where A T* is the final temperature change produced by initiating disturbance. The time con- 

 stant has been derived by Dryden and Keuthe and may be written in the form^^ 



M = m 



Values of m which depend only on constants of the wire materials are listed in Table 2. 



The response of a bare constant-current hot wire to a step-like change in current input 

 is also given by a simple exponential function. To the approximation used here, the time con- 

 stant for a change in current input is the same as the time constant for a change in convective 

 cooling.^ 



The frequency response of a system is defined as the frequency for which the response 

 is attenuated 70.7 per cent. Furthermore, if the response of a system to a step function is 

 given by a simple exponential function with time constant M, the frequency response is 

 1/2 7iM. If a hot wire for use in water has a diameter less than one mil:, it will have a frequency 

 response of several hundred cycles. If a higher frequency response is desired, a suitable com- 

 pensation circuit may be used. As the frequency response of a bare wire to a change in cur- 

 rent is the same as that for a change in convective cooling the elements of the compensation 

 circuit may be adjusted by applying a time-varying current input of the desired frequency to 

 the wire. 



If the wire has a coating or acquires a film the response of a constant-current wire is 

 no longer a simple exponential function but is given by an infinite sum of exponential terms. ^ 

 If the coating is not too thick the sum converges rapidly and an equivalent time constant may 

 be found as the time in which the exponential portion decays to e ~ ^ of its initial value. In 

 this case the time constant for a step-like change in convective cooling is greater than the 

 time constant for a change in current input. Therefore it would not be possible to fully cor- 

 rect for the time lag by adjusting the elements of the compensation circuit to obtain a good 

 frequency response to a time-varying current input. 



Even a constantrtemperature wire has a time lag in responding to a change in convec- 

 tive cooling if the wire is coated or acquires a film.^ If the film thickness is less than half 

 the wire diameter the time constant under probable operating conditions is no greater than the 

 time constant of a bare constant-current wire of the same diameter. Therefore, a thinly-coated 

 constant-temperature hot wire should have a reasonably good frequency response when it is 

 used in water. The simple method of setting the elements in a compensation circuit for a con- 

 stant-current hot wire can not be used here, as a constant-temperature wire responds with no 

 time lag to a change in current input. 



13 



