Recoil Curves as shown by the Hot- Wire Microphone. 287 



vection current in direction parallel to the displacements of the vibrating 

 particles, is entirely responsible for the term containing V sinpt and from 

 the equation it is seen that a simple harmonic vibration in the air is 

 recorded by : — 



(i) a displacement of the mean position proportional to the square of the 

 velocity ; 



(ii) a periodic term in tune with the air vibration, of amplitude proportional 

 to the velocity ; 



(hi) a periodic term an octave above this vibration proportional to the 

 square of the velocity. 



Terms (i) and (iii), therefore, are proportional to the kinetic energy in the 

 air, while (ii) is proportional to the square root of that energy. 



This relation has been checked by means of an artificial vibrating system 

 fixed to the platform referred to above, and consisting of a spiral spring 

 supporting a weight which, when displaced, vibrates vertically up and down. 

 The spring becomes, for the time, an artificial heart, imparting its vibrations 

 through the platform to the diaphragm and to the air in the microphone 

 chamber. 



The diaphragm is put under the same tension, etc., by placing weights upon 

 the platform equal to the weight of the case under comparison. 



Fig. 3a gives the galvanometer record which closely agrees with the above 

 equation in which the maximum velocity of the vibrating air is 2 cm. per 

 second, and the convection current about 2 cm. per second (Plate 5). 



One complete vibration corresponds to two peaks, the higher one of which 

 indicates a displacement of the vibrating air in the same direction as the air 

 current. 



At any point, the deflection of the galvanometer is proportional to the 

 function of U as quoted in the above equation, but if the function be inte- 

 grated with respect to time for a complete cycle, i.e., for a time 27r/p the 

 periodic terms vanish and a quantity proportional to TP, i.e., to the kinetic 

 energy of vibration, is obtained. 



If now the amount of kinetic energy contained in the spring is calculated 

 from the mass of the spring, its periodic time and its displacements, we can 

 calibrate the records in terms of such kinetic energy. 



The vibrating spring, however, fails to resemble the heart in its action since, 

 as seen from the record, the spring loses very little energy per period, i.e., it 

 is a nearly undamped vibrating system. Had it been heavily damped, the 

 spring would rapidly come to rest and the record would show markedly 

 decreasing amplitudes. 



With the heart quite a different condition obtains. The projected blood 



