TRANSACTIONS 



OF THE 



AMERICAN PHILOSOPHICAL SOCIETY, 8V. 



VOL. VI, PART II. 



No. XXXII. 



Appendix to a Memoir on the Mississippi, No. XXX. of the 1st 

 part of this Volume. — By William Dunbar, of the Natchez, 

 communicated by the Author, through the President of the 

 Society. 



Read Odtober 5th, 1804. 



ALTHOUGH the memoir was not intended to convey 

 opinions upon the theory of rivers, yet as it contains observa- 

 tions and remarks, which are at variance with the doctrines 

 delivered to us by several of the most eminent mathematicians 

 of Europe, it may seem that a short apology is necessary. 



This subject has been treated by mathematicians of the first 

 order in Italy, France and Germany, but more especially the 

 former; and generally such partial views only have been ta- 

 ken of the subject, as have furnished them with the amuse- 

 ment of an elegant application of calculus. The theorems of 

 Guglielmini have been held in the highest estimation, and, per- 

 haps unfortunately for the progress of science, prevail too ge- 

 nerally at this day. The theory of spouting fluids issuing from 



A 



