including acting as sunshades for the eyes, being used for display, and being used in combat against other members of the same species (although they were fragile). There was a ridge along the back of the skull roof for muscle attachment, as is also seen in tyrannosaurids. Inside the lacrimal bones were depressions that may have held glands, such as salt glands. Within the maxillae were sinuses that were better developed than those of more basal theropods such as Ceratosaurus and Marshosaurus; they may have been related to the sense of smell, perhaps holding something like Jacobson's organs. The roof of the braincase was thin, perhaps to improve thermoregulation for the brain. The skull and lower jaws had joints that permitted motion within these units. In the lower jaws, the bones of the front and back halves loosely articulated, permitting the jaws to bow outward and increasing the animal's gape. The braincase and frontals may also have had a joint. Postcranial skeleton Allosaurus had nine vertebrae in the neck, 14 in the back, and five in the sacrum supporting the hips. The number of tail vertebrae is unknown and varied with individual size; James Madsen estimated about 50, while Gregory S. Paul considered that to be too many and suggested 45 or less. There were hollow spaces in the neck and anterior back vertebrae. Such spaces, which are also found in modern theropods (that is, the birds), are interpreted as having held air sacs used in respiration. The rib cage was broad, giving it a barrel chest, especially in comparison to less derived theropods like Ceratosaurus. Allosaurus had gastralia (belly ribs), but these are not common findings, and they may have ossified poorly. In one published case, the gastralia show evidence of injury during life. A furcula (wishbone) was also present, but has only been recognized since 1996; in some cases furculae were confused with gastralia. The ilium, the main hip bone, was massive, and the pubic bone had a prominent foot that may have been used for both muscle attachment and as a prop for resting the body on the ground. Madsen noted that in about half of the individuals from the Cleveland-Lloyd Dinosaur Quarry, independent of size, the pubes had not fused to each other at their foot ends. He suggested that this was a sexual characteristic, with females lacking fused bones to make egg-laying easier. This proposal