42 ON MAGNITUDE [ch. 



bird; I, a linear dimension, the form of the bird being supposed 

 constant. j^j _ ^^ ^ ^3^ but M = mV , and m = W , 



Therefore M - ^272 _ ^3^ 



and therefore F = VI 



and Tf = MF = R 



The gist of the matter is, or seems to be, that the work which 

 can he done varies with the available weight of muscle, that is to say, 

 with the mass of the bird ; but the work which has to be done varies 

 with mass and distance; so the larger the bird grows, the greater 

 the disadvantage under which all its work is done*. The dispropor- 

 tion does not seem very great at first sight, but it is quite enough 

 to tell. It is as much as to say that, every time we double the 

 linear dimensions of the bird, the difficulty of flight, > or the work 

 which must needs be done in order to fly, is increased in the ratio 

 of 2^ to 2^*, or 1 : V2, or say 1:14. If we take the ostrich to exceed 

 the sparrow in linear dimensions as 25 : 1, which seems well within 

 the mark, the ratio would be that between 25^* and 25^, or between 

 5' and 5^; in other words, flight would be five times more difficult 

 for the larger than for the smaller bird. 



But this whole explanation is doubly inadequate. For one thing, 

 it takes no account of gliding flight, in which energy is drawn from 

 the wind, and neither muscular power nor engine power are em- 

 ployed; and we see that the larger birds, vulture, albatross or 

 solan-goose, depend on gliding more and more. Secondly, the old 

 simple account of the impact of the wing upon the air, and the 

 manner in which a downward momentum is communicated and 

 support obtained, is now known to be both inadequate and 

 erroneous. For the science of flight, or aerodynamics, has grown 

 out of the older science of hydrodynamics; both deal with the 

 special properties of a fluid, whether water or air; and in our case, 

 to be content to think of the air as a body of mass m, to which a 

 velocity v is imparted, is to neglect all its fluid properties. How the 



* This is the result arrived at by Helmholtz, Ueber ein Theorem geometrisch- 

 ahnliche Bewegungen fliissiger Korper betrefFend, nebst Anwendung auf das 

 Problem Luftballons zu lenken, Monatsber. Akad. Berlin, 1873, pp. 501-514. It was 

 criticised and challenged (somewhat rashly) by K. Miillenhof, Die Grosse der Flug- 

 flachen etc., PfiUger's Archiv, xxxv, p. 407; xxxvi, p. 548, 1885. 



