From what I can see, the underside has a small, circular depression. The species of Tulostoma are much like ordinary puffballs, the major difference being that the spore sac sits atop a stem, which may be buried in the soil. In many species (1) the stem fits into a small hollow the base of the spore sac and (2) the spore sac can break easily from the stem and then be blown about.
Thank you - that's so interesting. I thought they were lizard eggs at first, and found they have a very tough membrane. I didn't turn the one in the first photo around to look at the base. Just goes to show what you can see when you look down, rather that up for those birds!