298 PROCEEDINGS OF THE AMERICAN ACADEMY 



I have now traced the mathematical analysis and the experimental 

 illustration of the Lissajous curves from France to Great Britain, 

 and thence, across the ocean, to their home in Salem, Massachusetts. 

 The so-called Lissajous curves are the Bowditch curves, except so 

 far as the earth itself had been experimenting upon one set of them 

 for thousands of years. They will continue, probably, to be called 

 the Lissajous curves. But their history should be known, and will 

 be known ; though it is not necessary for the reputation of the self- 

 taught mathematician. Dr. Nathaniel Bowditch. The author of the 

 " Practical Navigator," and the translator of Laplace's " Mecanique 

 Celeste," with its rich commentary, has secured a place in the world 

 of commerce and in the world of science to which nothing need be or 

 can be added. 



Explanation of the Plate. 



Figure 1. Professor Dean's diagram, illustrating his pendulum. 



Figures 2, 3, 4, and 5. Dr. Bowditch's diagrams to show the 

 orbits in an imperfect unison. 



Figure 6. Dr. Bowditch's diagram to illustrate the progressive 

 changes in the orbit. 



Figures 7, 8, 9, 10 and 11. Dr. Bowditch's diagram to show the 

 orbits in an imperfect octave. 



Figures 12 and 13. Dr. Bowditch's diagram for special differences 

 of jihase in the ratio, 1 : 3. 



Figures 14 and 15. The same when the ratio was 1 : 4. 



Figure 16. General diagram of Dr. Bowditch's pendulum. 



All these figures are exact copies of those published in the Plates 

 of the Academy, vol. iii. 1st series, 1815. 



