8 Rayleigh, The MccJianical Principles of Flight. 



In order that this ma\' have a finite value, v must 



vary ; the principle beinij that to get the most advantage 



V must be great when du is positive, that is when the 



wind is freshening, and smaller when the wind is failing. 



The higher velocit\' required to meet the freshening wind 



is to be obtained by a previous fall to a lower level. 



As an example, let us suppose that n and v are 

 periodic, so that 



u = //o + y\ sin//, V = ?'o + i\ cos {pf + e); 



then 



/ V du = pii\Vij ZQ)%pt . cos {pt \ e)dt, 

 and, when / is great, 



J vdi/ = \ptiiyViCO%e (3). 



The mechanical advantage obtained in time / is 

 greatest when e vanishes, i.e., when du and i' are in the same 

 phase. This mechanical advantage is to be set against the 

 frictional and other losses neglected in our original 

 supposition. Were there no such losses, the value of v, 

 or of the elevation, might continually increase. 



This example shows that it is quite possible for a bird 

 moving in a ver\' natural manner against a strong and 

 variable wind to maintain himself and to advance over 

 the ground without working his wings. Observations of 

 this kind are recorded by Mr Huffakcr. It will be under- 

 stood, of course, that a bird, not being interested in 

 simplifying the calculation, will take any advantage that 

 offers itself of the internal energy of the wind and of 

 upward currents in order to attain his objects. 



In the preceding discussions we have assumed, for the 

 sake of simplicity, that a bird or a flying machine is able 

 to glide in still air without loss of energ}-. It is needless 

 to say that the truth of such an assumption can, at best. 



