I'm curious... I know the payload of the alchemist bomb is "traditionally" delivered via throwing arm, but is there anything keeping an alchemist from using a sling?
I've seen weapons in the past that increased the range of potions and alchemical items, like the flask launcher and a specially designed sling. Perhaps the APG will include something similar.
A glass ball would hold whatever he wants to put in it, and fire nicely from a sling. I have no problems with it if my players wish to give it a try..as long as they pay to have the balls crafted for them.
Gnome Calculus from Arms and Equipment guide is what you are searching for