PHYSICAL CHARACTERISTICS OF AUDITION 65 



as "lunipc'd," that is in which, for the pur[K)sc of {iractical sohition, 

 a finite number of degrees of freedom may be assumed, the method 

 is to find the most useful way of "lumping" these constants. The 

 motions are then represented by a series of equations, one for each 

 degree of freedom, between the forces acting and the impedances 

 and velocities. The determinant of the coefficients of these equations 

 is the Lagrange determinant of the system. The only caution to be 

 observed in lumping the constants is that the reciprocal relation, 

 which is a property of any linear system holds also for the physical 

 system which the assumed Lagrange determinant is supposed to 

 represent. 



The method may be illustrated by the following application to the 

 sensitivity measurements described above. 



The dynamical system used in calibration with the condenser 

 transmitter consists of three parts: 



(a) The very thin pulsating air film over the thermal receiver 

 filaments. The expansion of air around the wires is represented by 

 the "diffusion" equation, the solution of which in such a case of 

 cylindrical symmetry is given as a Bessel's function of the distance 

 from the wire.^ This wave is so quickly damped in travelling away 

 from the wire as to be negligible beyond the first zero point of the 

 Bessel's function. The vibrating system of this receiver may then 

 be considered as a cushion of air next to the wire of a thickness a little 

 less than the first half wave length of the heat w'ave. The thickness 

 of this cushion is an inverse function of the frequency. 



(b) The air chamber between the thermal receiver and con- 

 denser transmitter diaphragm having a volume of 1 cm.' and en- 

 closed by practically unyielding w^alls w^ith no openings. 



(c) The condenser transmitter diaphragm, being stretched very 

 tightly and air damped. It may also be regarded as unyielding, or as 

 having an impedance very high compared to that of the connecting 

 air chamber. 



If for simplicity the mass reaction and internal losses in the air 

 chamber may be neglected, it may be seen that the moving system 

 of the receiver may be regarded as a weightless and frictionless 

 "diaphragm" surrounding the wires at a distance equal to the effective 

 thickness of the active air film and may be shown to have an intrinsic 

 stiffness reactance of: 



Z.1 — -r- = 



JW JWVi 



'See Wente, Physical Review, April, 1922. 



