MOTION. 



421 



strokes made by tlie wings of insects as well as 

 of birds during flight, it is necessary to take into 

 the account the length of the arc in which they 

 oscillate. 



The oscillations of the wings of insects are 

 too rapid to be numbered by common observa- 

 tion. The principles of optics,* acoustics, and 

 dynamics have been employed to determine 

 them during their flight. According to Bur- 

 meister the pitch of the sound made during 

 flight varies with the number of strokes made 

 by the wings, although the production of the 

 sound is perfectly independent of them.f If 

 the number of strokes is synchronous with 

 the number of vibrations which produce the 

 sound, we can ascertain the number of their 

 oscillations very readily; but we are not yet 

 furnished with sufficient evidence that each 

 stroke of the wing is coincident with one 

 musical semi-vibration to determine this ques- 

 tion with precision. According to the analysis 

 made on the flight of birds, if the same data 

 may be considered applicable, we shall see by 

 Chabrier's investigations when all other things 

 remain the same, that the number of strokes 

 made by the wings of insects will vary as the 

 square roots of the weight directly, and of the 

 area of the wings inversely. 



In the Coleoptera, the ratio of the area of the 

 wings to the weight of the insect is small in 

 comparison with other orders. The elytra of 

 the Coleoptera add to their weight and surface 

 in passing through the air, without contributing 

 either to the vertical elevation or horizontal 

 velocity of the insect; on the contrary, as their 

 surfaces are inclined to the axis of the body 

 and the direction of motion, they retard the 

 velocity of the beetle in moving against the 

 wind. The centre of the forces lies posterior 

 to the articulation of the wings, and as the 

 angle of inclination of the elytra tends to ele- 

 vate the head and depress the abdomen by its 

 resistance to the wind, the axis of the body 

 becomes inclined vertically during flight. In 

 a stag beetle weighing forty grains, the area of 

 each elytra measured 0.366364 of a square 

 inch, and the true wings, calculated as the 

 quarter of an ellipse, gave 0.6263565 of a 

 squareinch each, orl. 2527126 in. for both. The 

 same measured by a graduated scale gave 

 0.62240 in. each, which shows how nearly the 

 form of the true wings approaches to a segment 

 of perfect ellipse. Those Coleoptera in which 

 the ratio of the surface of the wings is very small 

 cannot fly against a strong wind. Olivier says, 

 " None of this class can fly in opposition to the 

 wind," but this assertion is opposed by Kirby, 

 who states that the Melolonthae Hoplise fly in all 

 directions; others, as the Cicindeloe, take short 

 flights, and may be easily marked down by 

 the entomologist. The Cetoniae expand their 

 wings in flight without elevating their elytra, as 

 is done by other Coleoptera. 



The Dermapiera, though generally on their 

 legs, take flight towards evening. The wings 



* See Nicholson's Journal, 4to. vol. iii. p. 38. 



t Remarks on the causes of sound produced by 

 insects in flying, by Dr. H. Burmeister. Taylor's 

 Scientific Memoirs, vol. i. p. 378, 1837. 



of the earwigs are ample; the nervures radiate 

 from a common centre to the external margin 

 of the wings, which they expand like a fan. 

 According to Kay, the tegmina of the Orthop- 

 tera assist the wings in flight.- The Grillus 

 domesticus flies with an undulatory motion 

 like the woodpecker, alternately making a few 

 strokes with the wings in order to give a pro- 

 jectile velocity to the body upwards, and then 

 folding the wings to descend on the opposite 

 side of the vertex of a parabolic curve. Owing 

 to the analogous structure of their wings, the 

 Gryllus campestris and Gryllotalpa are capa- 

 ble of using them in a similar manner. The 

 Hemiptera employ their hemi-elytra to assist 

 the wings in flying.* By this means the area 

 of the wing is increased, a greater surface is 

 given to it for striking the air, the ratio of the 

 surface of the wings to the weight of the body 

 is augmented, the quantity of action and the 

 number of vibrations necessary to sustain it in 

 the air is diminished, and the power of flight 

 is consequently increased. 



The Lepidoptera are furnished with a far 

 greater area of wing in proportion to the weight 

 of their bodies than is observed in any other 

 flying animal. The under wing approaches in 

 figure to the quadrant of a circle, and in many 

 species the two meet posteriorly and form a 

 semicircle. The anterior and under wings are 

 locked together during their descent so as to 

 give them a synchronous action, and a compact 

 surface to resist the air. The surfaces of the 

 two wings on each side increase with the 

 distances of their sections from the axes of 

 motion; in the Morpho automedon (fig.220\ 

 in which the areas of the sections of the wings 

 lying between the parallels 1, 2, 3, 4, drawn at 

 equal distances from the axis of the body, will 

 V>e seen to increase (the last one excepted) as 

 the distances from the centre of motion of the 

 wings increase; the effect of which is, to throw 

 the centre of resistance to a greater distance 

 from the axis of motion, so that the muscles of 

 the wing act at a mechanical disadvantage; 

 and the weight of the body being small in 

 proportion to the area of the wing, the 

 body oscillates considerably at each elevation 

 and depression, and its flight is rendered un- 

 steady. 



The surface of the anterior wing is less than 

 that of the posterior, being as 2.08 : 2.4483471 

 square inches, and the sum of the surfaces of 

 the four wings is =9.0566942 inches. As the 

 solid contents of the body are very small when 

 compared to the surface of the wings, we 

 naturally conclude that the Morpho has pro- 

 longed powers of suspension. The great mag- 

 nitude of the wings of the Lepidoptera are 

 generally in proportion to the weight of their 

 bodies, and the force of their muscular system 

 endows them with great powers of flight; but 

 it is most frequently accomplished in a zig-zag 

 path. In the Pontia brassicae the weight of 

 the insect is found to be 1.525gr. ; the area 

 of the anterior wing 6 square inch, the area 



* See Dr. Rogct's Bridgewatcr Treatise, third 

 edition, vol. i. u. 313. 



