One copy of the picture is on this site of the British Dentistry Association, which offers the following commentary:
If you enjoyed this print why not visit the BDA shop on-line to buy a copy of 'Open Wide: A Series of Eighteenth and Ninetheenth Century Caricatures on Dentistry'?
Another copy of the picture is on this site, with this commentary:
This print is by Thomas Rowlandson (1756-1827) and is dated 1787. It is a satirical comment upon the real practice of rich gentlemen and ladies of the 18th century paying for teeth to be pulled from poor children and transplanted in their gums. The dentist present is portrayed as a quack. There are even two quacking ducks on the placard advertising his fake credentials. He is busy pulling teeth from the mouth of a poor young chimney sweep. Covered in soot and exhausted, he slumps in a chair. Meanwhile the dentist's assistant transplants a tooth into a fashionably dressed young lady's mouth. Two children can be seen leaving the room clutching their faces and obviously in pain from having their teeth extracted. As people lost most of their teeth by age 21 due to gum disease, teeth transplants were popular for some time in England although they rarely worked.
Thomas Rowlandson, "Transplanting Teeth," The Wellcome Library, Annotated by Lynda Payne.
How to Cite This Source
Thomas Rowlandson, "Transplanting Teeth (c.1790) [Engraving]," in Children and Youth in History, Item #164, http://chnm.gmu.edu/cyh/primary-sources/164 (accessed July 10, 2014). Annotated by Lynda Payne
(And here's an earlier post on transplantation of teeth: http://marketdesigner.blogspot.com/2011/04/live-donor-teeth-and-george-washington.html )