72 



JOURNAL OF THE 



A xMETHOD OF FINDING THE EVOLUTE OF THE 

 FOUR-CUSPED HYPOCYCLOID.* 



R. H. GRAVES. 



The following is a method, based on the Theory of Roulettes, 

 of proving the well-known result, that the evolute of a four- 

 cusped hypocycloid is also a four-cusped hypocycloid : 



Let AC=a move with its extremities always on the rectang- 

 ular axes Ox and Oy. The envelope of AC is the four-cusped 

 hypocycloid. 



*Published also in the " Annals of Mathematics." 



