τῇ as an adverb "thus" in place of ὡς?

Greek Homeric Greek and Early Greek Poetry
1

Iliad 5.752: τῇ ῥα δι’ αὐτάων κεντρηνεκέας ἔχον ἵππους·

τῇ here looked to me like a feminine dative, but I couldn’t see how that could make sense in context. (There is nothing singular and feminine to refer to, except maybe Hera, but that doesn’t make a lot of sense.) Buckley translates it as “in this way,” and Project Perseus tags it as an adverb, which I guess means it’s functioning the same way as ὡς. Can anyone explain what’s going on here?

2

I think “there” probably. Cunliffe ὁ , ἡ, τό 4 e α:

In dat. sing. fem. τῇ, in or at the place or spot in which, in or at which place or spot, where : τῇ ἔμελλε διεξίμεναι Il. 6.393. Cf. Il. 11.499, Il. 23.775, etc. : Od. 4.565, Od. 5.442, etc.

3

Oops i mean cunliffe 1c:

In dat. sing. fem. τῇ, in that place or spot, there : τῇ τόν γε μένον Od. 4.847. Cf. Il. 8.327, Il. 11.520, etc. : Od. 12.62, etc.

4

Aha, thanks, theoldlove!