PHYSIOLOGICAL ACOUSTICS 295 



funnel-shaped tympanic membrane and its connections we 

 have precisely such an unsymmetrical system, the restoring 

 force being somewhat greater for inward than for outward 

 displacements of the same extent*. If we keep only the first 

 two terms in (1), the equation of motion is of the type 



x+/juc = -auc*+X, .................. (2) 



where X represents the disturbing force f. The joint action 

 of two simple-harmonic forces will be represented by 



X =f 1 cosn l t+f z cosnj ................ (3) 



Neglecting, for a first approximation, the square of #, we have 



x = l .. cos nj -\ -- - cos n 2 t, ......... (4) 



/n-n,* fjL-nJ 



the terms which represent the free vibrations being omitted, 

 since these are rapidly destroyed by dissipation. If we sub- 

 stitute this value of x on the right hand of (2), and write for 

 shortness 



AAfc -%*)** / 2 /(/*-^ 2 )=# 2 , ......... (5) 



we obtain the differential equation 



x + x = X - a + 2 2 - af cos 2nJ - a. 2 cos 



- <*9i92 cos (HJ - O t - ag,g z cos fa + w 2 ) t, . . .(6) 

 correct to the second order of /i,/ 2 - The terms written in full 

 on the right hand may be regarded as a correction to the 

 disturbing force X. The solution of (6) gives, in addition to 

 (4), the terms 



The first term merely indicates a shift of the mean position 



* It may be noted that the same element of asymmetry is present in the 

 investigation of 63. When we proceed to the second order of small quantities, 

 the changes of pressure due to condensations s are no longer equal in 

 amount. 



f It is unnecessary to take account of the variability of inertia, since this 

 can be got rid of by a proper choice of the coordinate x. In any case 

 it will not alter the general character of the results obtained in the second 

 approximation. 



