I heard of this on an episode of QI (Series H, episode "Happiness").
In the 1830s, a French neurologist wanted to learn how the muscles of the face produced expressions. One item that specifically interested him was if the expression of happiness (a smile that lit up one's whole face) could be faked. So he utilized this newly invented device to deliver electric shock beneath the skin with sharp electrodes to stimulate the muscles:
This forced the muscles to do different things, including smile, based upon where he put the electrodes. He also used this strange new technology called "photography" to capture the resulting expression so he would have an empirical moment frozen in time that he could reference later. The result was some truly startling looking experiments:
Am I the only one who is really impressed that they managed to snap photographs of these expressions so quickly? Normally taking a photograph was a lengthy process that had to be set up just so, without any sudden movements happening. Perhaps the electrodes were capable of holding the expression for quite some time.
What Duchenne concluded from all of this was that an expression of true happiness cannot be faked. The muscles that stimulate the mouth are not connected to muscles around the eyes, creating a deadened, fake-looking grin. This originated the expression or idea that someone "doesn't smile with their eyes".