6 Rayleigh, The Mcchmiical Principles of Flii^ht. 



it is supposed without loss of relative velocit}' — until his 

 direction is reversed so as to be with the wind of the lower 

 stratum and contrary to the wind of the upper stratum. 

 A passage upwards through the plane now secures another 

 gain of relative velocit}-, or of potential elevation, of nearly 

 the same value as before. 'J'hc process may be repeated. 

 At every passage through the plane (whether in the 

 upwards or in the downwards direction) there is a gain of 

 potential elevation, and if this gain outweighs the losses 

 all the while in progress, the bird may maintain or 

 improve his position without doing a stroke of work. 



It may be of interest to consider a numerical example. 



Suppose that 



v = 30 miles i)er hour= i"34 x 10" cm. per second, 



and that 



li — ]i—\o feet = 305 cm. ; 



then in C.G.S. measuie 



(?' + 2uf = -J- + 2g {/i - h) 



— I "So X 10''+ '60 X 10''= 2 "40 X 10'"', 

 and 



jv + 2?^ - 1*55 X 10'' ; 

 so that 



211 = -21 X 10'' cm. sec =47 miles hour. 



In this case a freshening of the wind amounting to 47 

 miles per hour is cciuivalcnt to a gain of 10 feet of potential 

 elevation. 



In order to take advantage of the gradual increase of 

 wind with elevation usually to be met with, a bird may 

 describe circles in an inclined plane, always descending 

 when moving to leeward and ascending when moving to 

 windward. Whether the differences of velocity available 

 at considerable elevations in the atmosphere are suffi- 

 cient to allow a bird to maintain his position without 

 working his wings appears to be doubtful. Near the level 

 of the ground or sea these differences are greater, and 



