Green’s Dictionary of Slang

arrive at the end of the sentimental journey v.

[literary euph.; the conclusion of Laurence Sterne’s Sentimental Journey (1768), in which the narrator obviously retires to bed with a chambermaid]

of a man, to have sexual intercourse; one of many euph. terms for sexual intercourse.

[UK]Farmer Vocabula Amatoria (1966) 18: Arriver a ses fins. To copulate; ‘to come to the end of the sentimental journey’.
[US]Maledicta IV:2 (Winter) 183: Examples here include the flower of chivalry, End of the Sentimental Journey (by Laurence Sterne: ‘I put out my hand and caught hold of the fille-de-chambre’s — ’).