II] OF BORELLI'S LAW 37 



contracts. It follows from this that the velpcity is constant, what- 

 ever be the size of the animal. 



Putting it still more simply, the work done in leaping is propor- 

 tional to the mass and to the height to which it is raised, W oc mH. 

 But the muscular power available for this work is proportional to 

 the mass of muscle, or (in similarly constructed animals) to the mass 

 of the animal, W oc m. It follows that H is, or tends to be, a 

 constant. In other words, all animals, provided always that they 

 are similarly fashioned, with their various levers in Hke proportion, 

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

 height*. The grasshopper seems to be as well planned for jumping 

 as the flea, and the actual heights to which they jump are much of 

 a muchness; but the flea's jump is about 200 times its own height, 

 the grasshopper's at most 20-30 times; and neither flea nor grass- 

 hopper is a better but rather a worse jumper than a horse or a manf . 



As a matter of fact, Borelli is careful to point out that in the act 

 of leaping the impulse is not actually instantaneous, like the blow 

 of a hammer, but takes some httle time, during which the levers 

 are being extended by which 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, and tends to leave a 

 certain balance of advantage in regard to leaping power on the side 

 of the larger animal J. But on the other hand, the question of 

 strength of materials comes in once more, and the factors of stress 

 and strain and bending moment make it more and more difficult 

 for nature to endow the larger animal with the length of lever with 

 which she has provided the grasshopper or the flea. To Kirby and 

 Spence it seemed that "This wonderful strength of insects is 

 doubtless the result of something peculiar in the structure and 

 arrangement of their muscles, and principally their extraordinary 



* Borelli, Prop. CLxxvn. Animalia minora et minus ponderosa majores saltus 

 efficiunt respectu sui corporis, si caetera fuerint paria. 



t The high jump is nowadays a highly skilled performance. For the jumper 

 contrives that his centre of gravity goes under the bar, while his body, bit by bit, 

 goes over it. 



J See also {int. al.), John Bernoulli, De Motu Musculorum, Basil., 1694; 

 Chabry, Mecanisme du saut, J. de VAnat. et de la Physiol, xix, 1883;* Sur la 

 longueur des membres des animaux sauteurs, ibid, xxi, p. 356, 1885; Le Hello, 

 De Taction des organes locomoteurs, etc., ibid, xxix, pp. 65-93, 1893; etc. 



