From the library's website:
The Helen Kate Furness Free Library was founded in October 1902 by a group of Nether Providence citizens as the Horace Howard Furness Free Library, named in honor of one of the founders, a renowned Shakespearean scholar whose estate, Lindenshade, was located in what is now Furness Park.
In the early years, the library was housed in a room of the newly built Wallingford elementary school.
Dr. Furness' died in 1912, bequeathing $5,000 to the library on the condition that the Library's name be changed to The Helen Kate Furness Free Library to honor Dr. Furness' wife who was also a Shakespearean scholar.
In 1913, Dr. William Henry Furness III, a son of Dr. and Mrs. Furness, conveyed to the library an acre of land on which a native stone building was constructed in 1916. 
From the Delaware County Daily Times newspaper of Monday, November 6, 1916:
Wallingford's new free public library, to be known as the Helen Kate Furness Memorial Library, was formally opened Saturday, with appropriate exercises. A large number of residents of the township were present and took part in the exercises, at which, the speakers were Dr. Joseph H. Swain, president of Swarthmore College, and Dr. John Wesley Carr, principal of Friends' Central School, of Philadelphia. Dr. William Howard Furness, 3rd, president of the association, presided at the exercises and made the opening address. The library building, a handsome imall stone structure, was made possible by a. gift of $5000 from Dr. Horace Howard Furness, the eminent Shakespearean scholar and author. It was the intention at first to have it named for him.