Hitch-hiking in Error
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While the true origin of the term "to hitch-hike" is lost to us, there has been some curious speculation that missed the mark completely. So it is that in Everyman's Modern Phrase and Phable, Gyles Brandeth writes:
    hitch a lift means to beg a free ride in another person's vehicle. It is easy to imagine that this is a relatively new expression, coined since the advent of the internal combustion engine, but in fact the word hitch is, in this context, based on the verb to hitch-hike which has far older origins. To hitch-hike originally referred to a means of travel involving one horse and two people. One person would ride the horse a decent distance, then dismount, hitch the animal to a convenient tree or post, and hike on by foot. Eventually the second travellerwould reach the horse, mount it and ride until he caught up with his friend. This way of getting about was: widely used and was generallyknown as 'riding and tying'. In 1737 Dr Johnson and the actor David Garrick travelled from Lichfield to London using the method, but they were certainly not the first or last to do so.
Which, as Thomas F. Adams points out, is wrong! Cute, but wrong. This is what William and Mary Morris have to say in Morris Dictionary of Word and Phrase Origins :
    hitchhike evolved from the fact that a hitchhiker has to do some hiking between lifts and, at least in the early days, used to have to hitch (catch on to) a slowly moving vehicle. One time, in our syndicated column, we noted that hitchhike is a fairly recent coinage. Some sources, we said, used it in reference to a means of travel whereby two people would use a single horse in this fashion: one would ride for a fair distance while the other proceeded afoot. The first would then dismount, tie up the horse, and start walking. The second traveler, upon reaching the horse, would then mount and ride until reaching the one afoot, when the process would be repeated. We indicated some skepticism about this story, so Professor Thomas F. Adams of the University of Toledo very properly takes us to task. 
      I was surprised that our own best lexicographer should so forget his Johnson as to treat with disbelief the ancient and honorable method by which two poor men and one horse could proceed to London from the country. As far as the term hitchhike is concerned, your logic is impeccable; the word has nothing to do with this practice. The proper expression for this traditional, but neither fabulous nor legendary, mode of travel is "riding and tying." It is not a fable we may believe if we wish; it is the way by which, as the actor David Garrick told Boswell, Samuel Johnson and David Garrick traveled to London from Lichfield on March 2, 1737 ... It was common then to cast doubt on the extremity of Johnson's poverty, and Boswell casts doubt on the tale here. But you will note that he casts no doubt on the existence of the practice. 

      I don't wish to ride you for this, but I was almost fit to be tied when you scoffed at the authenticity of this attractive piece of literary history. 

    Thank you, Professor Adams, for catching us up-and may the shades of Dr. Johnson and David Garrick forgive us for our forgetfulness. 
Alas neither Morris, nor Brandeth, nor indeed Adams shed any real light onto the origins of this word. It does indeed appear to be a more recent coinage, appearing some time in the 1920's in the USA.