Short answers, pulled from the story.
Daniel Day established the Daniel Day Mill in 1809 at Elmdale, near Wheelockville in Uxbridge, Massachusetts. It was the first textile mill in Uxbridge, the first woolen mill in the Blackstone River Valley, and the third oldest woolen mill in the United States.
Daniel Day was born in 1767 in Mendon, Massachusetts. His parents were Joseph Day and Deborah Taft. He was a fourth-generation descendant of Robert Taft Sr., who settled in the western section of Mendon in 1679.
Daniel Day died on the 26th of October, 1848, in Uxbridge, Worcester County, Massachusetts, at the age of 81. His death was attributed to Consumption, or Tuberculosis, and is recorded on page 369 of Uxbridge Vital Records through 1850.
Daniel Day was an ancestor of a branch of the Wheelock family that established an early factory. That enterprise continued in business into the 21st century as Berroco, Inc., now headquartered in North Smithfield, Rhode Island.
The Rhode Island System was a network of mills, dams, and villages developed by John and Samuel Slater along the Blackstone River Valley. Daniel Day's woolen mill was only the second mill established in the valley, making it a foundational part of this system, which is considered a major contributor to the Industrial Revolution in the United States.
Luke Taft was a descendant of the American Taft family with roots in Mendon and Uxbridge. He married one of Daniel Day's daughters and went on to found his own mill in Uxbridge, which became known as the Waucantuck Mill.