( 187 ) 
As this is a mechanical operation, if the 
proportion be true, it may be mathemati- 
cally demonftrated : thus 
The part of the bow, in contact with the 
firing of the violin, is the centre of a circle, 
of which the hair of the bow, from that 
centre to the extremity of the little finger 
on the right hand, is the radius-, confequently 
this little finger moves in the circumference 
of a circle, which is greater or lefs, accord- 
ing to the length of that radius-, and, as the 
length of the arch to be defcribed, in the 
fame time, depends on the magnitude of the 
circle, it is evident that an artift who exe- 
cutes difficult quick pafTages with the part 
of the fiddle-flick neareft his hand, will, 
ceteris paribus, execute thofe paflages with 
the greateft eafe. Let us fuppofe the bow 
to be divided into four equal parts : the hand 
of the artift who plays quick paflages on the 
firft, diftant divifion, defcribes, we will fup- 
pofe, 20 archs of his circle, or plays twenty 
quarter-notes on different firings in a fecond 
of time : if he played with the centre on the 
fecond divifion of his bow, he would execute 
20 eighths^ and on the third, 2ojixteentbs t 
in the fame time. But this is not the only 
advantage of playing near the hand : it brings 
the. 
