THE HALTERES OF THE BLOW-FLY. 619 



Since the density of the atmosphere varies with the phase of 

 a sound-wave, and as such variations of density are an efficient 

 cause of retardation, and acceleration in a body vibrating in 

 air, it may be assumed that the rate of the vibration of the 

 halteres is affected by them. It can be shown that the more 

 rapidly a body moves, the greater the resistance of the atmo- 

 sphere becomes ; and this resistance increases with the square 

 of the velocity of the moving body (see p. 387). Sound vibra- 

 tions must therefore affect the moving halter and produce 

 disturbances of its movement. The more rapid the movement 

 of the halter itself the greater these disturbances become ; and 

 as they are produced by the varying density of the air through 

 which it moves, or by the waves of sound, we may regard 

 these disturbances as vibrations superimposed upon the proper 

 vibrations of the halter due to the action of its own muscles. 

 Since every form of ear possesses the power of analysing 

 sound-waves or separating superimposed vibrations, the vibra- 

 ting halter endowed with such a power would become a most 

 efficient organ of hearing. 



Airy [297, p. 142] states that : ' The only experiment which 

 is sufficiently delicate to give a measure of the pressure of a 

 sound-wave is the observation of its influence on the move- 

 ment of a pendulum whose bob is a sphere ' ; and he shows 

 that the effect is directly proportional to the square of the 

 number of vibrations per second or to what comes to the 

 same thing, the square of the mean velocity of the moving 

 pendulum bob. As we know that the movements of the tym- 

 panic membrane of the ear are entirely due to changes of the 

 density of the air in its vicinity, it is clear that these changes 

 would have a marked effect on a minute vibrating halter. So 

 the velocity of the movement of the insect in flight would give 

 rise to variations of a similar character, differing, however, 

 from those of sound in not being rhythmic, but more or less 

 constant pressures modifying the envelope of the curves in 

 which the halter vibrates. 



We may further assume that the fluid in the capitellum, stalk 

 and scalse of the halter moves as a rigid body, like the fluid in 



