716 Messrs. H. E. Ives and E. F. Kingsbury on tlw 



We assume the Fourier equation * 



Y = potential (temperature in the case 

 3*y _ 1_ BY X = distance, of heat) , 



dX 2 ~KBT £ = time, 



K = diffusivit y . 

 to represent the transmission of the stimulus through some 

 medium of " diff usivity " K . We then take as the stimulus, 

 for simplicity, a simple cosine function having no negative 

 values, 



I = I cos cot + 1 , (1) 



where co is the frequency, I is the amplitude. 



This stimulus is transmitted by the medium considered, in 

 the form 



/ W A 



I=S[V ™oo8(««-XVsy + I.], • ( 2 ) 



which indicates that the fluctuations are smoothed out and 



that a difference of phase — X\/ ott- exists between stimulus 



and record. The constant S is one of proportionality which 

 may be dropped. 



Now the range of the fluctuation in (2) is 



2I ,- XV ^ - ^ (3) 



and the percentage range in terms of the average value of 

 (2) is 



-XV va /~Z 



Io 



Introducing assumption (2) 



then log 8 = log 2 — X^/ ^ log e 



A log2-log_8 



(5) 



* For derivation and solutions of this equation and those following 

 e Ingersoll and Zobel, ' Mathematical Theory of Heat Conduction * 



see Ingersoll and Zobel, * Mathematical Theory 

 or other standard text. 



