HARMONIC CURVES OF THREE FREQUENCIES. 
CHARLES S. SLIGHTER, 
Professor of Applied Mathematics, University of Wisconsin. 
Much interest attaches to the plane curves which result from 
compounding two harmonic motions of different frequencies at 
right angles to each other. This interest is doubtless due as 
much to the intrinsic beauty of the curves themselves as to their 
actual importance in physics and mechanics. Lissajous’ famous 
memoir 1 on “L’Etude Optique des Mouvements Vibratoires” 
has probably contributed more to make his name known than 
all of the rest of his scientific work taken together. As a matter 
of fact, however, the path described by a particle of an elastic 
body is frequently not a plane curve resulting from the compo¬ 
sition of two harmonic motions, but is a curve of double curva¬ 
ture in space, being the resultant of three harmonic motions in 
three different directions and of different frequencies. The 
present paper has for its object the description of a simple form 
of apparatus designed to give stereoscopic photographs of curves 
of this class. The apparatus enables one to produce stereoscopic 
photographs of the path of a particle resulting from compounding 
three harmonic motions, provided the component motions are in 
phase and at right angles to each other. 
Plate XLIII represents the apparatus used. A Blackburn 
pendulum, B P', nearly three meters long, carries a small elec¬ 
tric pea lamp L, and can be adjusted by the clamp 01 so that 
the bob P' will describe a Lissajous’ curve having for its fre¬ 
quencies two of the three frequencies desired. A stereoscopic 
camera C is clamped in the Y of the pendulum shown in the 
left of the diagram, so that the optical centers of the lenses are 
1 Annales de Chimie et de Physique, 1857, 3e serie, tome LI. 
29 
