Form of Monochord. 49 
vibration-form of the thread and the period of corresponding 
number of vibrations can be at once exhibited. 
The problem, how to excite a thread to vibration by an 
external periodic action the period of which can be varied at 
pleasure, can only be solved by employing a motion of rotation 
to excite the vibration. If one end of the thread is to be used 
as the exciting-point, then, in order that the external motion 
shall take place at right angles to the thread, this point must be 
fastened in sucha way that it cannot be displaced in the direc- 
tion of the thread, but is capable of motion at right angles to 
it. This is nearly the case if the thread is attached to a rigid 
lever capable of motion, without much friction, on fixed points 
round an axis at right angles to the thread. If, then, by 
means of a revolving toothed wheel or some similar arrange- 
ment, periodical impulses can be given, this arrangement will 
render possible the solution of the problem proposed. 
As far as the nature of the vibrations of the thread thus 
produced is concerned, it is clear that stationary vibrations 
of the thread can only take place when the period of the 
external motion stands in some simple ratio to the period ofa 
component of the natural vibrations of the thread—if, at least, 
we make the assumption that the lever comes into contact with 
the rotating body only during an indefinitely small time in 
each impulse. 
We see at once that the vibrations of a thread of which one 
end is not fixed but takes part in the vibration cannot take 
place in the same manner as the free vibrations of a thread of 
which both ends are fixed. The mathematical theory, how- 
ever, which [ intend to give in another place, shows that the 
difference between the form of the constrained vibrations with 
which we are concerned and that of the free vibrations of the 
thread is only of small amount. In the constrained vibrations 
the thread swings without true nodes, i. e. points which are 
absolutely at rest; but instead it has apparent nodes which 
are points of minimum amplitude of vibration, and the moving 
end of the thread itself is such a node of minimum amplitude. 
This remark, of course, holds good only upon the assumption 
that the end of the thread attached to the lever makes only 
very small excursions. 
li is easy to take account of the relation which must exist 
between the period of the external excitation and the period 
of the vibrations of the thread. Let us Fig. 1. 
imagine that the oscillations of a pendulum 
are maintained by periodical blows, taking m—> @ wees. e 
place always in the same direction. Let a b 
a and 6 (fig. 1) denote the limiting positions 
Phil. Mag. 8.5. Vol. 19. No. 116. Jan. 1885. iD) 
