Miscellaneous. 157 



forwards, plus the movement of the centre of gravity of the bird, 

 which is transported horizontally forward. In the vertical direction, 

 the point in question rises during the elevation of the wing. The 

 resultant of the two movements is a straight or curved trajectory, 

 according to the relation of the movement of the wing forwards and 

 upwards. If the wing rises at first more than it moves forward, and 

 finally moves forward more than it rises, this curved trajectory will 

 present its concavity to the ground, But in all cases, as the hori- 

 zontal displacement of the centre of gravity of the animal is very 

 great in comparison with the amount to which the wing is elevated, 

 this trajectory is at all points very slightly inclined to the horizon. 

 If the animal keeps the wing inclined to the same extent, the wing, 

 in ascending, will only experience resistance at its edge, seeing that 

 its surface is constantly applied upon the trajectory described by the 

 anterior margin, this trajectory being curved when the wing is 

 curved, as in birds, flat when the wing is flat, as in the Neuroptera. 



Moreover, if the animal inclines the wing more than is necessary 

 to apply it upon the trajectory of its anterior margin, an ascending 

 component is produced, during the elevation of the wing, at the ex- 

 pense of the horizontal velocity. In this case the wing during its 

 elevation, far from destroying its descending effect, as is commonly 

 supposed, acts in the same direction as during its descent. 



The relation of the weight to the wing-surface increases as the 

 extent of wing. In an Urubu with an extent of wing of 1*37 metre, 

 the weight supported per square metre by the whole surface (ex- 

 tended wings and tail and body) was 4*82 kil., or, neglecting the 

 surface of the body and tail, 5'92 kil. In the Humming-Eird the 

 weight supported, referred in the same way to the square metre 

 of total surface, is only l'Oo kil. In normal flight the velocity of 

 the Urubu, determined by that of its shadow on the ground in calm 

 weather, varies between 10 and 12 metres per second. Lastly, from 

 the direct measurement of the resistance of the wings in a beat of the 

 same duration, and from the number of beats made in a given time 

 during horizontal flight, it appears that the amount of work produced 

 by birds of the size of the Urubu per second does not equal in 

 amount that necessary to raise one-third of the weight of the animal 

 ] metre. 



The movement of the wings is an accelerated movement. Expe- 

 riments have long since shown that the resistance to this kind of 

 movement is greater than that to a uniform movement. This is 

 due to the circumstance that, in the former case, a certain mass of 

 air which accompanies the body has to be set in motion. If the 

 accelerative force be very great, and the movement be annulled before 

 the final velocity has acquired a great value, as is the case in birds, 

 the term of the resistance depending upon the accelerative force is 

 very great in proportion to the term depending only upon the squares 

 of the velocities, which alone is manifested in uniform movements. 

 In the flight of birds, the phenomenon of reaction is therefore of 

 more importance than the other phenomena of resistance. Driving 

 downwards a certain volume of air, the body of the bird rises by 



