II] OF FROUDE'S LAW 33 



while the respiratory mechanism can only supply a store of energy 

 at a rate proportional to the square of the said dimensions, the 

 singular result ought to follow that, in swimming for instance, the 

 larger fish ought to be able to put on a spurt of speed far in excess 

 of the smaller one; but the distance travelled by the year's end 

 should be very much ahke for both of them. And it should also 

 follow that the curve of fatigue is a steeper one, and the staying 

 power less, in the smaller than ixx the larger individual. This is the 

 c^ase in long-distance racing, where neither draws far ahead until 

 the big winner puts on his big spurt at the end; on which is based 

 an aphorism of the turf, that "a good big 'un is better than a good 

 httle 'un." For an analogous reason wise men know that in the 

 'Varsity boat-race it is prudent and judicious to bet on the heavier 

 crew. 



Consider again the dynamical problem of the movements of the 

 body and the hmbs. The work done (W) in moving a Hmb, whose 

 weight is p, over a distance s, is measured hy ps; p varies as the 

 cube of the hnear dimensions, and s, in ordinary locomotion, varies 

 as the linear dimensions, that is to say as the length of Hmb : 



Wocpsocl^ xl^lK 



But the work done is limited by the power available, and this 

 varies as the mass of the muscles, or as l^; and under this hmitation 

 neither p nor s increase as they would otherwise tend to do. The 

 limbs grow shorter, relatively, as the animal grows bigger; and 

 spiders, daddy-long-legs and such-hke long-limbed creatures attain 

 no great size. 



Let us consider more closely the actual energies of the body. 

 A hundred years ago, in Strasburg, a physiologist and a mathema- 

 tician were studying the temperature of warm-blooded animals*. 

 The heat lost must, they said, be proportional to the surface of the 

 animal : and the gain must be equal to the loss, since the temperature 

 of the body keeps constant. It would seem, therefore, that the 

 heat lost by radiation and that gained by oxidation vary both alike, 

 as the surface-area, or the square of the Hnear dimensions, of the 

 animal. But this result is paradoxical; for whereas the heat lost 



* MM. Rameaux et Sarrus, Bull. Acad. R. de Me'decine, in, pp. 1094-1100, 

 1838-39. 



