204 THE EAR 



Now, eliminate r from equations (1) and (2), and we obtain 



This equation gives the amount of shortening of the chord 

 which occurs when the curve of the arc is increased ; that is to 

 say, it gives the extent to which the two ends of the fibre are 

 drawn together. Now, if s, the displacement of the middle of the 

 fibre, be very small in comparison with I, then I - X obviously 

 becomes very small in comparison with s. Conversely, the very 

 small increase in the magnitude of Z-A must cause a relatively 

 great increase of s ; that is to say, it must cause a relatively great 

 displacement of the centre of the fibre. 



Again, if t = the tension of the fibre, p = the pressure on each 

 unit of its length, and r = the radius of curvature, then 



t=pr, 



and the forces which act upon both ends of the fibre must be 

 equal to the pressure which acts upon the diameter of the semi- 

 circle through a width equal to that of the fibre (Helmholtz). 

 Therefore 



2t = 2pr. 



Hence the greater the radius of curvature, the greater will be 

 the alterations in tension of the fibre caused by alterations in 

 the pressure of the air. Further, as the radial fibres are those 

 which are attached to the malleus, it is evident that the variations 

 in the tension of the fibres cause movements of the bones when 

 sound-waves strike the drum-head. Thus a very small change 

 of pressure in the air causes a considerable change in the tension 

 of the fibres ; and further, in accordance with the laws regulating 

 the action of the lever, as the force which fibres exert upon the 

 handle of the malleus increases, amplitude of movement of that 

 bone diminishes. In this way, the special form of the drum-head 

 secures a maximum of efficiency for tones of the feeblest intensity" 

 (M'Kendrick). 



Briefly, energy applied to the membrane is passed on to the 

 handle of the malleus diminished in amplitude but with increased 

 intensity. 



(b) Ossicles. The three bones of the middle ear, the malleus, 

 the incus and the stapes, stretch across the tympanic cavity 

 forming an articulated chain of levers, so that every normal move- 

 ment of the tympanic membrane is transmitted by the stapes to 



