(57) A polishing apparatus comprises a rotatable table 10 on which the article to be polished 12 is mounted. An arm 18 carrying a rotatable polishing head 20 of abrasive material is mounted above the table 10 and is capable of being traversed towards and away from the table. The mounting of the polishing arm includes a pivot 28 sothatthe arm may be tilted under the action of a fluid operated cylinder 34 whereby to bring the polishing head 20 into contact with the surface to be polished 16. The fluid operated cylinder, preferably a pneumatic cylinder, is connected into a fluid circuit having a pressure regulator in its outlet so as to apply constant pressure to the arm 18.