I , too, was impressed with this domed building, patterned after the Pantheon in Rome. I think the open space is known as an ocula or eye which allowed sunlight in and left the reflection trace its way along the dome. Of course when it rains, the sight of water pouring inside a building is an odd sight.
The names of Illinois soldiers adds a personal touch, although including Grant's 12 year old son as a member of Grant's staff seems to stretching a point.