18S0.] 



[Frazer. 



Three Methods and Forty-Eight Solutions of the Fifteen Problem. By 

 Persifor Frazer, Jr. 



{Bead before the American Philosophical Society, March 5, 1880.) 



First Method. 



Second Method. 



Third Method. 



TROC. AMER. PHILOS. SOC. XVIII. 105. 3M. PRINTED MARCH 29, 1880. 



