The meaning of a sentence. Please.
What does “While the pulling-round process was completing itself” and“ to give her rime” mean？ Thanks.
context：While I sat I stole an occasional covert look at the girl. Her clothes, or the remnants of them, were good quality. It seemed likely that beneath the smudges and smears she was good-looking.
The drink gradually did good work. By the end of it she was sufficiently recovered for habit of mind to assert itself. ’God, I must look awful,‘ she remarked. She got up and walked over to a mirror.
‘I certainly do, ’she confirmed.‘ Where’
‘You might try through there,’ I suggested.
Twenty minutes or so passed before she came hack. She approximated now the film directors idea of the heroine after a roughhouse, rather than the genuine thing.
‘ Cigarette? ’I inquired， as I slid another fortifying glass across.
While the pulling-round process was completing itself we swapped stories. To give her rime, I let her have mine first......