A NEW THEOEY OF HEARING. 325 



The errors involved in so regarding it have been roughly 

 estimated and their effect on the conclusions which follow 

 is nil. The chief of them is involved in the assumption 

 as to the incompressibility of the fluids (perilymph and 

 endolymph). These fluids are almost identical in physical 

 properties with water and if we consider the modifications 

 of the following account which would have to be made in 

 the case of water we shall see that the error is one which 

 does not affect the theory as a whole. 



Water is compressed to the extent of rather less than 

 aMooth part of its volume by an increase of pressure equal 

 to one atmosphere. No such pressure as this is ever 

 brought to bear on the fluids in the ear ; if it were the 

 transmission of the effects, i.e., of the movements, would 

 be accelerated. As I shall give a justification for the 

 assumption that this transmission is infinitely rapid 

 nothing tending to increase that velocity can possibly 

 affect our conclusions except in the direction of increased 

 accuracy. 



The velocity of sound in water is almost one mile per 

 second. The distance between the fenestrse ovalis and 

 rotunda is about |- inch. The time required for trans- 

 mission of a pressure wave ("sound wave") from one 

 fenestra to the other is less than TooVoo^h of a second, 

 i.e., less than T Vth part of the time-interval between two 

 successive waves of the highest audible note. I shall 

 regard this interval as nil, and shall regard the movements 

 of the two fenestra as simultaneous, which is equivalent 

 to regarding the velocity of sound in the fluids as infinite 

 and the fluids themselves as incompressible. It will be 

 seen later on that the error involved in this assumption 

 does not, even in the most minute degree, affect the 

 soundness of the conclusions. 



The assumptions being justified I will take a series of 

 problems in the following order : — 



