"in the third week" is a valid phrase in written English and can be used in many contexts.
For example, "My class begins in the third week of August."
Relative consumption rates (RCRs), during the first week were higher than in the third week.
Rumen, plasma, and milk samples were collected in the third week of each period.
The student substantially revises and resubmits the essay in the third week of Spring Quarter.
Interns' satisfaction with the training differed significantly in the third week, which focused on the physician patient relationship.
The birth of a third calf, Toruño, is expected in the third week of August.
AROUND 9 one morning in the third week of July, and already 70-some degrees.
On Tuesday, in the third week of the trial, the government rested its case.
"It all came together in the third week in June," Clarke said.
"Still can't read yet," Crishad reported excitedly in the third week of September.
Before the Atlanta game in the third week of October, he sensed complacency setting in.
That's every training camp: in the third week everything runs together.
