208 THE EAR 



Helmholtz, the distance p -a is 9-5 mms., and i-a is 6-3 mm. 

 The movement at i therefore will be only f,- of the movement at p, 

 but will have Ij times the intensity. We have now to consider 

 the transmission of this power to the foot of the stapes. If x - y 

 represents the range of the tip of the incus, c-d the distance from 

 c, the hinge (lower annular ligament) to d the centre of the foot 

 of the stapes, and c -r, the distance from the tip of the incus to 

 the lower end of the stapes, then the range of motion of the centre 



of the foot of the stapes will be - - which, according 



to the scale of a drawing given by Helmholtz, would give a leverage 

 of about 2 - 1 . 



So that, on the whole system of bones there is a leverage of 

 about 3-1. This theoretical value is, however, reduced by the 

 friction of the levers and by the damping effect of the air filling 

 the internal ear. It has been estimated that half the force is thus 

 dissipated. 



Three further points about the chain of ossicles claim our 

 attention. Firstly, by the position of the axis, a - b, the mass of 

 the heads of the hammer- and anvil-bones are above the line, 

 while the lever arms are below the line on which the bones rotate. 

 This keeps these two bones suspended in equilibrium. Secondly, 

 there are tooth-like processes on the surface of the hammer which 

 engage with the body of the anvil, enabling each to move the other 

 in the to-and-fro movements of the drum. In the case of unusually 

 sudden alterations in air-pressure, e.g. a blow on the ear, these 

 processes slip over each other and prevent damage to the internal 

 ear. Thirdly, by the way in which they are hung on opposing 

 ligaments, and controlled by opposing muscles, they form a kind 

 of balance wheel which is very sensitive to the transmission of 

 power in small vibrations. Its efficiency in this respect is derived 

 from the fact that the elastic forces balance one another in the 

 mechanical centre of the system, and so practically the whole 

 power applied to the drum is transmitted to the foot of the stapes. 



B. The pressure in the internal ear is reinforced not only by 

 the system of lever transmission but by the relative sizes of the 

 membranes at either end of the chain of ossicles. The area of 

 the tympanic membrane is about twenty times the area of the 

 fenestra ovalis. This means that, keeping the total power constant, 

 the power per unit area is increased twenty times. This is 

 augmented by the intermediate leverage (correcting for air- 

 damping, friction, etc.), which we have seen has been estimated 





