The Woman in White by Wilkie Collins. This novel was published in 1860.
While these ideas were passing through my mind I saw the woman in the cloak approach close to the grave, and stand looking at it for a little while. She then glanced all round her, and taking a white linen cloth or handkerchief from under her cloak, turned aside towards the brook. The little stream ran into the churchyard under a tiny archway in the bottom of the wall, and ran out again, after a winding course of a few dozen yards, under a similar opening. She dipped the cloth in the water, and returned to the grave. I saw her kiss the white cross, then kneel down before the inscription, and apply her wet cloth to the cleansing of it.
After considering how I could show myself with the least possible chance of frightening her, I resolved to cross the wall before me, to skirt round it outside, and to enter the churchyard again by the stile near the grave, in order that she might see me as I approached. She was so absorbed over her employment that she did not hear me coming until I had stepped over the stile. Then she looked up, started to her feet with a faint cry, and stood facing me in speechless and motionless terror.
'Don't be frightened,' I said. 'Surely you remember me?'