Page 257. " these chalky hogs'-backs "
Unpainted pig sculptures being prepared for
GNU Free Documentation LicenseUnpainted pig sculptures being prepared for "Pigs on Parade" in downtown Seattle - Credit: Joe Mabel

Hogs'-backs are hills.

The Hog's-back is a raised part of the North Downs in Surrey. Hardy is using the term in a more general sense here to describe any hills, ridges or escarpments that mimic the narrow, rounded shape of a pig's back. 

Page 268. " 'the old Adam of my former years' "
Adam comes to Eden (a mosaic in Montreal Cathedral)
Public DomainAdam comes to Eden (a mosaic in Montreal Cathedral)

Alec is referring to his former self, as he was before he converted to Christianity.

The term "old Adam" was a common short-hand for the evil that is supposed to be inherent in human nature and can only be washed clean through baptism.

Page 268. " Come out from among them and be ye separate, saith the Lord "

A quotation from St Paul's second letter to the Corinthians (6:17) in the New Testament. Theologians differ as to how to interpret these words. While some believe they advocate closed religious communities, others read them as injunctions to keep separate mentally and emotionally from the ways of the secular world. 

Page 272. " petite mort "

A celtic stone. The Cross-in-Hand would have looked something like this
Creative Commons Attribution Share AlikeA celtic stone. The Cross-in-Hand would have looked something like this - Credit: Hugh Mortimer
Although this French phrase, which translates literally as "little death", is often used to refer to orgasms, it has a wider meaning. In this context, Hardy uses it to imply that a part of Tess has died on hearing the man's gruesome tale and connecting it with the oath that she was forced to swear on the spot.