DRS. GUY BARLOW AND H. B. KEENE ON THE ANALYSIS OF SOUND. 
165 
If we take for the limit of resolution a ratio 5/6, i.e. a drop of 16 per cent, at the 
centre, this corresponds to the condition q = 2 n 0 . Hence the least difference of fre¬ 
quency resolvable is twice the frequency of the galvanometer. For the experiments 
this limit is f/sec., but practically a rather higher degree of resolution was obtained. 
Undoubtedly this is due to the fact that the above ratio is that of the maximum ampli¬ 
tudes obtained by taking the two vibrations always in the same phase. If they are 
taken in opposite phases the two peaks are completely separated, as indicated by the 
dotted curve in fig. 16. The motion of the galvanometer is in general compounded of 
Fig. 16. Resolving power. 
two S.H. motions of different amplitude and different frequency, but the maximum 
excursion is the easiest observed. Midway between, the two components become equal 
in amplitude and frequency, giving rise to pronounced beating. The beats have a 
frequency which is variable between the two peaks, but on either side it has the constant 
value q. For extremely close components (q/n 0 very small) practically the whole 
response is characterised by beating with frequency q, so that from this point of view 
the resolving power is unlimited. With components very unequal in magnitude the 
presence of the companion is generally detected by beating on one side only of the 
response. This will be understood by examination of fig. 15, where the response curve 
due to a companion of amplitude f of the primary is represented by the broken line. 
The region of most distinct beating is where the two amplitudes approach equality. 
Time Required for Analysis .—We shall suppose that the interrupter frequency n is 
• • • (1/Tb 
increasing at a uniform rate, — — c, in going through a response due to an isolated 
OjL 
component of frequency n x . It is required that the value of the maximum deflection 
shall not possibly be less than a certain fraction, say 90 per cent., of the full response 
obtained by an infinitely slow rate. Measuring the time t from the instant of synchronism, 
we may put n = n x -f- ct. 
If at the instant t — 0 the phase difference between current and interrupter happens 
to be 0, or n, the conditions will be as favourable as possible. It is only necessary for 
this phase condition to persist practically unchanged for a time interval sufficient for 
the galvanometer to deflect. For a galvanometer in the dead-beat condition this interval 
