I've seen one... there was one in operation as late as 1996 in a store in Schenectady, NY. (I don't know if it was a "Brown's Cash Carrier.") There was an ancient hardware store named "Wallace Armer" on Erie Blvd. in Schenectady. They were in business I presume since the 1800s, along what was then the Erie Canal. Until 1996, when they went bankrupt, they were *still* using such a cash carrier.
It was an overhead cord-and-pulley system with an endless loop of cotton cord that traversed a route around the entire store, going to each check-out area (there were maybe five of them), and then up to a "crows nest"/office in the *upper* back corner of the store. The checker would write up your items, take your cash, fold it up, and put it inside a small shiny rectangular metal box, I'm guessing from memory, approximately 2.5"x4"x1.5" in size. The checker would also flip something on the box, like metal flaps (a code of some sort, I presume), that uniquely identified the "address"/location of the office. Then the checker would reach up, and hook the box onto a line-mounted metal attachment. In a second, the ever-moving endless cotton cord would pick up the cashbox, whisk it off, and it would zoom around the store overhead (maybe ten feet off the ground), bypassing all the other "stops" along the route, and go up to the cashier in the crows-nest office. The cashier would make change, write "paid" on your bill, stick it all back in the box, and attach the box back to the moving cord. The box would zoom around the store, again avoiding all the other possible stops, and like magic, derail off the cord at the correct check-out.
This conveyor system had a perpetual distinctive soft clickey-clack sound, since the cord had little metal hooks or grabbers on it every few feet (I never knew exactly what caused the sound, as I never saw it idle). There was a looped black metal wire-frame cage at each sales area that I suspect was somehow "hard coded" with the address. When derailed, the cashbox would zoom off the cord, and onto the metal wire frame. The cashier would reach up, take down the box, open it, and give you your change and receipt.
I used to *love* going to that store as a kid, just to see them use this device. I never knew until your post that it had a name, "cash carrier". Thanks! Hope my info helps out. Rick Inzero