Henry Melvill said it

For the record, Google Books has the volume of Henry Melvill's sermons with this globally quoted and misquoted passage:

"Ye live not for yourselves; ye cannot live for yourselves; a thousand fibres connect you with your fellow-men, and along those fibres, as along sympathetic threads, run your actions as causes, and return to you as effects." -- Golden Lectures, 1855 sermon on "Partaking in Other Men's Sins" by the Rev. Henry Melvill.

The Rev. Henry Melvill on "Partaking in Other Men's Sins"
1855 sermon in The Golden Lectures (London, 1856) page 454

Often ascribed, wrongly, to Herman Melville, as in Hillary Clinton's book, It Takes a Village:

We cannot live for ourselves alone. Our lives are connected by a thousand invisible threads, and along these sympathetic fibers, our actions run as causes, and return to us as results. 

HERMAN MELVILLE

Besides mistaking the author, Hillary Clinton's influential published version alters the real author's original terms, making them "invisible threads" and "sympathetic fibers." The roots of this interesting switch, and so perhaps the honor of the first (mis)attribution to Herman Melville, may be traceable to worthy volunteer organizations and community activists of the 1970's and early 1980's.

In any case: what a perfect time, now, to restore due credit to the eloquent Anglican preacher, Henry Melvill. I mean, think of the implications for global intellectual property rights!

Related posts on Melvilliana:

•  the finest thing Herman Melville never said
  https://melvilliana.blogspot.com/2011/09/finest-thing-herman-melville-never-said.html
  

• Henry Melvill's thousand fibres and sympathetic threads, proved
  https://melvilliana.blogspot.com/2013/02/henry-melvills-thousand-fibres-and.html
  

• Pseudo-Melville and Fake Fanon
  https://melvilliana.blogspot.com/2021/12/pseudo-melville-and-fake-fanon-prophets.html