The grip of a violin bow (or bow of any other stringed instrument) is often mistakenly referred to as the 'frog'.
According to The Oxford Dictionary of Music, The Grove Concise Dictionary of Music, The New Grove Dictionary of Musical Instruments (vol 3, P-Z) and the Collins English Dictionary (3rd. ed.) the frog is in fact the nut in the heel of the bow which tightens the horsehair of the bow.

The reason the heel of the bow is often referred to as the frog is because of the manner in which the musician holds the bow. S/he holds the bow near the frog, and the index and second and third fingers rest on the stick while the thumb presses on the underside of the frog.

http://everything2.com/index.pl?node_id=23449
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Reviewing the sources and descriptions of violin bows, I see that musical experts often report that the reason for the name frog for this piece of the violin bow is unknown.
I can therefor only give my own opinion and reasons. It seems to me that the derivation of this usage is basically the same as the derivation of the word frog as a name for part of the horses hoof. And that is that the word "frog" is in this case a variation on the word "fork", possibly corrupted from the French or Italian words for fork. At some early point in the development of the bow the part providing the tension to the strings may well have been fork shaped or resembling a fork.
Source(s):
http://www.takeourword.com/TOW180/page2.html

http://www.theviolinsite.com/violin_bows/index.html

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I actually never thought about why we call the frog of the bow the frog. I started playing the violin when I was 6, so there's a good chance that I knew about bow frogs even before the amphibian ones. :-)
Here is a URL that gives a number of ideas about it.
http://www.violinist.com/discussion/response.cfm?ID=8725
I'm going to go with Rob Schnautz's idea of the happy frog. :-)
"my frog bounces a lot...but I call it spiccatto or col legno most of the time. My frog is a lot happier when it is bouncing. "
Source(s):
http://www.violinist.com/discussion/response.cfm?ID=8725

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