36 ON MAGNITUDE [ch. 



Such problems were admirably treated by Galileo and Borelli, 

 but many writers remained ignorant of their work. Linnaeus 

 remarked that if an elephant were as strong in proportion as a 

 stag-beetle, it would be able to pull up rocks and level mountains; 

 and Kirby and Spence have a well-known passage directed to shew 

 that such powers as have been conferred upon the insect have been 

 withheld from the higher animals, for the reason that had these 

 latter been endued therewith they would have "caused the early 

 desolation of the world*." 



Such problems as that presented by the flea's jumping powersf , 

 though essentially physiological in their nature, have their interest 

 for us here: because a steady, progressive diminution of activity 

 with increasing size would tend to set Hmits to the possible growth 

 in magnitude of an animal just as surely as those factors which 

 tend to break and crush the living fabric under its own weight. In 

 the case of a leap, we have to do rather with a sudden impulse than 

 with a continued strain, and this impulse should be measured in 

 terms of the velocity imparted. The velocity is proportional to 

 the impulse (x), and inversely proportional to the mass (M) moved : 

 V = xjM. But, according to what we still speak of as "Borelh's 

 law," the impulse (i.e. the work of the impulse) is proportional to 

 the volume of the muscle by which it is produced {, that is to say 

 (in similarly constructed animals) to th^ mass of the whole body; 

 for the impulse is proportional on the one hand to the cross-section 

 of the muscle, and on the other to the distance through which it 



* Introduction to Entomology, ii, p. 190, 1826. Kirby and Spence, like many less 

 learned authors, are fond of popular illustrations of the "wonders of Nature," 

 to the neglect of dynamical principles. They suggest that if a white ant were as 

 big as a man, its tunnels would be "magnificent cylinders of more than three 

 hundred feet in diameter"; and that if a certain noisy Brazilian insect were as 

 big as a man, its voice would be heard all the world over, "so that Stentor becomes 

 a mute when compared with these insects!" It is an easy consequence of 

 anthropomorphism, and hence a common characteristic of fairy-tales, to neglect 

 the dynamical and dwell on the geometrical aspect of similarity. 



•f The flea is a very clever jumper; he jumps backwards, is stream-lined ac- 

 cordingly, and alights on his two long hind-legs. Cf. G. I. Watson, in Nature, 

 21 May 1938. 



X That is to say, the available energy of muscle, in ft.-lbs. per lb. of muscle, is 

 the same for all animals: a postulate which requires considerable qualification 

 when we come to compare very different kinds of muscle, such as the insect's and 

 the mammal's. 



