The thought that the fingers on the bow complete a kind of circuit the way batteries in a battery case complete a circuit has been taking over my mind while practicing lately. Music is, after all, a series of vibrations that travel through the air (and through the bow and the violin) in much the same way electricity travels.
When an electric circuit is not complete due to a faulty connection or a frayed wire, the energy cannot get from the wall to the toaster, and you end up with plain old bread instead of toast. If the springs in a battery holder are worn out and don't hold the batteries properly, your flashlight flickers on and off.
If my right hand is not in contact with the bow in a firm yet flexible way, the energy from the right side of my body will not be able to travel properly to my instrument (the left side of the body) through the strings, so that it can come out of the f holes and be free to travel through the air. If the fingers of my left hand are not strong enough to make the vibrating frequency of a string (or a set of double-stops) a true pitch, the transfer of "electricity" is compromised, and my sound won't be filled with as much energy as I would like it to have. My musical intentions can only be realized if I take care of the physical transfer of energy. Once I do, it's remarkably easy to play well.
When I think about my "circuitry" while practicing Sevcik, Dounis, and Kreutzer, and I concentrate on the points of contact with the violin and the bow, I can feel in any given difficult situation where the imbalance lies; and it usually lies in only a few fingers at a time. Identifying and fixing the imbalance strengthens my "electrical" connections, and it makes everything sound better when I'm practicing music.
I hope my experience might be of help to other string players. It certainly helps me to articulate it, and attempt complete some kind of larger circuit by sharing it.