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On Some Microscopic Tracings of Lissajous' Curves. 



By Robert G. West. 

 (Read February 22nd, 1878/) 



In inviting your attention to the above subject, it is perhaps appro- 

 priate to give you some facts of the history of these curves, to offer 

 some explanation of their nature, and of the various contrivances for 

 producing them, and to endeavour to show something of what has 

 been previously done in microscopic writing and ruling. 



The earliest discovery of these curves of which I have been able 

 to find any record, is that of Mr. Sang, of Edinburgh, made about 

 forty years ago. Mr. Sang embodied his results in a contribution 

 to the Edinburgh Philosophical Transactions, entitled " On the 

 Vibration of an Elastic Spring." About two years afterwards Mr. 

 Perigal followed in the same line with his " Kinematic Curves." 

 In 1844 Professor Blackburn, of Glasgow, invented a form of 

 pendulum capable of swinging in two planes, the curves produced by 

 which were recorded by a fine stream of sand falling from the pendulum- 

 bob, and were similar to those afterwards produced by Lissajous. In 

 the " Annales de Chinicie et de Physique" for 1857, Lissajous con- 

 tributed the results of his investigations, which had chiefly an 

 acoustical bearing, and were conducted by means of mirrors attached 

 to tuning-forks and reflecting a beam of light, so as to produce, by 

 the persistence of the retinal impression, a continuous curve, 

 characteristic in each case of a particular ratio of the fork-vibrations. 

 In 1871 Mr. Hubert Airy was independently led to the discovery 

 of these curves by observing the accidental gyrations of an acacia- 

 shoot. Mr. Airy narrated his experiments in two very interesting 

 papers in Nature for the 17th August and 7th September, 1871, 

 and has given a lucid analysis of the figure produced by nearly 

 coincident vibrations. I have made some experiments with the 

 apparatus devised by Mr. Airy and Mr. Routh ; but that described 

 by Professor Swan, of the University of St. Andrew's, in a letter 

 appearing in Nature for the 7th September, 1871, seems better, as 



