II] OF FROUDE'S LAW 23 



lung, that is to say (other things being equal) with the square of 

 the linear dimensions of the animal. We may of course (departing 

 from the condition of similarity) increase the heating-surface of 

 the boiler, by means of an internal system of tubes, without 

 increasing its outward dimensions, and in this very way nature 

 increases the respiratory surface of a lung by a complex system 

 of branching tubes and minute air-cells ; but nevertheless in 

 two similar and closely related animals, as also in two steam- 

 engines of precisely the same make, the law is bound to hold that 

 the rate of working must tend to vary with the square of the 

 linear dimensions, according to Froude's law of steamshij) com- 

 parison. In the case of a very large ship, built for speed, the 

 difficulty is got over by increasing the size and number of the 

 boilers, till the ratio between boiler-room and engine-room is 

 far beyond what is required in an ordinary small vessel * ; but 

 though we find lung-space* increased among animals where 

 greater rate of working is required, as in general among birds, 

 I do not know that it can be shewn to increase, as in the 

 " over-boilered " ship, with the size of the animal, and in a ratio 

 which outstrips that of the other bodily dimensions. If it be the 

 case then, that the working mechanism of the muscles should be 

 able to exert a force proportionate to the cube of the linear 

 bodily dimensions, 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 alike for both 

 of them. And it should also follow that the curve of fatigue 



* Let L be the length, S the (wetted) surface, T the tonnage, D the displacement 

 (oi" volume) of a ship; and let it cross the Atlantic at a speed V. Then, in com- 

 paring two ships, similarly constructed but of different magnitudes, we know that 

 L = V", S = L~ = V*, D = T=L^ = V«; also R (resistance) = S . F- = F« ; H (horse- 

 power) = R .V ^V ; and the coal (C) necessary for the voyage = HjV = F*. That 

 is to say, in ordinary engineering language, to increase the speed across the Atlantic 

 by 1 per cent, the ship's length must be increased 2 per cent., her tonnage or 

 displacement 6 per cent., her coal-consumpt also 6 per cent., her horse- power, 

 and therefore her boiler-capacity, 7 per cent. Her bunkers, accordingly, keep 

 pace with the enlargement of the ship, but her boilers tend to increase out of 

 proportion to the space available. 



