I ended up contacting the company that makes the antler chews that my dog is eating and this is what they said:
As your dog is getting use to a new product it is best not to let her have too much at one time to avoid a tummy ache. Once you know it does not bother her she can have all she wants. If you got a split open one the inner marrow is salty stating and dogs tend to drink a lot of water when chewing. This is normal but she might need a extra bathroom break. Hope this helps.
I had not heard of the 1 inch. I don't think they eat that much a day though. When I get new antlers, I only let them have them for about an hour a day or they will chew obsessively. They become amazingly high value treats. Once the novelty wears off a new one, into the toy box they go.
Since this came back up to the top, I have a new antler story.
My dogs (and thank you veggielove, they are super cuddle buddies and a blast to play with) are the pickiest dogs in the universe. They were doing well with the splits, so I got whole antlers, hoping they would last longer. Well, they ONLY like the very tips of antlers, where they are very narrow, despite the fact that they would chew any size split.
I went to get new ones and they did not have any of the "tips" but they did have deer antlers, which were nice and narrow. No go. Elk only for these princesses. Nice waste of $35.