II] OF EYES AND EARS 53 



strings, N oc 1//^, and for a circular membrane, of radius r and 

 thickness e, N oc ll(r^ Ve). 



But the deHcate drums or tympana of various animals seem to 

 vary much less in thickness than in diameter, and we may be content 

 to write, once more, N oc l/r^. 



Suppose one animal to be fifty times less than another, vocal 

 chords and all: the one's voice will be pitched 2500 times as many 

 beats, or some ten or eleven octaves, above the other's; and the 

 same comparison, or the same contrast, will apply to the tympanic 

 membranes by which the vibrations are received. But our own 

 perception of musical notes only reaches to 4000 vibrations per 

 second, or thereby; a squeaking mouse or bat is heard by few, and 

 to vibrations of 10,000 per second we are all of us stone-deaf. 

 Structure apart, mere size is enough to give the lesser birds and 

 beasts a music quite different to our own: the humming-bird, for 

 aught we know, may be singing all day long. A minute insect may 

 utter and receive vibrations of prodigious rapidity; even its little 

 wings may beat hundreds of times a second*. Far more things 

 happen to it in a second than to us ; a thousandth part of a second 

 is no longer neghgible, and time itself seems to run a different course 

 to ours. 



The eye and its retinal elements have ranges of magnitude and 

 Hmitations of magnitude of their own. A big dog's eye is hardly 

 bigger than a little dog's; a squirrel's is much larger, propor- 

 tionately, than an elephant's; and a robin's is but little less than 

 a pigeon's or a crow's. For the rods and cones do not vary with 

 the size of the animal, but have their dimensions optically limited 

 by the interference-patterns of the waves of light, which set bounds 

 to the production of clear retinal images. True, the larger animal 

 may want a larger field of view ; but this makeg little difference, for 

 but a small area of the retina is ever needed or used. The eye, in 

 short, can never be very small and need never be very big; it has 

 its own conditions and limitations apart from the size of the animal. 

 But the insect's eye tells another story. If a fly had an eye like 

 ours, the pupil would be so small that diffraction would render a 

 clear image impossible. The only alternative is to unite a number 



* The wing-beats are said to be as follows: dragonfly 28 per sec, bee 190, 

 housefly 330; cf. Erhard, Verh. d. d. zool. Gesellsch. 1913, p. 206. 



