52 ON MAGNITUDE [ch. 



insect finds itself imprisoned in a drop of water, and a fly with 

 two feet in one drop finds it hard to extricate them. 



The mechanical construction of insect or crustacean is highly 

 efficient up to a certain size, but even crab and lobster never exceed 

 certain moderate dimensions, perfect within these narrow bounds as 

 their construction seems to be. Their body lies within a hollow 

 shell, the stresses within which increase much faster than the mere 

 scale of size ; every hollow structure, every dome or cyhnder, grows 

 weaker as it grows larger, and a tin canister is easy to make but a 

 great boiler is a complicated affair. The boiler has to be strengthened 

 by "stiffening rings" or ridges, and so has the lobster's shell; but 

 there is a limit even to this method of counteracting the weakening 

 effect of size. An ordinary girder-bridge may be made»efficient up 

 to a span of 200 feet or so ; but it is physically incapable of spanning 

 the Firth of Forth. The great Japanese spider-crab, Macrocheira, 

 has a span of some 12 feet across; but Nature meets the difficulty 

 and solves the problem by keeping the body small, and building up 

 the long and slender legs out of short lengths of narrow tubes. 

 A hollow shell is admirable for small animals, but Nature does not 

 and cannot make use of it for the large. 



In the case of insects, other causes help to keep them of small 

 dimensions. In their peculiar respiratory system blood does not 

 carry oxygen to the tissues, but innumerable fine tubules or tracheae 

 lead air into the interstices of the body. If we imagine them growing 

 even to the size of crab or lobster, a vast complication of tracheal 

 tubules would be necessary, within which friction would increase 

 and diffusion be retarded, and which would soon be an inefficient 

 and inappropriate mechanism. 



The vibration of vocal chords and auditory drums has this in 

 common with the pendulum-hke motion of a hmb that its rate 

 also tends to vary inversely as the square root of the linear dimen- 

 sions. We know by common experience of fiddle, drum or organ, 

 that pitch rises, or the frequency of vibration increases, as the 

 dimensions of pipe or membrane or string diminish; and in like 

 manner we expect to hear a bass note from the great beasts and a 

 piping treble from the small. The rate of vibration {N) of a stretched 

 string depends on its tension and its density; these beins^ equal, it 

 varies inversely as its own length and as its diameter, i^or similar 



