152 BRIDGMAN. 



where <p is an arbitrary unknown function of its two arguments. For 

 high frequencies g/oi is a small quantity. It is obvious in the first 

 place that at high frequencies the temperature amplitude cannot 

 approach a constant value, but must vanish. Hence developing the 

 function ip for small values of the argument g/w, putting the constant 

 term zero, and retaining only the first order terms, we have for high 

 frequencies the approximate relation 



If now we make the further assumption that the conductivity cannot 

 enter at high frequencies, the effect being determined by the specific 

 heat alone, we get the approximate relation 



Ti = Const — —' 



The striking thing about this relation is that the velocity of flow has 

 disappeared, the amplitude of temperature fluctuation being propor- 

 tional to the heat input, and inversely as the frequency. This again 

 is a result that can be tested by experiment, and its verification would 

 go far toward making probable the assumptions underlying the dis- 

 cussion. 



These values which we have found by dimensional analysis for the 

 steady and alternating changes of temperature may now be substi- 

 tuted back in the relation ti/tq = iiAR'/liAR which we obtained from 

 the equations for the bridge. The rate of heat input entering the 

 dimensional formulas for to and ti may be written down at once in 

 terms of the currents, namely 



Q = Pi R' 

 Qi=2IAR', 



where R' is the resistance per unit length. Substituting these values 

 in the dimensional formulas for tq and ri, and these again in the value 

 of ti/to above, gives 



/cgP_ g\ 

 AR' ^V k ' J 



AR 



= 9 



i 



