Rabies?

[Rondar]

We had a bat fluttering in our yard and I went and got a shovel to carry it to a burn barrel we have on the farm.  I assume it had rabies because it was a bat and seemed to just flutter and not fly.  It was not foaming at the mouth (at least not yet) and wasnt trying to attack, just kind of fluttering around every so often.   It was kind of fun to play with, watching it move its head and making that high pitched chatter for its  sonar to work.  It was amazing how accurate it followed me around it.  

But anyway, as I was carrying it on a shovel, and a couple cats following me as it was intersting for the cats, it fell off and before I could pick it up again a cat pounced on it, and ran off with it, and I know it ate it.

Now, can the cat get rabies by eating the bat or only by getting bitten?  I dont know how much of the bat was eaten but I assume by the birds the cats eat only feathers and wings and feet and that kind of stuff is left.  I cant find any remains so far of the bat to see just what was eaten.  The cat is semi wild and will not let anybody pet it or get close, but will stay 10-15 feet from people and just be in the neighborhood so to speak.

[SuperDud]

I'm almost 100%you have to be bit and have it enter the blood stream. Digesting it takes it down to the stomach and acids which will destroy anything harmful. I would be more concerned as to whether the cat got bit during it's meal. Bats teeth can be like needles making any bite wound hard to see. Just keep an eye on the cat if you see it.

[Angus]

Call the vet. The cat can be vaccinated if you're quick enough. You don't want a possible rabies cat at the home...
It can probably be checked as well.
As a sidenote the word "vaccination" comes from the french word "vache" which means cow, and is related to the infamous pox. Anyway, certain Englishman, Dr Jenner, noticed that milkmaids with warts from cows did not get the deadly smallpox, so he developed a crude method of infecting people with warts (using a needle), and it worked. The vaccination was born, although Dr Jenner had no idea what he was dealing with. Pox is a virus, and Jenner found the trick on that particular one, as well as the method before anyone even knew there was such a thing, even bacteria.
So, bacteria got busted by a Frenchman basically, - Dr. Lois Pasteur. And the first breakthrough was rabies. Pasteur Vaccinated with weakened bacteria, and PRESTO, the human body would build up it's defences and be able to hold back the invader. Pasteur's first successful rabies vaccination was actually on a boy who got bitten by a rabid dog, - the method was still on the testbed, but Pasteur was pressed by the boy's mother. After all, rabies kills you, and quite horribly.
So, go Wiki on Jenner and Pasteur, rabies and pox, while you wait for the vet, - this is all from memory you see. I think Jenner's first name was Edward though, but cowpox should land you close enough.
All interesting stuff, but it's been a tad long since I read up on it.