After shuffling them a sufficient length of time, the dealer suddenly, and with a slight movement of his hands, pulls or strips the deck as above described; then taking one half the deck in one hand, and the other half in the other hand, and placing the ends together, runs them in, thereby displacing every card in the deck by the process of running them.
Here are a couple of descriptions of Faro Shuffles from newspapers that interdate An Adept and Koschitz/Maskelyne.
From the Chicago Inter Ocean, 7/10/1875, p. 5:
[after a discussion of a stripped/roughed deck, in which half are convexly belly-stripped and lightly sanded on the faces ("rounds") and half are simply made slightly narrower and sanded on the backs ("straights")]
The dealer in shuffling can separate the rounds from the straights by holding the cards near the end with his left hand, and drawing the rounds out with his right. Having the cards separated, twenty-six in each hand, he makes the ends even by gently tapping the end of one-half against the faces of the other half. He then places the two ends together on the table, and by pressing them together and raising his hands he passes each alternate card over the other, from the bottom to the top of the deck, thus bringing the sanded face of one card to the sanded back of the other.
From the Brooklyn Standard Union, 12/08/1888, p 5
The sandpaper is again brought into use. The two narrow edges of the even cards are filed down, wedge like, the movement of the sandpaper being from the back of the card to front. This delicate work being done, the odd cards are treated likewise, only the rubbing is done from the front to the rear. When this process is completed, it is found that the two piles, odd and even, being put end to end for shuffling purposes, the sharp end of the even cards will dovetail in the filed-off place of the odd cards in such a way that, the two piles being pushed together, they will form into one entire pack, running odd and even, card for card, from bottom to top.
[Note that Alex Elmsley reinvented the sanding technique -- see Minch, Collected Works of Alex Elmsley Vol 2 (1994) pp 295-296]