180 On Musical Temperament. 
The sign plus denotes that the degree to which it belongsis — 4 
to be raised, and minus, that it is to be depressed. The correc- 
tions in each succeeding operation are to be added to those in 
the preceding. The errors, in the 3d approximation, are $0 
trifling, that a 4th would be wholly useless. Bree 
Nore. The foregoing calculations will be rendered much 
more expeditious and sure, by reducing the theorem, in some 
sense, to a diagram, as in the first of the following figures; an 
by applying the successive corrections to the circumference of 
a circle divided into parts proportioned to the intervals of the 
enharmonic scale, as in the second. 
Prorosirion VII. 
together with the values of the diatonic and chromatic inter 
of a stride 
vals, and the lengths and vibrations per second | 
from the 
producing all the sounds, of the system resulting 
last proposition. 
The temperaments of all the concords are easily deduced 
from Table V. The Vth CG, for example, has its lowe 
extremity lowered 12, and its upper extremity 14. 7° 
it is flatter by 2 than at first, and corisequently its yar 
ment=156. The temperaments of all the concords, | 
To determine the temperaments and beats of all the concord’; | 
