I had a look at
this edition of Martineau's autobiography: it is also dated 1877, but evidently for the US market, and published by James R Osgood and Company, of Boston.
The references to Miss Brontė are on page 324 of the book (335 of the pdf).
Here it is a curious fact that the "i" at the end of her name has no dot at all - and certainly not a double dot as AlexBell has found in the Smith, Elder edition.
And now, putting on my pedant's hat, if there are two dots on the "i" in that edition (I couldn't find it), that would be a
diaeresis rather than an
umlaut (
see here), as in the normal spelling of Brontė.
It would hardly be necessary on an "i": it's there on the "e" to show that her name has two syllables.