Here is a small addition from the old paper with a drawing:
Source: H. Cotton, Electric Discharge Lamps, page 346, London 1946, Chapman & Hall Ltd.
Technically, the manufacturers have all realized it a little differently, but it was always for the stabilization of the arc tube in the outer bulb.
In the last years of production of these lamps, OSRAM and MELZ used stamped pieces of sheet metal instead of coiled wires.
CROMPTON fixed it without metal, just with two glass tubes bent open on one side and (presumably) small discs of asbestos as padding.