CH. II] OF DIMENSIONS 23 



From these elementary principles a great many consequences 

 follow, all more or less interesting, and some of them of great 

 importance. In the first place, though growth in length (let us say) 

 and growth in volume (which is usually tantamount to mass or 

 weight) are parts of one and the same process or phenomenon, 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 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 an understanding of the correla- 

 tion 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 likely; but as long as growth lasts changes of form, even 

 though inappreciable to the eye, are apt and hkely to occur. Now 

 weighing is a far easier and far more accurate operation than 

 measuring; and the measurements which would reveal slight and 

 otherwise imperceptible changes in the form of a fish — slight relative 

 differences 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 much the easiest linear 

 dimension to measure, and correlate it with the weight, then the 

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

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

 general form, or, in other words, a difference in the rates of growth 

 in different directions. To this subject we shall return, when we 

 come to consider more particularly the phenomenon of rate of growth. 



double-hogshead. But Gilbert White of Selborne could not see what was plain 

 to the Lilliputians; for finding that a certain little long-legged bird, the stilt, 

 weighed 4J oz. and had legs 8 in. long, he thought that a flamingo, weighing 4 lbs., 

 should have legs 10 ft. long, to be in the same proportion as the stilt's. But 

 it is obvious to us that, as the weights of the two birds are as 1 : 15, so the legs 

 (or other linear dimensions) should be as the cube-roots of these numbers, or 

 nearly as 1 : 2^. And on this scale the flamingo's legs should be, as they actually 

 are, about 20 in. long. 



