Thanks Della.
A whole host of these kind of vases, in varying shapes and sizes, but all with the horizontal rolls, were on display on the Crown Crystal (Australia) stand at the 1938 Sydney Show. A photo of the stand is shown in "Carnival Glass of Australia".
They have been known for many years as Melon Rib vases. That's just the way it is.
I suspect the manufacturer was European. In fact I think I may be on the track of the maker right now - but as I am in the early stages of the research I'll have to hold on a little before I stick my neck out.
Glen