The second week in December Dorian went into action in search of Carlia Duke.

He acknowledged to himself that it was like searching for the proverbial needle in the haystack, but inaction was no longer possible.
Carlia very likely had no large amount of money with her, so she would have to seek employment.

She could have hidden herself in the city, but Dorian reasoned that she would be fearful of being found, so would have gone to some nearby town; but which one, he had no way of knowing.
He visited a number of adjacent towns and made diligent enquiries at hotels, stores, and some private houses.

Nothing came of this first week's search.
A number of mining towns could easily be reached by train from the city.
In these towns many people came and went without notice or comment.
Dorian spent nearly a week in one of them, but he found no clue.

He went to another.