CH. II] OF SURFACE AND VOLUME 17 



us say) and growth in volume (which is usually tantamount to 

 mass or weight) are parts of one and the same process or pheno- 

 menon, the one attracts our attention by its increase, very much 

 more than the other. For instance a fish, in doubhng its length, 

 multipHes its weight by no less than eight times ; and it all but 

 doubles its weight in growing from four inches long to five. 



In the second place we see that a knowledge of the correlation 

 between length and weight in any particular species of animal, 

 in other words a determination of k in the formula W ^ k . L^, 

 enables us at any time to translate the one magnitude into the 

 other, and (so to speak) to weigh the animal with a measuring- 

 rod; this however being always subject to the condition that the 

 animal shall in no way have altered its form, nor its specific 

 gravity. That its specific gravity or density should materially or 

 rapidly alter is not very hkely; but as long as growth lasts, 

 changes of form, even though inappreciable to the eye, are likely 

 to go on. Now weighing is a far easier and far more accurate 

 operation than measuring; and the measurements which would 

 reveal shght and otherwise imperceptible changes in the form of 

 a fish — shght relative difiierences between length, breadth and 

 depth, for instance, — would need to be very dehcate indeed. But 

 if we can make fairly accurate determinations of the length, 

 which is very much the easiest dimension to measure, and then 

 correlate it with the weight, then the value of k, according to 

 whether it varies or remains constant, will tell us at once whether 

 there has or has not been a tendency to gradual alteration in the 

 general form. To this subject we shall return, when we come to 

 consider more particularly the rate of growth. 



But a much deeper interest arises out of this changing ratio 

 of dimensions when we come to consider the inevitable changes 

 of physical relations with which it is bound up. We are apt, and 

 even accustomed, to think that magnitude is so purely relative 

 that differences of magnitude make no other or more essential 

 difference ; that Lilhput and Brobdingnag are all ahke, according 

 as we look at them through one end of the glass or the other. 

 But this is by no means so; for scale has a very marked effect 

 upon physical phenomena, and the effect of scale constitutes what 

 is known as the principle of similitude, or of dynamical similarity. 



