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EATING AIR .

A Strange Expression That Is Not Entirely Without Reason .

According to a missionary in the East Indies , the native of Hindustan recognizes as one of the differences between a dog and a man , the superior breathing capacity of the latter ; for example : We say in English , A dog walks out , and A man walks out ; but in Hindustanee the expression is : A dog walks out , and A man goes forth eating air . The expression is said to be three thousand or more years old , and so its origin must be lost in obscurity , nevertheless it is significant as expressing the importance of air in the maintenance of human life . In a certain sense , air is food ; it is indeed the most necessary of all substances required by the body . A man can live a month , or even two months , without solid food , and a week , or perhaps eight days , without drinking , but the vital processes are suspended within a few minutes when the supply of air is cut off .  - Good Health .

in the 18th and 19th centuries, a Chinaman was a merchant's sailing vessel.  In mining, a chinaman is a chute.  A baler that makes square bales has ab plunging feeder called a chinaman.  In Chicago politics, your chinaman is what in NYC politics is called a rabbi - someone who pulls strings for you.  It can be the flat conical hat worn by coolies in the field, especially in offensive political cartoons.  It can be the breaking googly (pitch) of a southpaw in cricket. It cam be a dealer in porcelain or a porcelain figurine.

I can't imagine that a statue would need much polishing, nor that they would be removed for polishing, or that they would accidentally switched.  I would rather think that the term is for a piece of furniture that serves as a clothes hamper or wash station, given the 'chinese laundry' stereotype, or perhaps a piece holding a tea set and maybe crumpets, to make serving tea more convenient, tea also being stereotypically Chinese.  But this is obviously just conjecture.