Of Winds and Sounds.

•Lengths of Musical Intervals, or the LengthsE Strings sounding Musical Notes ; and of

three

is.. •

r orce; it must therefore be equal to it, and confe-S^ently proportional to the Line C D, Wherefore the^oint D is carried towards C with a Force every whereProportional to the Distance or Space passed over. Buthave strewn, that the Spaces passed by Bodies in"lotion are as the Times and Velocities conjointly,is, S : TV ; (See Annotation XXII.) also that theforce of moving Bodies is as the Quantity of Matterjfd Velocity conjointly, viz. M — Q_V ; therefore

8

'p = V = or T M = S Q. But in the present

^-•ase Q_ is a given Quantity, therefore T M is as S ;

because it has also been strewn that M is as S insi>e present Cafe of the String, therefore T, or the Timeln which the Vibrations are made, whether throughheater or smaller Spaces* is ever the fame, or a givenQuantity.

5- The Restituent Force of the String, as it actsJj'tough very small Spaces, may be looked upon as uni-°rrn; and then the Motion generated in the Stringbe as the said Force and Time of its acting, that is,: E T. Now in all Cafes it is M : Q_V.; but here

TM

E

L V,

but before, we had E ;

t ls Oct D 1 L, (supposing D = Diameter and^ e ngth of the String) therefore M : ET : D 21 ]3 z j j y

consequently T :

Js ■

which substituted in tbe above Ratio gives ss

E-V _ . _ _ V x

—. But (since S : T V) we have ^

so.

ire -p

D l L’

L

FT

i that is, F T 2

DT.

S ' Ttherefore F

tnere-

f t consequently, T :

DL

9 fballon is as the Diamiti

V OL. II. S

£7

at

I ha'

th 2 Time of

\d T,;ngth of

he String

Ci'i / tV if),