the Temperament of Mujical InJlrumenU. 2 5 1 
feries of thirteen numbers, the extremes of which are the 
whole firing and its half, viz. any number and its half. The 
ratio of this feries is found in the fame manner as in the other 
feries, viz. the greatefl extreme is divided by the leafl, and the 
twelfth root of the quotient is the ratio fought. But the ex- 
tremes are any affumed number and its half: and as the quo- 
tient of a number divided by the half of the fame number is 
always equal to two ; therefore, whatever be the length of 
the firing, the ratio is always Th 1 ' = 1,0594+, and if the 
j 
length of the whole firing be divided by this ratio, viz. 
1,0594 + , the quotient will be the length of the firing ex- 
prelfing the fecond note, which, divided by the fame ratio, 
gives the third note, and fo on ; or elfe, inflead of dividing 
the length of the whole firing by the ratio, you may multiply 
the half of it by the ratio, the produdl of which will give the 
feventh note, which multiplied by the fame ratio gives the 
fixth, and fo on in a retrograde order, which will give the 
tempered notes of the odlaves as well as the former method. 
By this means the following divilions for the notes of an 
o£lave have been calculated, the length of the whole firing 
having been fuppofed equal to 100000. 
I. 
100000 
* b 
94387 
II. 
89090 
* b 
84090 
III. 
79370 
IV. 
749*5 
* b 
O 
O 
V. 
66743 
* b 
62997 
VI. 
59462 
& b 
56123 
Vol. LXXVI 1 I. ' M m VII. 
