Archer had posted on Twitter of being racially abused during the first Test against New Zealand at Mount Maunganui which was won by the hosts.
Kane Williamson and Ross Taylor hit spirited centuries to steer New Zealand safely to a draw in the second Test and seal the two-match series 1-0
It took a five-wicket haul for the tireless Neil Wagner to bring England's first innings to an end at 476, a lead of 101.
He was unbeaten on 114* before the rain interrupted play, though they still trail by 106 runs.
When New Zealand had the wobbles, their first-Test hero partnered debutant Daryl Mitchell in a 124-run stand for the sixth-wicket.
Tom Latham's unbeaten hundred and his century stand with Ross Taylor laid a solid foundation for New Zealand before rain brought an early end to day
The most important thing for England is to reflect on their performances and sort out their batting and bowling woes in the first Test
England, though, have another injury concern over wicketkeeper batsman Jos Buttler, who pulled a back muscle while exercising
The England and Wales Cricket Board in a statement said Silverwood would depart home following day two of the second Test at Hamilton
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