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The separation of Angel and Tess begins on their wedding night before they even consummate their marriage as man and wife. This is one of the greatest tragic moments of the story both because they separate and because of all that Tess tried to do to protect Angel and spare him the suffering he ultimately forced upon himself.
Tess tells Angel over and over and over ... and over ... that she must not marry him and that he must not persist in asking her to marry him. She tries many times to turn his attention to the other three attractive dairymaids at Talbothays dairy. She refuses his attentions though he forces his affections on her (of course though not in the same way Alec Stokes-d'Urberville did). Yet, Angel (ironically named by Hardy) treated Tess the same way Alec treated her: they both disregarded her wishes and forced their own wills upon her.
When they share their confessions, as Angel promised they would do after their wedding, Angel tells of "eight-and-forty hours" of drunken dissipation and promiscuity. Tess takes heart believing that Angel must now forgive her as she has readily forgiven him because their falls from religious and moral virtue were the same: "'tis just the same!"
Angel, however, is trapped in the double moral and spiritual social standard that divides men and women by allowing men dissipation while socially scourging women for bearing a child though the fault may not be their own due to seduction and force. Angel feels Tess's purity is an illusion and sees no way to avoid turning upon her in hatred and resentment but by the escape of estrangement, though not complete abandonment (though Tess feels he means abandonment).
[Angel mused] Could it be possible ... that eyes which as they gazed never expressed any divergence from what the tongue was telling, were yet ever seeing another world ... discordant and contrasting?
This is the route leading to Angel's and Tess's separation. This section of the story is significant for its focus on two prominent themes: (1) Hardy is redefining the idea of woman's purity as an internal purity, not one of external deeds, especially when men are the propagators of those deeds; (2) Hardy is denouncing the double standard of his harsh Victorian society that condemns women yet exonerates men for promiscuity while ignoring the responsibility of men in the moral downfall of pure women like Tess.
[Alec] shrugged his shoulders. [Tess] resumed—
"I didn't understand your meaning till it was too late."
"That's what every woman says."
"How can you dare to use such words!" she cried, ... her eyes flashing as the latent spirit ... awoke in her. "My God!... Did it never strike your mind that what every woman says some women may feel?"