Take a powder

Factual Questions
#1

What is the origin of ‘Take a powder.’?

Does it have to do with women applying make-up? That is, ‘Let’s excuse ourselves from this situation. We’ll be right back.’? Or is it, ‘Oh, go powder your nose, you girl!’ or ‘Will you please excuse us? Perhaps you can go powder your nose.’?

Or does it have to do with taking powdered medicine? (Though that doesn’t make as much sense to me as the make-up origin.)

#2

The status of the unknown origin as of 2001.

#3

Hmmm…

I always assumed it was to do with the fact that medicines such as asprin etc used to come as a powder rather than as a tablet. So if you wanted to excuse yourself from a situation you could say you need to take a powder (ie I have a headache and need a lie down) even if you didn’t need to.