II] BORELLFS LAW 29 



Such problems as that which is presented by the flea's jumping 

 powers, 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 limits 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 = x/M. But, according to what we still speak 

 of as " Borelli'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 the 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 contracts. It follows at once from this that the 

 velocity is constant, whatever be the size of the animals : in 

 other words, that all animals, provided always that they are 

 similarly fashioned, with their various levers etc., in like proportion, 

 ought to jump, not to the same relative, but to the same actual 

 height f. According to this, then, the flea is not a better, but 

 rather a worse jumper than a horse or a man. As a matter of 

 fact, Borelli is careful to point out that in the act of leaping the 

 impulse is not actually instantaneous, as in the blow of a hammer, 

 but takes some little time, during which the levers are being 

 extended by which the centre of gravity of the animal is being 

 propelled forwards ; and this interval of time will be longer in 

 the case of the longer levers of the larger animal. To some extent, 

 then, this principle acts as a corrective to the more general one, 



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

 big as a man, its voice would be heard aU 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 principle of dynamical, while dwelling on the aspect of geometrical, similarity. 



* I.e. 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 are 

 comparing very different kinds of muscle, such as the insect's and the mammal's. 



t Prop, clxxvii. Animaha minora et minus ponderosa majores saltus efficiunt 

 respectu sui corporis, si caetera fuerint paria. 



