DRS. GUY BARLOW AND H. B. KEENE ON THE ANALYSIS OF SOUND. 
133 
a rapid oscillation of small amplitude followed by slower oscillations of greater amplitude 
until the maximum is reached. Afterwards the oscillations die down in the reverse 
order. This characteristic motion exhibited by the galvanometer will be referred to 
by the term “ response.” In this way the amplitude of each component may be deter¬ 
mined. At the same time the corresponding frequency is obtained by observing, at 
the moment of maximum, the frequency at which the interrupter is driven. For a 
component of given amplitude the range of frequency over which the response is greater 
than half its maximum value, and which may be called the “ width of response,” is 
the same at all frequencies. For example, if a response at 10/sec. falls to half value 
for frequencies of interruption of 9 and 11/sec., then one at 1000/sec. will fall to half 
value at 999 and 1001/sec. It will therefore be seen that it is necessary to have perfect 
control over the speed of interruption, especially in the higher frequency region, and 
the same time must be spent in sweeping over a range such as 1000-1100/sec. as over 
10-110/sec. In measuring a response the rate at which the speed of interruption may 
be changed is conditioned by the period of the galvanometer. It is necessary that the 
speed should not change sensibly during an interval of time of the order of the galvano¬ 
meter period. The galvanometer may be of any type, but its vibrations should be 
well damped so as to be nearly dead-beat. A suitable period is 3 seconds. Under 
these conditions the width of response is 0-7/sec. 
It is a peculiarity of this method of analysis that a single simple harmonic component 
of frequency, n, gives rise to responses not only when the frequency of interruption is 
n, but also when it is \n, \n, \n, &c., and these responses have amplitudes j, y of the 
fundamental response. These responses will be called “ Subharmonics.” Their origin 
is made clear in fig. 1, which also shows why the even-order subharmonics \n , \n , \n, 
&c., are non-existent. When the alternating current represented by (a) is interrupted 
at its frequency n, all the negative elements are suppressed as shown in ( b ), giving a 
unidirectional current in the galvanometer. When interrupted at \n , as in (c), an 
equal number of positive and negative elements are passed through giving no resultant 
current in the galvanometer. But when interrupted at \n as represented in (d), there 
is a resultant current due to the odd positive elements. This is the third order sub¬ 
harmonic, and it will be seen by comparing ( b ) and ( d ) that it has one-third the magnitude 
of the fundamental. 
The presence of these subharmonics is not so objectionable in practice as one might 
expect, in fact their frequencies and relative magnitudes have on certain occasions 
assisted in the identification of the fundamental with which they are associated. There 
is a close analogy with grating spectra, inasmuch as each subharmonic corresponds to 
a spectrum of a different order. The even orders are absent just as in a grating where 
the opaque and transparent parts of the grating-element are equal in width. If the 
intervals of make and break are unequal, then the even-order subharmonics are 
introduced. 
A type of interrupter has been constructed in which by repeating the sequence of 
u 2 
