DRS. GUY BARLOW AND H. B. KEENE ON THE ANALYSIS OF SOUND. 
159 
Let the current to be analysed be a function of the time expressed by 
y=f( 0 
and represented by (a) in fig. 14. We may regard the effects of interruption as merely 
Fig. 14. Interruptions of current. 
the result of multiplying the instantaneous value of the current y by a factor which 
has periodically the values 1 and 0. For equally spaced interruptions of frequency n* 
and giving equal time intervals for open and closed circuit, this factor is represented 
graphically by the periodic form (b) (fig. 14), and has for its expression the Fourier 
series : 
2 
tt+ - (sin nt + 1} sin 3 nt + 1- sin but + &c.). 
The resulting intermittent current, represented by (c) (fig. 14), is therefore given by 
y' = ■<■§•+— (sin nt + \ sin 3 nt + \ sin 5 nt+ &c.) \f(t) 
This expression must now be resolved into S.H. components. These may then be 
regarded as forces of S.H. type acting on the galvanometer system—or on the telephone 
diaphragm—and giving rise to a forced motion which is readily calculated. If the 
galvanometer possesses very little damping, only those components which have a fre¬ 
quency near that of the galvanometer will produce any appreciable motion. But we 
shall suppose, in accordance with experimental requirements, that the galvanometer 
is heavily damped, and for convenience we shall here take it as being exactly “ dead¬ 
beat.” Lhider these conditions there will be no resonance, and a component is only 
* The quantities n, n v , no, p, &c., really angular velocities, are, for the sake of brevity, here referred to 
as frequencies, the 2 it being everywhere omitted. They are strictly the radian frequency of phase change. 
