we need attach no great practical importance to this bold conception; for even though stellar space be shewn to be _mare liberum_ to minute material travellers, we may be sure that those which reach a stellar or even a planetary bourne are infinitely, or all but infinitely, few. But whether or no, the remote possibilities of the case serve to illustrate in a very vivid way the profound differences of physical property and potentiality which are associated in the scale of magnitude with simple differences of degree. {50} 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 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,—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 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 “grows” hot or cold. When in a two-dimensional diagram, we represent a magnitude (for instance length) in relation to time (or “plot” {51} length against time, as the phrase is), we get that kind of vector diagram which is commonly known as a “curve of growth.” We perceive, accordingly, that the phenomenon which we are now 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.