"You see, wire telegraph is a kind of a very, very long cat. You pull his tail in New York and his head is meowing in Los Angeles. Do you understand this? And radio operates exactly the same way: you send signals here, they receive them there. The only difference is that there is no cat."
I've also seen it attributed to Thomas Edison. Sadly all evidence indicates this quote is a hoax dating to the mid-1980s. The long animal metaphor (usually dog or cat) has been used to describe telegraphy since the 1860s. More here. In the year 1877 over 60 years earlier the book Lightning Flashes and Electric Dashes: A Volume of Choice Telegraphic Literature, Humor, Fun, Wit & Wisdom was published in the USA. It's in the public domain and you can get it here. It records the same story more-or-less in an exaggerated Brooklynite pidgeon English. It had previously appeared in the Journal of the Telegraph in 1873.
“Now, you see, Sam, s’pose da was a dog, and dat dog’s head was in Hoboken and his tail in Brooklyn.” “Go ‘way, da ain’t no such dog.” “Well, s’pose da was.” “Well, s’pose da was.”
“Well, den de telegram is jest like dat dog. If I pinch dat dog’s tail in Brooklyn, what he do?” “Dunno.” “Why, if I pinch that dog’s tail in Brooklyn, he go bark in Hoboken. Dat’s the science"But the quote is older than that.It dates to at least 1866 where it appears in an issue of The Telegrapher. This may be it's origin in print as it also appears word for word in The Country Gentleman & Cultivator in 1867.
“Imagine that the telegraph is an immense long dog-so long that its head is at Vienna and its tail is at Paris. Well, tread on its tail, which is at Paris, and it will bark at Vienna..."