While further researching Lord Kelvin, I came across an interesting quote. The Universe a Vast Electric Organism (George Woodward Warder, 1903) quotes Prof. Garrett P. Serviss -- the author of Edison's Conquest of Mars, which co-stars Lord Kelvin -- in the New York American, May 16, 1903 (bold mine):
"The undulatory theory of energy is carrying everything before it. It is not saying too much to aver that wave motion is concerned in nearly all the phenomena of physical life . . . Think for a moment of what is included in the science of waves. In the air all sounds, all musical harmonies are waves; in the solid globe, all earthquakes are waves; in the ether light, electricity and heat are waves. It is waves that make the stars visible, and yet more mysterious oscillations picture for us on photographic plates marvelous nebulous objects. Lord Kelvin has been credited with the statement that the fluttering of a butterfly's wing sets up vibrations that shake the universe." (p.288)
I've searched for the original quote by Kelvin but have come up empty. The only references to it I can find on the Internet are in Warder and a mention in passing in Science of the New Thought (Erastus Whitford Hopkins, 1904). If anyone can find what statement of Kelvin's Serviss was referring to, please contact me, as this would add chaos theory to the multitude of scientific fields that Kelvin influenced in some way.
According to the Wikipedia article on the "butterfly effect", the connection of butterflies to the idea of sensitive dependence on initial conditions came from Ray Bradbury's 1952 short story "A Sound of Thunder". Granted it's Wikipedia, so it might as well say John Seigenthaler Sr. first came up with the idea, but if that's the accepted wisdom on the metaphor's origin, what shall we make of Kelvin's use of it half a century earlier? Time travel?
[UPDATE 2010-01-28: Looks like it was originally a mosquito, and Kelvin didn't recall saying it.]
Since I don't have Kelvin's original quote, I'll leave you instead with some entertaining figures from Hopkins' book above: