294 PROCEEDINGS OF THE AMERICAN ACADEMY 



complex and diversified motions, whether produced bj the vibration 

 of elastic bodies or by machinery. Lissajous and Desains, with an 

 apparatus constructed by Froment, scratched the curves upon smoked 

 glass, the style being moved by one vibrating body and the glass by the 

 other. Professor Pickering* moved a pen and paper in rectangular 

 directions by machinery, and described the curves on a much larger 

 scale. Donkin f contrived a machine for the graphical representation 

 of a number of parallel vibrations ; but the most complete apparatus 

 of the kind is Tisley's harmonograph, $ which can be suited to 

 parallel, perpendicular, or oblique vibrations ; and in a great variety 

 of ratios. The motions of the pen and paper are produced by two 

 independent pendulums, delicately mounted and heavily loaded, so as 

 to maintain their vibration for a long time. The ratios can be altered 

 by a change of weight, combined with a change in the length of one 

 of the pendulums. The latter adjustment can be neatly applied, for 

 making or disturbing the exact ratio of the required interval, without 

 stopping the motion of the pendulum. 



As far back as 1800, Dr. Young § experimented upon the variegated 

 path described by a single point of a silvered vibrating cord, illumi- 

 nated by strong sunlight. In 1827, || Wheatstone invented the kalei- 

 dophone : which was simply a vibrating wire, with a bead at the free 

 end, and short enough to give persistent vision for the orbit. But 

 neither Young nor Wheatstone have given a mathematical analysis of 

 the motions; the exquisite figures they obtained were due, mostly, 

 to the superposition of the higher harmonics, and few of them are 

 identical with the Lissajous curves. In 1832, Edward Sang U of Edin- 

 burgh developed mathematically the resultant of two rectangular 

 vibrations, having different periods and phases, and illustrated his 

 subject b}' experiments with round and flat wires, which produced the 

 peculiar Lissajous curves. Drach, who himself, in 184G,** published 

 his theoretical studies on the combination of two circular motions, with 

 their resulting epicyclical curves, states that Perigal devised ma- 

 chinery which traced curves identical with those of Airy, and, there- 

 fore, with those of Lissajous. This machine was exhibited, in 1846, 



* Journal of Franklin Institute, January, 1869. 

 t Proo. Koy. Soc. London, vol. xxii. (1874), p. 197. 

 } Engineering, vol. xvii. (1874) p. 101. 

 § Trans. Roy. Soc, London (1800). 

 II Collected Papers. 



1 Edinb. Phil. Jour., vol. xii. (1832) p. 817. 

 ** Phil. Mag., London, vols, xxxiv. pp. 418, 440 and xxxv. (1849-50). 



