AN IMPROVED HARMONOGRAPH. 
CHARLES H. CHANDLER, 
Professor of Mathematics , Ripon College. 
This harmonograph shows the composition of two simple 
harmonic motions in the same plane, agreeing or differing in 
any or all of the following elements: direction, amplitude, 
period, epoch. 
The resultant is described by a pencil (or other recording 
point) borne upon one end of a straight rod, termed the “record¬ 
ing rod, ” which is attached at the other end by a ball and 
socket joint to a bar sliding with a simple harmonic motion in 
a direction transverse to the recording rod; its motion being 
given by the familiar device of a crank playing in a transverse 
slot in the sliding bar. The recording rod at some intermediate 
point passes freely through another ball and socket joint on a 
second sliding bar similar to the first, and similarly actuated to 
a simple harmonic motion. 
Obviously the motion of the first sliding bar, the second 
remaining unmoved, gives the recording point a simple harmonic 
motion, having the same period as the motion of the sliding bar, 
but at all times differing from it in phase by one half its period, 
and of an amplitude having a ratio to the amplitude of the 
motion of the sliding bar equal to the ratio between the lengths 
of the segments of the recording rod formed by the intermediate 
joint. Similarly the motion of the second sliding bar, the first 
remaining unmoved, gives the recording point a simple harmonic 
motion of the same period and phase as the motion of the sliding 
bar, but of larger amplitude, the two amplitudes being propor¬ 
tional to the distances of the recording point and the sliding 
bar from the end of the recording rod remaining unmoved. 
Evidently by simultaneous motions of the two sliding bars 
the resultant of the two simple harmonic motions may be 
recorded upon a tablet placed in a plane parallel to the planes 
