30 ON MAGNITUDE [ch. 



and tends to leave a certain balance of advantage, in regard to 

 leaping power, on the side of the larger animal*. 



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, so to speak, more and more difficult 

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

 with which she has provided the flea or the grasshopper. 



To Kirby and Spence it seemed that " This wonderful strength 

 of insects is doubtless the result of something pecuhar in the 

 structure and arrangement of their muscles, and principally their 

 extraordinary power of contraction."' This hypothesis, which is 

 so easily seen, on physical grounds, to be unnecessary, has been 

 amply disproved in a series of excellent papers by F. Plateau "f. 



A somewhat simple problem is presented to us by the act of 

 walking. It is obvious that there will be a great economy of 

 work, if the leg s'wing at its normal 'pendnlum-rate; and, though 

 this rate is hard to calculate, owing to the shape and the jointing 

 of the limb, we may easily convince ourselves, by counting our 

 steps, that the leg does actually swing, or tend to swing, just as 

 a pendulum does, at a certain definite rate J. When we walk 

 quicker, we cause the leg-pendulum to describe a greater arc, but 

 we do not appreciably cause it to swing, or vibrate, quicker, until 

 we shorten the pendulum and begin to run. Now let two indi- 

 viduals, A and B, walk in a similar fashion, that is to say, with 

 a similar angle of swing. The arc through which the leg swings, 

 or the amplitude of each step, will therefore vary as the length 

 of leg, or say a? ajh ; but the time of swing will vary as the square 



* See also (int. al.), John Bernoulli, de Motu Musculorum, Basil., 1694; 

 Chabrj', 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, p. 65-93, 1893, etc. 



t Recherches sur la force absolue des muscles des Invertebres, Bull. Acad. B. 

 de Belgique (3), vi, \ti, 1883-84: see also ibid. (2), xx, 1865, xxii, 1866; A^ut. 

 Mag. ]<:. H. x\ti, p. 139, 1866, xix, p. 95, 1867. The subject was also well treated 

 by Straus-Diirckheim, in his Considerations generales sur Vanatomie comparee des 

 animaux articules, 1828. 



X The fact that the limb tends to swing in pendulum-time was first observed 

 by the brothers Weber [Mechanik der menschl. Gehicerkzeuxje, Gottingen, 1836). 

 Some later writers have criticised the statement (e.g. Fischer, Die Kiuematik des 

 Beinschwingens etc., Abh. math. phys. Kl. k. Sachs. Ges. xxv-xxvm, 1899-1903), 

 but for all that, with proper qualifications, it remains substantially true. 



