﻿484 Mi\ M. H. Belz on the Heterodyne Beat Method 



variations in the inductance o£ Set 1, this arrangement 

 increases the sensitiveness of the method. For let "N" be the 

 frequency, determined at the centre of the region of silence, 

 of the fundamental oscillation in Set 2, n the frequency of 

 the fundamental oscillation in Set 1, then since the rirst 

 overtone of Set 1 is employed to produce the note, ~N = 2n« 

 Let the frequency of the audible note from the third circuit 

 be m. Then when the heterodyne note is adjusted, by 

 slightly varying the capacity of Set 2, so that q beats per 

 second are counted, the frequency of Set 2 is (N±??2±g) 

 — (2n + m±q). If now the frequency of the fundamental 

 oscillation of Set 1 is altered by dn per second, the frequency 

 of the first overtone is altered by an amount 2dn per 

 second, so that the frequency of the heterodyne note is 

 now (2n±m + ^)~ (2n±2dn) — (m + q±2dn), whence if a 

 change of p beats per second is observed when the induc- 

 tance change is accomplished, p = 2dn. The sensitiveness 

 is thus doubled, and could similarly be increased by em- 

 ploying higher overtones of Set 1. Against this, however, 

 is the fact that the notes so obtained are very feeble, and 

 counting becomes increasingly difficult. 



From equation (i.) we see that the sensitiveness depends 

 on n. It is now possible to maintain oscillations of frequencies 

 up to 10 7 per second, but in cases where the change in in- 

 ductance is caused by inserting a specimen within the coil, 

 there is an upper limit to n determined by the form and 

 function of the coil L. It is necessary to divide this coil 

 into two parts between which there is no mutual inductance, 

 one part L t being coupled to the grid circuit in order to 

 maintain the oscillations, the other part L 2 serving as the 

 coil in which the inductance changes occur. This latter 

 part must be a fairly long coil in order that there may be an 

 appreciable region within it through which the magnetic 

 field is constant, in which region the specimen is placed. 

 On account of the dimensions of this coil, the first part has 

 to possess a fairly large inductance in order to get sufficient 

 mutual inductance with the grid coil : further, a certain 

 amount of coupling is required with Set 2 to produce the 

 heterodyne note. 



Experimental. 



In the present experimental arrangements the details of 

 the coils are as follows :— 



Coil Lj. 



The coil was 10 cm. long, and consisted of 100 turns of 

 22 s.w.g., double cotton covered. It was 



