I agree with Emile on the meaning of transom for the general meaning of the word as a lintel, a horizontal beam. In yachting terms, often found as "transom stern", the stern being the back end of the boat and the transom stern referring to yachts with piece running from one side to the other thus :
http://en.wikipedia.org/wiki/SternThat's for a rough idea and in nautical contexts, "transom" for "caisson" would be potentially misleading.
Focus rather on the idea of some sort of chest, trunk whatever for your context. Do you have further context. I was simply wondering if it might not have a meaning closer to "caisse" here? The horse has eaten all available reserves. The "caisson" can be empty as the horse has eaten whatever was in available :
- describing the volume/chest carrying whatever the horse has now eaten
- describing the fact that everything having been eaten, there is no money left to replace it.