Using a sharply-serrated knife on the kitchen bench, I cut open the case. What I found inside was astonishing.
I preserved the dead, partly-developed shark pup and his egg sack in a bottle of methylated spirits -- and named him Samuel. You can see him in the photo, with the distinctive screw-shaped egg case alongside.
The egg case is made of a material that looks very much like seaweed, presumably to help protect the developing embryo from attack. The female shark lays her eggs, pushing each egg into an underwater rock crevice for safekeeping The spirals on the egg case hold it in a safe position -- until the embryo is fully developed.
The empty egg cases are sometimes called mermaid's purses.