O. Henry characterizes the doctor in a subtle way in the following passage of dialogue.
“She has one chance in—let us say, ten,” he said, as he shook down the mercury in his clinical thermometer. “And that chance is for her to want to live....Your little lady has made up her mind that she's not going to get well.”
The thermometer is, of course, calibrated. The doctor is shaking the mercury back down while estimating that Johnsy has one chance in possibly ten. This is obviously an expert who thinks in such precise, "calibrated" terms. He is not unsympathetic, but he has seen many people die and has learned to accept reality as well as to accept his limitations as a medical doctor. The fact that O. Henry shows him shaking the thermometer as he makes his calculation also indicates that he has just taken Johnsy's temperature and that it was probably dangerously high. Johnsy has only one chance in ten "if she wants to live," according to this gray-haired authority. If she doesn't want to live, she has no chance at all.