423 



MOTION. 



dissimilar orders, the areas of the wings do not 

 vary as the weights of the birds. 



The ratio of the times of the descent and as- 

 cent of the wing will cause a corresponding 

 difference in the ratio of the resistance of the 

 air, which is not as the velocity simply, but as 

 the square of the velocity. The velocity of the 

 wing varies according to the celerity with which 

 the bird moves, and it moves through a greater 

 or less arc according as the bird merely sus- 

 pends itself in the air ot is in rapid motion, on 

 the rational supposition that birds employ their 

 locomotive organs in such a manner as to econo- 

 mize as much as possible the expenditure of 

 their muscular power. We find by the an- 

 nexed analysis that for this purpose the ratio of 

 the time of the descent of the wings to that of 

 their ascent is nearly as one to two, and that the 

 ratio of the resistance of the up to that of the 

 down stroke lies between one-half, one-fourth, 

 and one-fifth. In the Swallow, for example, in 

 order that the bird may merely sustain itself in 

 the air, the centre of the wings, according to 

 Chabrier, must descend with a velocity of about 

 seven metres, or 22-9662944 feet per second, 

 which, we find by the annexed analysis, gives 

 15 - 3 for the number of vibrations, and for the 

 minimum amount of action expended in the 

 same time, a force which would raise its own 

 weight to the height of 26'246 feet. 



The ratio of the time of the ascent and de- 

 scent of the wing becomes much greater when 

 the bird moves against the wind, suppose about 

 forty-eight feet per second, or in rapid flight; 

 and the velocity of the descent of the wings, 

 and quantity of action expended, will augment 

 in proportion. The great quantity of action ex- 

 pended in flight tends to confirm the views of Bo- 

 relli respecting the vast power with which the pec- 

 toral muscles of birds are endowed. In small 

 birds the oscillations are performed with such 

 great rapidity, that they cannot be numbered 

 by the eye; but in the finches and humming- 

 birds, the oscillations of which produce a musi- 

 cal note, the pitch will enable us to determine 

 with accuracy the number of oscillations in a 

 given time. In large birds, the wings move 

 through arcs of greater circles than in small 

 ones, and the times of their periodic oscilla- 

 tions decrease in the same ratio, and may thus 

 be more easily numbered : the areas of their 

 wings, and the resistance which they encounter, 



bear some proportion to the greater weight of 

 the body : but although theory ascribes to the 

 wings a large number of oscillations, it by 

 no means follows that they perform the 

 exact number assigned at least for any length- 

 ened period. On the contrary, we observe 

 that many birds, such as the Woodpecker,* 

 and most Insessores, give a few strokes of the 

 wings by which the body acquires a projec- 

 tile velocity sufficient to elevate it through a 

 considerable space, and that when the im- 

 pulse thus given is nearly expended, they re- 

 peat this action, and again suspend it. If they 

 are moving horizontally, their progression is 

 performed in a similar manner; the axis of the 

 bird is inclined upwards at each impulse like a 

 projectile, but the mean motion is horizontal. 

 The curve described during each projection is 

 a parabola. After a few strokes, during the 

 ascent, the wings are folded until the bird has 

 passed the vertex of the curve, and has de- 

 scended to some distance on the opposite side, 

 when they suddenly expand their wings again, 

 and by a few strokes describe a new curve. In 

 this mode of progression the velocity is very 

 variable, being equal to that which a body 

 would acquire by falling through one-fourth of 

 the parameter of each point in the curve. 

 Many large birds, such as the Rooks, Pigeons, 

 &c. when descending from great heights ex- 

 pand their wings, and incline the axis of their 

 bodies obliquely downwards, as in Jig. 222. 



Fig. 222. 



In this case the air opposes sufficient resistance 

 in a vertical direction upwards to keep in equili- 

 brio the force of gravity acting upon the body 

 vertically downwards, so that the motion of the 

 bird becomes uniform, without requiring any 

 movement of the wings.f Another mode of de- 



where the formula gives 7.38, and observation from 2 to 3 flappings per second. It is worthy of 



remark, that by supposing V to be equal to the cube root, instead of the square root of 





. 

 p q irKA. 



the number of flappings in each of the last two cases by the formula, agrees very closely with the 

 number determined by the mean of several observations. 



The quantity of force expended would be greater if the density of the air were less, but it 

 would only increase in the ratio of 1.4 to 1 if the air were but half as dense. We may, therefore, 

 conclude that the height to which a bird can raise itself is limited not so much by want of sufficient 

 support in the resistance of the air as by the difficulty of respiring in too rare an atmosphere. 



* The Rook appears to make from ten to fifteen, and the Pigeon from ten to twenty-three effective 

 strokes of the wing in five seconds. 



t The soft downy feathers which line the wings of the nocturnal rapacious birds, as the Owl, permit 

 the wings to perform its evolutions during flight in search of their prey without noise. On the contrary, 

 in the diurnal species of this order, which chase and capture their prey in open day, and where no 

 secn-cy would suffice, the feathers are strong, and their passage through the air is accompanied with 

 a rushing noise. 



