Factor of a Shunted Telephone to the Antenna Current. 187 



can be determined for which, with a certain shunt S, the 

 sound of the signals, made by tapping the key K, can just be 

 differentiated. The value of the mutual inductance M was 

 then found by the use of a curve calculated from the formula 

 of Maxwell-Rosa *. 



M = 27r%n 2 ^6^A/j 3 ' 2 {l + 3/8P + 15/64^ }, 



where %, n 2 are the number of turns of L^ and L 2 , 



a, A are the mean radii of the coils L x and L 2 , 

 and 



{^/( a + A) 2 + d 2 -fd} 2 ' 



where d is the distance between the flat coils. 



In the experiments coupling coefficients were used only 

 between the limits 



& = -003 and -0002. 



The wave-length used was about 1125 metres. 

 The results of these measurements are recorded in the 

 following table : — 



, R+S 





, R4-S 





log-g-. 



log M. 



log— • 



log M. 



•0816 



1-419 



•7104 



1-875 



•0962 



1-446 



•8573 



1-902 



•1173 



1-471 



•9671 



1-980 



•1502 



1-520 



1-1271 



2 060 



•2095 



1-583 



1-2175 



2*102 



•2617 



1-628 



1-3359 



2164 



•3502 



1-680 



1-4116 



2-197 



•4065 



1-704 



1-5051 



2-251 



•4427 



1-738 



1-6266 



2313 



•4869 



1-762 



1-7993 



2-394 



•5416 



1-804 



1-9227 



2-473 



•6128 



1-813 



20969 



2-515 



A curve (see fig. 2) was then plotted for which the 

 ordinates indicate the logarithms of the mutual inductance 

 for a constant current [which is proportional to the antenna 

 current for a constant coupling], and where the abscissae 

 give the logarithm of the audibility factor (R + S)/S. 



For values of log (R + S)/S from '6 to 2-2 (audibility 



* See Bulletin of the Bureau of Standards, toI. viii." 

 02 



