30 ON MAGNITUDE [ch. 



to exist in, will militate against that existence in a degree 

 proportionate, perhaps in a geometrical ratio, to the bulk of the 

 species. If a dry season be greatly prolonged, the large mammal 

 will suffer from the drought sooner than the small one; if any 

 alteration of climate affect the quantity of vegetable food, the 

 bulky Herbivore will be the first to feel the effects of stinted 

 nourishment." 



But the principle of GaHleo carries us further and along more 

 certain lines. The strength of a muscle, like that of a rope or 

 girder, varies with its cross-section; and the resistance of a bone 

 to a crushing stress varies, again hke our girder, with its cross- 

 section. But in a terrestrial animal the weight which tends to 

 crush its limbs, or which its muscles have to move, varies as the 

 cube of its hnear dimensions; and so, to the possible magnitude 

 of an animal, living under the direct action of gravity, there is a 

 definite limit set. The elephant, in the dimensions of its limb-bones, 

 is already shewing signs of a tendency to disproportionate thickness 

 as compared with the smaller mammals; its movements are in 

 many ways hampered and its agility diminished: it is already 

 tending towards the maximal Hmit of size which the physical forces 

 permit*. The spindleshanks of gnat or daddy-long-legs have their 

 own factor of safety, conditional on the creature's exiguous bulk 

 and weight; for after their own fashion even these small creatures 

 tend towards an inevitable limitation of their natural size. But, as 

 Gahleo also saw, if the animal be wholly immersed in water like the 

 whale, or if it be partly so, as was probably the case with the giant 

 reptiles of the mesozoic age, then the weight is counterpoised to 

 the extent of an equivalent volume of water, and is completely 

 counterpoised if the density of the animal's body, with the included 

 air, be identical (as a whale's very nearly is) with that of the water 

 around^. Under these circumstances there is no longer the same 

 physical barrier to the indefinite growth of the animal. Indeed, in the 

 case of the aquatic animal, there is, as Herbert Spencer pointed out, 



* Cf. A. Rauber, Galileo iiber Knochenformen, Morphol. Jahrb. vii, p. 327, 1882. 



t Cf. W. S. Wall, A New Sperm Whale etc., Sydney, 1851, p. 64: "As for 

 the immense size of Cetacea, it evidently proceeds from their buoyancy in the 

 medium in which they live, and their being enabled thus to counteract the force of 



gravity." 



