1S6 ANIMAL MECHANISM. 



which the wing describes, its point evidently moves on the 

 surface of a sphere, the radius of which is the length of ihe 

 wing, and the centre at the point of attachment of this organ 

 with the niesolliorax. But a sphere can only touch a pi. me or 

 convex surface at one point ; thus, we only olitain a number 

 of points for a series of revolutions of the wing, if the turn- 

 ing cylinder be only tangential to the extremity of the wing. 

 More complicated tracings can only be obtained by more 

 extensive contacts, in which the wing bends, and thus rubs 

 a, portion of its surfaces or its edges on the blackened paper. 



We will explain the means by which the graphic method 

 can serve to determine the movements of the wing, but let 

 us first show the results obtained by another method, in 

 order to render the explanation more clear. 



2. Ojitical method of the determination of the inurements of 

 the uing. Having being convinced by the former experi- 

 ments, of the regular periodicity of these movements, we have 

 thought it possible to determine their nature by the eye. In 

 fact, if we can attach a brilliant spot to the extremity of the 

 wing, this spot passing continually through the same space 

 would leave a luminous trace which would produce a figure 

 completely regular, and free from the deformity incident to 

 that effected by the friction on the cylinder. This optical 

 method has already been employed for a similar purpose by 

 Wheatetone, who placed brilliant metallic balls on rods pro- 

 ducing complex vibrations, and thus obtained luminous 

 figures varying according to the different combinations of the 

 vibrating movements. 



By fixing a small piece of gold-leaf at the extremity of the 

 wing of a wasp, and throwing upon it a ray of the sun while 

 the insect was executing tin; movements of flight, we have 

 obtained a brilliant image of the successive positions of iho 

 wing, which gave i.e.uly the appearance represented iu 

 fig. 71. 



This figure shows that the point of the wing descvil es a 

 very elongated figure 8; sometimes, indeed, the wing sn 

 to move entirely in one plane, and the instant afterwards the 

 terminal loops which form the 8 are seen to open more ami 

 more. When the opening becomes very large, one of the 



