OP ARTS AND SCIENCES. 293 



curves would be presented in succession. From the rapidity of this 

 succession, the rate at which the phase changed would he known, and 

 hence the degree of imperfection in the assumed interval. 



The admiration of physicists was elicited by Lissajous's method of 

 magnifying tlie mere trembling of a rigid tuning-fork into a visible 

 magnitude ; and especially by his optical method of tuning, which, in 

 the hands of even a deaf person, would give better results than were 

 possible to the nicest musical ear. Of these groups of beautiful 

 curves, a few, as the circle, ellipse, parabola, and lemniscate, were not 

 unfamiliar to mathematical and physical science. But most of them 

 were supposed to be novel, and have been introduced into later works 

 on Mechanics and Acoustics under the name of the " Lissajous curves." 

 Many uuHlifications have been introduced into the original experi- 

 ments of Lissajous, either by himself or others. Reeds, driven by a 

 bellows, have been substituted for tuning-forks. A steel rod, with 

 an approjiriate cross-section and mounted with a mirror, admits of the 

 two elementary vibrations in rectangular planes. Two vibrating disks, 

 with rectangular slits, which allow the light to pass only at their in- 

 tersection, answer the same purpose. Sometimes one vibration is given 

 to a small aperture through which the light passes, and the other to 

 a lens which forms its image on a screen or in the eye. Wheatstone 

 produced, in a single reflector, the two rectangular movements by 

 mechanical means. Konig, and more recently Ritchie, have used 

 mechanism with two mirrors. The tonophant of Ladd consists of a 

 compound rod, flattened in two rectangular planes. Barrett succeeded 

 with a round and bent steel wire. 



It appears that in 1844, Professor Blackburn * of Glasgow experi- 

 mented with a pendulum, in which the bob was suspended by a Y- 

 shaped cord ; the length of the pendulum being virtually the total 

 length, or only that of the lower branch, in the two principal planes of 

 vibration. In 1871, Mr. Hubert Airyf noticed the curious curves 

 described by the end of a twig of acacia and of hazel. In pursuing the 

 subject, he finally adopted Blackburn's compound jjendulum, and 

 reproduced many of the Lissajous curves ; but he makes no allusion 

 either to Lissajous or to Blackburn. Airy calls the orbits he obtained 

 autographic curves, as they were neatly drawn by a pencil or pen, 

 attached to the pendulum. Before and since that time, various ma- 

 chines were contrived for obtaining a permanent record of these 



* Tait's Dynamics of a Particle, 3d ed. p. 221. 

 t Nature, vol. iv. pp. 310 and 370. 



