
What's the purpose of "of"?

If you read "admit" as 'allow the possibility', it makes sense.

OK, ta!

No worries!
Fowler's Modern English Usage (1996, 3rd edition) puts it more clearly:
"...*admit of* is restricted to the senses 'present an opening' and 'leave room for'." It goes on to say that: "Even in these senses, the construction seems old-fashioned."
Here are a couple of example sentences:
https://dictionary.cambridge.or...glish/admit-of
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