That J.M White was one of 4 boats to bear the name, but in Steamboat circles the Natchez (at least 2 old ones and 1 new one built in 1974 and still floatin'} was probably a more famous boat in the 19th century. I believe she was the winner of a famous steamboat race, and Courrier & Ives print of same.

If the quote is from a newspaper article from 1876 that puts the 1878 launch of a J.M. White out of the question.

I will defer to someone with superior geekitude of mid 19th century steamboat racing.

I've got a few books on such, but that's all you get at 1:30 AM!