I take it to mean the very first part of the evening.
And yes, I'd write that way too, but (thank you for posting the source) as you can see, the author wrote in 1923 and has a very flowery, long-flowing style of writing. While you may read this for pleasure, I do not recommend you use this as a model for writing in the 2016.
EDIT: Oh - I didn't notice the "a" - while "a milk" could be "a glass of milk" I agree with Goes that it should be "as milk."
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