Ever have a window which has so much text in it that the vertical scrollbar moves too coarsely to allow you to find the position you want? Like you have an entire dictionary loaded as a text file and you're trying to find the word "madrigal". You get to "machine" and (after some fiddling with the mouse) manage to move the scroller one pixel down only to find that you have overshot all the way to "magical". Then you have to scroll all the way back up to madrigal or go back to machine and scroll down. Either of which, depending on the size of the dictionary, may take quite some time. Most annoying.
Wouldn't it be good if, for long documents like this, you had two scrollbars side-by-side. These would work like the hour hand and minute hand on a clock. The rightmost one would set the position in the document coarsely and the leftmost one would be for fine-tuning it. Once you had got to the "early Ms" with the rightmost scrollbar you could quickly get to any nearby word with the leftmost one.
For best distribution of precision between the scrollbars, the region of the document corresponding to the entirety of the leftmost scrollbar (X) would be to the entirety of the document as the window would be to X (i.e. the pixel size of the two scrollers would be the same).
The scrollbars would be set up so that moving the scroller of the leftmost scrollbar one pixel scrolled the document by at most one line. If the document is too large, than a new scrollbar is added - particularly long documents might have 3 or even more scrollbars, each with the same virtual document size to virtual window size ratio.