Tool adapter/connector for Dyson DC30 (and other models)

I had a useful brush from an very old Dyson. It didn't fit my hand-held DC30. This adapter fastens the two together.

I believe it will also fit DC30, DC31, DC32, DC33, DC34, DC35 and DC36, and possibly other models.

The brush is 32 mm, the Dyson is 35 mm.