240 Mr. Cavallo’s Qbfervatiom on 
length, compared to that of the whole firing, being as 2 to 
3, and fo qf the reft. 
The higheft found of the oftave is exprefltd by the half of 
the firing ; and if this half be divided again in the fame man- 
ner or proportion, a higher o6tave will be obtained, the higheft 
note of which will be exprefied by a quarter of the original 
firing. This quarter may be divided again into a higher 
odtave, and fo on ; therefore, a firing fo divided may exprefs 
the founds of all the keys of an harpfichord or organ. 
In regard to thofe divifions it muff be obferved, that as the 
notes of the fecond odtave bear the fame proportion to the firft 
note of that octave as the notes of the firft octave refpedtively 
bear to the firft note of that odtave, or to the whole firing ; 
and as the length of the firing exprefling the firft note of the 
fecond o< 5 tave, viz. cZ , fig. 1. is half the length of CZ, the 
Aril note of the firft ofitave, it follows, that the length of the 
firing of every note in the fecond ofilave is half the length of 
the correfponding note in the firft odtave ; thus g in the fecond 
ofitave is 120 inches long, and G in the firft octave is 240 
inches long, viz. twice 120. Hence, when the divifions of 
the firft odlave are afcertained, in order to find the divifions of 
the notes of the fecond odlave, we need only take the half of 
the lengths exprefling the notes in the firft oftave. By the 
very fame reafoning it is evident, that to find the divifions for 
the third odlave, we need only take the halves of the lengths 
which exprefs the notes of the fecond odtave, or the quarters 
of thofe of the firft odlave, and fo of the reft. 
The firing or line CZ, fig. 1. is divided in the above-men- 
tioned manner, and in order to avoid confufion, the divifions 
of the principal notes only of the firft and fecond odtave are 
annexed to it. The numbers under the line exprefs the lengths 
from 
